tag:blogger.com,1999:blog-10523329939883760532024-03-27T11:42:21.878-07:00The Search for Planet NineUnknownnoreply@blogger.comBlogger24125tag:blogger.com,1999:blog-1052332993988376053.post-54134969189587228602021-10-25T20:36:00.000-07:002021-10-25T20:36:28.331-07:00The hunt is on!<p> Back in August, we published our <a href="http://findplanetnine.blogspot.com/2021/08/the-orbit-of-planet-nine.html">detailed analysis</a> which gave predictions of where we should expect to find Planet Nine and how big and bright it might be when we do find it. One of the very interesting parts of the analysis was the result that Planet Nine should be on the closer and brighter end of our initial range of expectations. Planet Nine might be close enough and bright enough, that it might even already have been imaged in one of the many ongoing sky surveys taking place on moderately small telescopes all around the world. </p><p>In many ways, the idea that Planet Nine might have already been imaged should not be a surprise. All of the planets discovered had been seen before they were recognized. Galileo saw Neptune -- without realizing it was a planet -- in 1612, more than 200 years before Neptune was found. Flamsteed cataloged Uranus as a star in 1690 -- a century before its discovery -- and it is even possible that Uranus was observed and cataloged by eye in the second century BCE. Eris, which I first spotted in 2005, showed up on photographic plates from the 1950s (from the same Palomar 48-inch Schmidt telescope used to discover it in 2005!). Images of Pluto have been found from 16 years before its discovery.<br /></p><p>The problem, of course, is that just getting an image of an object in the solar system is not enough. You need to <i>recognize</i> it as something interesting. In all of the historical cases, the solar system body was simply cataloged as a star. The only way to know that it is <i>not</i> a star is to see it move. <br /></p><p>Can't be too hard, right? Herschel saw Uranus one night and came back the next and saw that it had moved. We found Eris by taking three images of the right place in the sky over three hours and noticing one little bright star slowly sliding east. <br /></p><p>Sadly, Planet Nine will be a little harder, but only because the data are not designed for searching for Planet Nine. Most of the big surveys out there cover large fractions of the sky, but only ever couple of days or weeks or months. If you look one night and see something where nothing has ever been before (a "transient" in astronomical language) it could be an asteroid, a supernova, a variable star, a satellite glint, a defect in the camera. Who knows? And when you see the same area of sky a month later there might be dozens of other transients nearby. Is one of them the same object, just moved? Who knows? </p><p><a href="http://arxiv.org/abs/2110.13117">In our new paper out today</a>, we search for Plane Nine by combing through the transients from the Zwicky Transient Facility (ZTF; which, once again, uses the Palomar 48-inch Schmidt!), of which there are ~13 million over a three year period. Finding one Planet Nine in that big of a haystack is daunting.</p><p>The good news is we figured out a cool trick to make the searching moderately efficient. It relies on a simple yet delightfully clever insight from Matt Holman at the Harvard-Smithsonian Center for Astrophysics. While it is true that, when viewed from the Earth, asteroids and planets have complicated looping paths across the sky that are difficult to link, if viewed from the <i>sun</i> they simply travel on great circles. Since we're unlikely to move all of our telescopes to the sun, we have to fake it, by transforming everything we see in the sky into what it would look like if we were on the sun. It's more complicated than this, as we don't know how far away solar system things that we haven't discovered are, so we have to search over a range of potential distances and do more stuff too, but in the end the algorithm is able to smoothly link single detections of Planet Nine over many years. Check out the paper for the gory details.<br /></p><p>Given the 13 million transients in the sky, sometimes they will accidentally line up and look like something real. We find that requiring 7 detections over 3 years allows us to avoid all of the coincidental detections and only find the real Planet Nine.... which we don't. It's not in the ZTF data. Insert sad face emoji.</p><p>Searching for and not finding Planet Nine is only useful if we can somehow figure out what it means, and here is the second part of this paper about which I am excited. We take the results from our paper two months ago and make what we call the <b>Planet Nine Reference Population</b> -- a collection of 100,000 statistically sampled realizations of our Planet Nine prediction, we inject these into the ZTF data, and we see which we would detect. Astonishingly, this one survey would detect 56% of the reference population, or, said differently, this survey covers 56% of the Planet Nine parameter space. </p><p>Knowing this 56% is great, of course, but even better is that we know where (and how bright) the remaining 44% of the reference population is. Basically we took the <a href="http://findplanetnine.blogspot.com/2021/08/the-orbit-of-planet-nine.html"><i>treasure map</i> from the last paper </a>and we've removed 56% of the search area, giving us an updated treasure map (the updated treasure map is noisier looking than the original because it is a little more sparsely sampled with only 100,000 members of the reference population, but you can see the important points there).</p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvFlI8My77BmUZAyL209klyPNhLophsydiCciFzKm687_68JLMv1ZfJ6J9JQ1o2Rj0hh3GiwJ_CgLdW74NTOHFdQHVP5h6xBEfXbD4-DCNciCJSMBj_SSDD1KfgJlq7twy_f7zBtQKXpA/s1136/overview_map_with_ZTF.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1136" data-original-width="800" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvFlI8My77BmUZAyL209klyPNhLophsydiCciFzKm687_68JLMv1ZfJ6J9JQ1o2Rj0hh3GiwJ_CgLdW74NTOHFdQHVP5h6xBEfXbD4-DCNciCJSMBj_SSDD1KfgJlq7twy_f7zBtQKXpA/w450-h640/overview_map_with_ZTF.png" width="450" /></a></div><p><br /> In this map you can see not only <i>where </i>Planet Nine is predicted to be, but how far away and how bright at all of the points across across the sky. And you can see what the ZTF analysis has done. ZTF would have found most Planet Nines brighter than ~20.75th magnitude, as long as they weren't too far south or in the southern galactic plane. </p><p>My final favorite part of this paper is that now the reference population and treasure map are easily accessible for anyone who either wants to look for Planet Nine, wants to think about how to look for Planet Nine, or wants to ponder whether or not they have a telescope/survey/whatever that could possibly detect Planet Nine. Just go to the <a href="https://data.caltech.edu/records/2098">permanent archive of the reference population</a> , download the reference population, and start making plots like the above. Software to help is even included, conveniently written in IDL for those born before 1970 (ahem). </p><p>The reference population includes a flag of everything that would have been detected in ZTF, so you know where not to look. We're happy to include similar flags for any other survey that would have detected any part of the reference population. We've got a couple of new surveys that we are working on including, but get in touch if you'd like yours there. </p><p>Planet Nine is out there. Except in the 56% part of parameter space we have now ruled out.<br /></p><p></p><p><br /></p>Unknownnoreply@blogger.com27tag:blogger.com,1999:blog-1052332993988376053.post-83446239746189466352021-08-23T17:50:00.000-07:002021-08-23T17:50:07.307-07:00The orbit of Planet Nine<p> Five and a half years after our proposal of the existence of Planet Nine, we have finally accomplished what is perhaps the most important task in aiding the search: we now know where to look. We've had a <i>pretty</i> good general idea for years now, but we couldn't really give a full assessment of the range of uncertainties for where in the sky Planet Nine might be, how massive it might be, and how bright it might be. Now we can. You can read <a href="https://arxiv.org/abs/2108.09868" target="_blank">all of the details here</a>.<br /></p><p>Figuring all of this out sounds somewhat straight forward. Our task is simply to take the observations of all of the distant Kuiper belt objects (KBOs) whose orbits are affected by Planet Nine and use those to determine everything we possibly can. It only took five years. </p><p>You can read the full paper for the details, but the five years consisted of a couple of critical steps:</p><ul style="text-align: left;"><li>Understand the physics. Until we had explored all of the various ways that P9 affects objects in the outer solar system, we didn't know which objects were most critical for constraining properties of P9. Many objects are more influenced by Neptune than by P9; if we had included those the signal from P9 would basically be washed out.</li><li>Understand the observations. There has been a lot of talk of observational bias in the population of objects in the outer solar system. Why? Because there is a lot of bias. Without fully characterizing the bias, we would have a difficult time disentangling what we are seeing from just the simple bias.</li><li>Understand how changes to parameters of Planet Nine change the outer solar system. We accomplished this through a huge number of numerical simulations where we placed a bunch of objects in the outer solar system, added the 4 giant planets, and then added different incarnations of Planet Nine, and watched the outer solar system evolve. Every parameters of Planet Nine (almost) has huge impacts on the outer solar system. Which is good, since that means we have leverage to learn about Planet Nine from the outer solar system.</li><li>Figure out a statistical treatment to compare the observations and the simulations. In practice this meant creating a maximum likelihood model combining the simulations, the bias, and the observations of each relevant object. </li><li>Put it all together! Using the maximum likelihood model and what appears to be everyone's favorite statistic technique (MCMC), we now have probability distributions of all of the Planet Nine parameters.</li></ul><p>Sorry it took so long.</p><p>Here are some fun numbers from the analysis. Planet Nine has a mass of 6.2/+2.2/-1.3 Earth masses, a semimajor axis of 380/+140/-80 AU, and inclination of 16+/-5 degrees, and perihelion of 300/+85/-60 AU. We can turn all of that into a map of where to look in the sky and of how bright and far away Planet Nine would be at any position in the sky (brightness depends on some assumption; you might want to read the detail in the paper).</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXbE8CbI2aLRuVPNqlLbRqTuDTWuRwIJwZ8SUc3XqjeF2QAVVR79BLeqyGnnOStwGCcCyPsu8GQuemsiI4KhbQ30IYMDD-TuctRzw74VkR5XiDtqDk6oHD-Nfp8YEE_iF0PEDPFG-LRbM/s682/Capture.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="682" data-original-width="543" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXbE8CbI2aLRuVPNqlLbRqTuDTWuRwIJwZ8SUc3XqjeF2QAVVR79BLeqyGnnOStwGCcCyPsu8GQuemsiI4KhbQ30IYMDD-TuctRzw74VkR5XiDtqDk6oHD-Nfp8YEE_iF0PEDPFG-LRbM/w510-h640/Capture.JPG" width="510" /></a></div><br /><p>That plot on top if a full-sky view going from 360 to 0 in Right Ascension. The equator, ecliptic, and +/-15 degrees of the galactic plane are shown, if that helps to orient you. The colors show the probability of find P9 at any point in the sky. The highest probability is near aphelion, around ~60 degrees in RA, pretty close to the galactic plane. Not surprisingly, this is where we have been concentrating with our Subaru search. The bottom two panes show the distance and brightness. The median distance at aphelion is around 500 AU. The median brightness is around 22nd magnitude. There is a lot of room for variation however! At its brightest predicted magnitude, P9 could be found in many ongoing all-sky surveys. At its faintest, it will require dedicated searches with large telescopes.</p><p>------------------------------------------------------------------------------------------</p><p>That plot above is truly the point of the whole paper, but there are two more plots of which I am a big fan so I want to share these also. </p><p>As mentioned earlier, there had been a lot of discussion of bias and its effect on what we see in the outer solar system. I am here to tell you <b>bias is real.</b> Also I am here to show you that it doesn't cause the clustering that we see.</p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgd6XbJOI0zanxJcTWq2AeZN9HFLYfFhfjP9nhsu6wB5oOLNDsxMQwz6BF6oATHFO25ryk7ER0P9h95wG3zoaaMrKHsjBhg6nklNg52EumEf5FGa2oOebk2DNHEMgcUFYJ-VQvqsQscjHc/s726/Capture.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="470" data-original-width="726" height="414" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgd6XbJOI0zanxJcTWq2AeZN9HFLYfFhfjP9nhsu6wB5oOLNDsxMQwz6BF6oATHFO25ryk7ER0P9h95wG3zoaaMrKHsjBhg6nklNg52EumEf5FGa2oOebk2DNHEMgcUFYJ-VQvqsQscjHc/w640-h414/Capture.JPG" width="640" /></a></div><br /> <br /><p></p><p>Here is a plot that shows a lot of things all at the same time. First, lets concentrate on the green points. Those are 11 real objects in the sky and they show those objects semimajor axis ("a") versus their longitude of perihelion aka the direction their orbits point in space aka "delta varpi". The fact that 10 of those 11 are aligned is the whole reason we are here. </p><p><b>But wait!</b> There is bias. Maybe those are all lined up like that simply because that's where people have looked? Now look at the blue bars. These show, for each object, the probability of the object having been found at all values of longitude of perihelion if the true longitudes of perihelion were distributed uniformly in space. There are two major regions of bias. One is at longitude of perihelion of ~90, and a weaker one is at ~300. These are caused by the DES and OSSOS surveys which both looked in very specific directions and found many objects. But <i>that's not where the cluster is!</i> </p><p>Now look at the red in the background. This shows how the green points should be distributed if Planet Nine were out there messing things up. Looks pretty good, no?</p><p>OK, one more:</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgp4TFpW-TM_jMDKKK9Lo9MNIeMCuRhEAM0441UErm_-WG2uY8xtpNQf0m3ZJZcTNhLWKfDYeE-f4u3xCEX7rWA50iMLG1Di6pV4y2RI6Z2_Sp6AOGEBzc9HxQEaVyi0J68p3R00ITP7QY/s896/Capture.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="632" data-original-width="896" height="452" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgp4TFpW-TM_jMDKKK9Lo9MNIeMCuRhEAM0441UErm_-WG2uY8xtpNQf0m3ZJZcTNhLWKfDYeE-f4u3xCEX7rWA50iMLG1Di6pV4y2RI6Z2_Sp6AOGEBzc9HxQEaVyi0J68p3R00ITP7QY/w640-h452/Capture.JPG" width="640" /></a></div><p>This is the same general idea as above, but now we are plotting the pole position of the orbit of each of the distant objects. A point right in the middle has an orbital plane exactly the same as the planets, a point displaced in any direction from the center is tilted, and the direction of displacement tells the direction of the tilt. As you can see from the green points, the real objects have, on average, about a 15 degree tilt towards zero. Red again shows the Planet Nine prediction. Blue shows the biases. The biases here look weird and spider webby, again mostly because of DES and OSSOS. There is a lot of bias, and the observations generally fal along the lines of bias. But the bias clearly cannot account for the fact that the orbits are tilted and that they are tilted in one direction.</p><p>Put these two plots together and you get a 99.6% chance that the objects are clustered, rather than uniform. That sounds pretty good to me.</p><p>--------------------------------------------------------------</p><p>The paper has even more inside (at 26 pages believe me, there is a lot more), but these are my favorite highlights. I think of that first plot as the Planet Nine Treasure Map. Time to start hunting, my fellow pirates.<br /></p><p><br /></p><p><br /></p>Unknownnoreply@blogger.com106tag:blogger.com,1999:blog-1052332993988376053.post-46434702548095042032021-04-13T19:54:00.002-07:002021-04-13T19:54:29.829-07:00The Inner Oort Cloud Connection<p><span style="caret-color: rgb(102, 102, 102); font-family: "Helvetica Neue"; font-size: 13px;">The census of Kuiper belt objects spanning the distant solar system has sure come a long way. Even if we strictly limit our object sample to those with semi-major axes above 250 AU, or equivalently, an orbital period greater than about 4,000 years, the number of TNOs clocks in at nineteen — a staggering improvement from the six we had back in 2016. </span></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuoMhnTkVmDl_0Zv8ChmtWi2E8ZJjs5SlW2di9Y6bVmSc_JL1hvHY6lSxvhB2wEo19BAyYJ2ws2CbcjinWNyEqQZPR-FBLEHzNS1jDegf0IJTm4Kz2Uo7BKBhhjG7ADU_2I3emKOtxrx8/s1650/orbs.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1598" data-original-width="1650" height="546" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuoMhnTkVmDl_0Zv8ChmtWi2E8ZJjs5SlW2di9Y6bVmSc_JL1hvHY6lSxvhB2wEo19BAyYJ2ws2CbcjinWNyEqQZPR-FBLEHzNS1jDegf0IJTm4Kz2Uo7BKBhhjG7ADU_2I3emKOtxrx8/w565-h546/orbs.png" width="565" /></a></div><span style="font-family: "Helvetica Neue"; font-size: 13px;"><p><span style="font-family: "Helvetica Neue"; font-size: 13px;"><br /></span></p>Some of these TNOs cluster together, while others do not. More importantly, a simple glance at the orbital structure of the outer solar system reveals an intriguing pattern: the degree of clustering is intimately connected to their present-day dynamical stability. In other words, orbits strongly perturbed by Neptune and those on their way out of the solar system (rendered in green) are all over the place. Meanwhile, long-term stable Sedna-like orbits (rendered in purple) appear as though a cosmic florist has carefully arranged them into a bunched bundle of trajectories. Meta-stable orbits (shown in gray) experiencing slow orbital diffusion are caught somewhere in the middle.</span><p></p><span class="im" style="font-family: tahoma, sans-serif;"><p style="font-family: "Helvetica Neue"; font-size: 13px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal; margin: 0px;"><br /></p></span><p style="caret-color: rgb(102, 102, 102); font-family: "Helvetica Neue"; font-size: 13px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal; margin: 0px;">The degree to which the <i>overall</i> orbital clustering is a physical effect, as opposed to being a figment of observational bias or a statistical chance, has been a subject of discussion ever since the Planet Nine Hypothesis saw the light of day (see <a href="https://arxiv.org/pdf/1706.05348.pdf" target="_blank">here</a>, <a href="https://arxiv.org/pdf/1706.04175.pdf" target="_blank">here</a>, <a href="https://arxiv.org/pdf/1901.07115.pdf" target="_blank">here</a>, <a href="https://arxiv.org/pdf/2003.08901.pdf" target="_blank">here</a> and <a href="https://arxiv.org/pdf/2102.05601.pdf" target="_blank">here</a>, as well as Mike’s post below). To this end, individual surveys having only searched limited areas of the sky cannot sufficiently overcome their own observational biases to determine the absence or presence of orbital alignment rigorously. However, even after taking observational biases into account, a combined observability analysis of all available data shows that distant KBOs jointly cluster in eccentricity and angular momentum vectors at the ~99.8% significance level.</p><p style="caret-color: rgb(102, 102, 102); font-family: "Helvetica Neue"; font-size: 13px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal; margin: 0px;"><br /></p><p style="caret-color: rgb(102, 102, 102); font-family: "Helvetica Neue"; font-size: 13px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal; margin: 0px;">Dynamical sorting of KBOs is another matter: although there are distinct biases pertinent to high-eccentricity orbits documented in the literature, no conceivable observational bias can differentiate KBOs based upon their dynamical stability, thereby causing long-term stable orbits to cluster more strongly than their unstable counterparts. Put simply, when astronomers discover TNOs, pretty much the only well-known information about them is RA/DEC, heliocentric radius, and Vmag for approximately one year preceding follow-up. For this reason, it is impossible for surveys to bias themselves based on the <a href="https://en.wikipedia.org/wiki/Lyapunov_exponent" target="_blank">Lyapunov exponent</a>, or the rapidity of exponential divergence of cloned initial conditions, of an orbit. On the contrary, within the framework of the Planet Nine hypothesis, there is a close link between the degree of orbital clustering and dynamical stability. Thus, if we interpret the picture insinuated by the data at face value, the observed “width” of the stable-orbit cluster tells us something about Planet Nine’s mass and orbit.</p><p style="caret-color: rgb(102, 102, 102); font-family: "Helvetica Neue"; font-size: 13px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal; margin: 0px;"><br /></p><p style="caret-color: rgb(102, 102, 102); font-family: "Helvetica Neue"; font-size: 13px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal; margin: 0px;">A couple of years ago, we published a <a href="https://arxiv.org/pdf/1902.10103.pdf" target="_blank">review article</a> detailing thousands of simulations suggesting that P9 is less eccentric and less massive than we initially thought (i.e., m~5 Earth masses and e~0.3 instead of m~10 Earth masses and e~0.6). Even more refined models having more particles and matching the data more precisely are possible and are worthwhile to pursue. However, the question we asked ourselves during the height of the pandemic is a different one: are essential <i>physics</i> missing from our simulations? Through our continued and incessant probing of the model, we have discovered that the answer to this question is “yes.”</p><p style="caret-color: rgb(102, 102, 102); font-family: "Helvetica Neue"; font-size: 13px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal; margin: 0px;"><br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdl-u7sOVYu96NX3ybJzbXp9zUgoH4vm4CM0G5c8EcSq4P3ZkPTrFScg0Or2WhV07Z8Fu9WC-Zr4duyLydQ11KIG7IKtHjEDiZXIuJjrtjWBdnbnmyU11tSdfY_Lf0zUocP55IYZEqIE4/s2048/Screen+Shot+2021-04-13+at+7.40.20+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1136" data-original-width="2048" height="311" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdl-u7sOVYu96NX3ybJzbXp9zUgoH4vm4CM0G5c8EcSq4P3ZkPTrFScg0Or2WhV07Z8Fu9WC-Zr4duyLydQ11KIG7IKtHjEDiZXIuJjrtjWBdnbnmyU11tSdfY_Lf0zUocP55IYZEqIE4/w557-h311/Screen+Shot+2021-04-13+at+7.40.20+PM.png" width="557" /></a></div><br /><p style="caret-color: rgb(102, 102, 102); font-family: "Helvetica Neue"; font-size: 13px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal; margin: 0px;">All our P9 calculations thus far have treated the solar system as an isolated entity, with the sun at the center of the simulation and all objects that attain a heliocentric distance over 10,000 AU as being forever lost to the abyss. Although this is a viable approximation scheme for understanding the present-day solar system, it is an unrealistic full-scale model considering the sun’s birth environment. After all, enrichment of meteorites in short-lived radiogenic isotopes suggests that the sun formed in a massive cluster of stars, somewhat akin to the Orion Nebular Cluster. This fact immediately renders the formation of a perihelion-detached quasi-toroidal cloud of icy debris at a few thousand AU all but inevitable. As our <a href="https://arxiv.org/pdf/2104.05799.pdf" target="_blank">newly published P9 simulations</a> show, this cloud of debris does not remain dormant throughout the lifetime of the solar system. Instead, Planet Nine’s gravity acts to inject these “inner Oort Cloud” objects into the trans-Neptunian region of the solar system, mixing them in with the distant scattered disk. A necessary consequence of the process is that newly-injected debris tends to broaden the cluster, requiring a more eccentric P9 to match the data.</p><span class="im" style="font-family: tahoma, sans-serif;"><p style="font-family: "Helvetica Neue"; font-size: 13px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal; margin: 0px;"><br /></p></span><p style="caret-color: rgb(102, 102, 102); font-family: "Helvetica Neue"; font-size: 13px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal; margin: 0px;">Let us discuss this process in greater detail. The formation of giant planets, particularly Jupiter and Saturn, happens while the sun is encircled by its primordial disk of gas and dust during the first three million years of its lifetime. As the giant planets gain mass, they necessarily scatter icy debris outwards. If the solar system were to evolve in isolation, the debris would eventually attain positive orbital energy and become unbound from the sun. In a star cluster, however, the situation is more delicate. As the planetesimal obits become sufficiently elongated, they become susceptible to perturbations from passing stars that can detach them from the gravitational bashing of newly-born Jupiter and Saturn, thereby “freezing” them in place. Distinct from the classical Oort Cloud that likely formed later, we refer to this hypothetical population of icy asteroids envisioned to orbit the sun at thousands of astronomical units as the inner Oort Cloud.</p><span class="im" style="font-family: tahoma, sans-serif;"><p style="font-family: "Helvetica Neue"; font-size: 13px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal; margin: 0px;"><br /></p><p style="font-family: "Helvetica Neue"; font-size: 13px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal; margin: 0px;">We have simulated the formation of the inner Oort Cloud, modeling the sun’s birth cluster as a Plummer sphere, with parameters chosen to mimic the Orion Nebular Cluster and solar residence time chosen such that it does not violate cold classical Kuiper belt constraints. Shown in terms of Keplerian orbital elements, a typical inner Oort Cloud that forms in our simulations looks as follows:</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgy3RMXhPNsPN02xlW0dDuw-KnEtfX_bK9SnJiHvyvLmAhBYHn-hfCzw7YnK2Q5vyZIEBkYTipIUG1VrfDzORC0WnCpzbSCqdF2men3_4ycDO4jr5DnDKFLLOH2uraABlsa7g4dRy9y7C4/s1634/IOC.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1218" data-original-width="1634" height="426" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgy3RMXhPNsPN02xlW0dDuw-KnEtfX_bK9SnJiHvyvLmAhBYHn-hfCzw7YnK2Q5vyZIEBkYTipIUG1VrfDzORC0WnCpzbSCqdF2men3_4ycDO4jr5DnDKFLLOH2uraABlsa7g4dRy9y7C4/w571-h426/IOC.png" width="571" /></a></div><br /><p style="font-family: "Helvetica Neue"; font-size: 13px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal; margin: 0px;"><br /></p><p style="font-family: "Helvetica Neue"; font-size: 13px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal; margin: 0px;">Now, the conventional story is that the inner Oort Cloud formation stops the moment the sun leaves its birth cluster, and this frigid cloud of icy debris sits there “forever.” Planet Nine, however, alters this picture on a qualitative level. Due to the long-term gravitational pull of P9’s orbit, inner Oort Cloud objects evolve on billion-year timescales, slowly getting re-injected into the outer solar system. So what happens to them? We have simulated this process, accounting for perturbations from the canonical giant planets, P9, passing stars, as well as the galactic tide, and have found that these re-injected inner Oort Cloud objects can readily mix in with the census of distant Kuiper belt objects, and even exhibit orbital clustering. However, the degree of clustering they show is prominently weaker, suggesting that a more eccentric P9 is required to explain the data. Another intriguing aspect of these calculations is that they produce a more radially extended distribution of long-period TNOs, providing an intriguing potential explanation for the abundance of highly long-period orbits, such as that of the <a href="https://en.wikipedia.org/wiki/541132_Leleākūhonua" target="_blank">Goblin</a>.</p><p style="font-family: "Helvetica Neue"; font-size: 13px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal; margin: 0px;"><br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhb5pANHKoIUuAXG4qOfqyfzKXwuNXLPpMHpOYM8EtAWBtwDU40aLs0qnaWzktPecpTc5IfLUXxiB3VH1SNX8Lrj_cMg-MJDjo1QPC954Y77V9RyNHI581aVZTY_QO3W5w2rEiULuNeavo/s2048/res.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="1757" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhb5pANHKoIUuAXG4qOfqyfzKXwuNXLPpMHpOYM8EtAWBtwDU40aLs0qnaWzktPecpTc5IfLUXxiB3VH1SNX8Lrj_cMg-MJDjo1QPC954Y77V9RyNHI581aVZTY_QO3W5w2rEiULuNeavo/w549-h640/res.png" width="549" /></a></div><br /><p style="font-family: "Helvetica Neue"; font-size: 13px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal; margin: 0px;"><br /></p></span><p style="caret-color: rgb(102, 102, 102); font-family: "Helvetica Neue"; font-size: 13px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal; margin: 0px;">All in all, as scientists, our primary role is to continue hammering away at the hypothesis, and our <a href="https://arxiv.org/pdf/2104.05799.pdf" target="_blank">new simulations</a> indicate that there exists an intriguing additional mode of P9-induced dynamics affecting our efforts to pin down the orbit of Planet Nine. With each theoretical breakthrough, the observational search comes into sharper focus.</p>Konstantinhttp://www.blogger.com/profile/14245543234165152508noreply@blogger.com64tag:blogger.com,1999:blog-1052332993988376053.post-60521239369880495442021-02-16T11:04:00.005-08:002021-02-16T14:29:45.719-08:00Is Planet Nine finally dead?<p> Konstantin and I have a recurring conversation. One of us says "Wait! I think we're wrong about the evidence for Planet Nine. Here's why..." and proceeds to spin a hypothesis about how we could have been misled by the data or that we are predicting something that is not happening, and then we will carefully go through the entire Planet Nine analysis over again before convincing ourselves that, no, all is normal in the outer solar system (where by <i>normal</i> we mean that Planet Nine is happily orbiting the sun waiting to be seen). So far, we have not found a reason to discard the Planet Nine hypothesis. Will one some day? Perhaps. If the evidence for the existence of Planet Nine were to unravel we would be sad, but we would have to give up the idea. We have been prepared for that moment since the day we first proposed Planet Nine.<br /></p><p>Has the moment now come? A new paper by Napier et al. appeared on the archive the other day with the fairly conclusive title of <a href="https://arxiv.org/pdf/2102.05601.pdf" target="_blank"><i>No Evidence for Orbital Clustering in the Extreme Trans-Neptunian Objects</i></a>, which, well, sounds pretty bad for Planet Nine. There was a quick flurry of requests for comments on the paper, but it seemed like it was better to carefully read and go over the analysis than to simply glibly comment. It's a substantial paper with a lot buried in it, so it took a while, but I think I have now fully digested the paper and can comment on what is going on.</p><p>The central idea of the paper is pretty simple: do a careful analysis of where three separate surveys pointed their telescopes and use that analysis to examine whether or not their is any clear sign of orbital clustering in the outer solar system. The specific method is different, but the paper follows the general prescription of <a href=" https://arxiv.org/pdf/1901.07115.pdf">our paper from 2019</a> in trying to determine if the orbits of distant KBOs are aligned in the same general direction and if the orbits are tilted in the same direction. These effects are precisely what is predicted by the Planet Nine hypothesis. In our 2019 paper, we analyzed the 14 objects known as of that time that have semimajor axis (average distance from the sun) beyond 230 AU. We found that we could rule out a non-clustered outer solar system at the 99.8% confidence level. Pretty good right?</p><p>Our 2019 paper performed one other critical analysis (this will matter below!). We showed that the 4 objects found by the OSSOS survey were too few to be able to detect the clustering. If you think of the measure of clustering as a single number (which it isn't; it's a 4-dimensional point, but we'll pretend), you could say that we measured a clustering of 4+/-1, for example. But the OSSOS survey could not detect clustering because they measured 0+/6. The uncertainty on their measurement was larger that the expected effect. All was happy in Planet Nine land.</p><p>OK, so back to the Napier et al. analysis. They look at 14 objects that have been discovered since our original 2015 paper. After much work they conclude that they can rule out a non-clustered outer solar system at only the 83% confidence level. Bad news for Planet Nine! Taken at face value it seems that the evidence for clustering has weakened or gone away entirely. </p><p> Statistically, it is weird that a 99.8% significant result would fade so quickly with just a little new data. Interestingly, when Napier et al. looked only at the objects which are identical between their analysis and our analysis, they see clustering at the 99.5% significance level in excellent agreement with our original analysis, so we all agree that those 2019 results appear on firm ground. So: what is up with the 7 new objects in their analysis that suddenly drops the significance? Let's find out who they are and what surveys they came from.</p><p>First, let's look at the measure of clustering from our 2019 paper:</p><p> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5MJMTkH5ddmXHf5GFtrYm44ccWT4Z09FCVLAyfhj-puwlmABSoo7UFvdXwWvoVXuY99d0bRH3RO0rdsQb2bP7jCbGhtIdNqY012Tt_0_l4y0sRPKT0tkUPcdjrsUttsdTT9KVEJOneeQ/s637/Capture.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="358" data-original-width="637" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5MJMTkH5ddmXHf5GFtrYm44ccWT4Z09FCVLAyfhj-puwlmABSoo7UFvdXwWvoVXuY99d0bRH3RO0rdsQb2bP7jCbGhtIdNqY012Tt_0_l4y0sRPKT0tkUPcdjrsUttsdTT9KVEJOneeQ/w640-h360/Capture.PNG" width="640" /></a></div><br /><br /><p></p><p>What you are looking at are measures of two parameters for each of the 14 distant objects in our analysis. <i>x,y</i> shows, basically, the direction that the orbit points (with some additional complications). <i>p,q </i>shows the direction that the orbit tilts (with some additional complications). As you can see, the orbits of 11 of the 14 objects point towards one quadrant and, on average, they are tilted in a common direction. Napier et al. followed our prescription here, so you can see their versions of these same plots in their Figure 4. The big red dots are the average position of the black dots and show the strength of the clustering. (To complete the analysis we must determine if, when observational biases are included, the red dots are far enough away from zero [unclustered] to be significant; they are, at the 99.8% confidence level). </p><p>Let's add the new Napier et al. objects to these plots:</p><p> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEju2rO1w5vVmE591zfD-XnHwEHZHKHZh_B-8JioiRHtIUGX2lxigYU492CbKaKKvbuXcNbPbShdFugw-C_5NY2toyUVn6i5SLEiMbFjAD-_1k2OBsaWt30NF6ww-O8-pNdbYpHHW18uN1I/s636/Capture.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="349" data-original-width="636" height="352" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEju2rO1w5vVmE591zfD-XnHwEHZHKHZh_B-8JioiRHtIUGX2lxigYU492CbKaKKvbuXcNbPbShdFugw-C_5NY2toyUVn6i5SLEiMbFjAD-_1k2OBsaWt30NF6ww-O8-pNdbYpHHW18uN1I/w640-h352/Capture.PNG" width="640" /></a></div><br /><br /><br /><p></p><br /><p> The green points are from the spatially concentrated (thus highly biased) DES survey, the purple from the much broader survey of Sheppard and Trujillo (there is one additional object that Napier et al. include that was never reported to the Minor Planet Center; we restrict our analysis to objects whose detection history we can track; that one unreported object is down in the lower left of the lefthand plot). According to Napier et al., the inclusion of these points <i>which are clearly consistent with the previous measurement of clustering </i>into the analysis makes the evidence for clustering inconclusive. <b>WHAT?</b></p><p>It took my a long time to understand this strange-looking behavior (again, instant commentary is not always the best commentary). But I think I get it. I believe it is all about the measurement uncertainty that we talked about above. Our paper says that the clustering statistic is 4+/-1. Their paper says the clustering statistic is consistent with zero. But I believe that their clustering statistics is something more like 4+/-6. Thus consistent with zero, as they correctly claim, but not good enough to detect the clustering that exists. Do I know this for sure? No, because they did not publish their uncertainties (an interesting question would be how did whoever refereed the paper let them get away without publishing their uncertainties!). </p><p>OK, but wait. They have about the same number of objects in their analysis as we did in our 2019 analysis, so why would our uncertainties be smaller? I think that the answer is primarily due to the fact that DES, which only looked in one direction in the sky, happened to look right in the direction of the clustering. Why? Dumb luck. Their survey was designed long before there was an inkling of Planet Nine. And the Planet Nine clustering is independent of any DES data.<br /></p><p>Why is that a problem, though? Imagine a situation where I look around for a few nights and notice that the sun is setting in the west the modest number of times I happened to notice the sunset. You then decide to studiously look west. You see sunsets, but only in the west. You have performed a very biased survey, so when you do your statistically correctly you state that you cannot confirm that the sun sets exclusively in the west because your large survey would only see western sunsets thus the direction of the setting sun is statistically conclusive with being in all directions. It seems weird, but adding in highly biased data that is <i>biased in the precise direction as the signal for which you are looking </i>makes it harder to confirm the signal in the first place. But there is a solution. That solution? Publish your uncertainties. </p><p>Napier et al. get it right, in the end:</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFp8Ae3Y-tHOqkyeYVbdwt05725khklVoLH2TuB0sROCJjYKLVOLOsHVs30gmjnpbPnQlhDfxDIPDX1pRfTgQ6PALKXd0KrPXuOKm8MYdlq13fRomMT9DCZq9G9bZQL7xryth9xX74F3E/s978/Capture.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="113" data-original-width="978" height="74" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFp8Ae3Y-tHOqkyeYVbdwt05725khklVoLH2TuB0sROCJjYKLVOLOsHVs30gmjnpbPnQlhDfxDIPDX1pRfTgQ6PALKXd0KrPXuOKm8MYdlq13fRomMT9DCZq9G9bZQL7xryth9xX74F3E/w640-h74/Capture.PNG" width="640" /></a></div><p></p><p>Ah ha! Sadly, they don't check for consistency with the previously measured clustering, or they would see that, indeed, the ETNOs were already known to be clustered precisely where DES has looked. </p><p>I think this solves the mystery of how adding in objects which appear quite clustered makes the significance of your clustering appear to go away.</p><p>I think that the right conclusion is that the highly-biased DES data is consistent with the previous measurements of clustering, but that the bias from DES is strong enough that we should probably not be surprised by this. In the end, the previously measured clustering from our 2019 paper is still valid (and has actual uncertainties published), and the conclusions of that paper remain. The clustering of distant Kuiper belt objects is highly significant. It's hard to imagine a process other than Planet Nine that could make these patterns. The search continues.<br /></p><p><br /></p><p><br /></p>Unknownnoreply@blogger.com104tag:blogger.com,1999:blog-1052332993988376053.post-39436257148400041182019-02-26T22:55:00.000-08:002019-02-26T22:55:34.661-08:00version 2.X<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Helvetica Neue"; font-stretch: normal; line-height: normal;">
<span style="-webkit-font-kerning: none;">I finished the last post by stating the obvious: the Planet Nine hypothesis - as imagined by us - is NOT the first (or even the latest) proposal of a trans-Neptunian planet. So what distinguishes all these hypotheses? Are all putative trans-Neptunian planets the same Planet? Clearly not. Put simply, each theory is characterized by 1) the anomalous data it seeks to explain, and 2) the dynamics through which the putative planet explains the data. One of the key goals of the new paper was to place P9 hypothesis within this framework by delineating a series of purely analytical models, as well as a suite of large-scale numerical simulations. As a result, the discussion below will inevitably touch on some technical points. For those of you only interested in the final answer, however, I will take a shortcut and summarize our conclusions:</span><br />
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<span style="font-kerning: none;">Planet Nine is a factor of ~2 smaller in all quantities compared to what we reported in the original paper. The new estimate of the semi-major axis is a~400-500AU (could potentially be even smaller, but only marginally so). P9’s orbital eccentricity is about e~0.15-0.3. The inclination is around i~20 deg. Last but not least, the mass is about m~5 Earth masses. Planet Nine is probably not a relative of Neptune — it’s a Super-Earth. Now let’s dig into the details a bit.</span></div>
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<span style="font-kerning: none;">As always, the best starting point is the observational data. Compared with three years ago, the dataset has expanded by a factor of a couple, and now contains 14 objects with semi-major axis beyond 250 AU and inclinations lower than 40 degrees. The diagram below shows the orbits in physical space, as viewed from the north ecliptic pole, while the inset presents a polar plot of the orbital inclinations and longitudes of ascending node (which dictate the orientations of the orbital planes):</span></div>
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Generally, the distant KBOs span a broad array of perihelion distances, ranging from ~35AU to ~80AU. As a result, some KBOs interact with Neptune (which lives at 30AU) much more strongly than others, yielding a wide spread in dynamical lifetimes. For the purposes of the P9 hypothesis, it is useful to sub-divide the data into three categories: stable, metastable, and unstable orbits, which are shown on the above plot as purple, gray, and green ellipses respectively. Although the orbital confinement among the plotted long-period KBOs is easy to see by eye, it is also evident that the degree of clustering is far more striking among dynamically stable (purple) and metastable (gray) orbits than their unstable (green) counterparts.<span style="font-kerning: none;"></span></div>
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<span style="font-kerning: none;">Intuitively, the weaker clustering of unstable orbits is easy to understand — KBOs that interact with Neptune most strongly experience relatively rapid dynamical chaos. In turn, these stochastic perturbations erase any innate orbital structure of the distant belt. While all KBOs tell <i>some</i> story within the framework of the Planet Nine hypothesis, some tell a deeper story than others. The most cautious/conservative thing to do then, is to focus exclusively on the (meta)stable objects, which are not contaminated by strong interactions with Neptune.</span><br />
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<span style="font-kerning: none;">Ok, so these orbits are clustered together — why is that a big deal (i.e., couldn’t they just have formed that way)? In essence, this dynamical structure is puzzling because if left to their own devices, the orbits would disperse on a timescale far shorter than the age of the solar system (due to precession induced upon them by Jupiter, Saturn, Uranus, and Neptune). To give you an example, we can plug in numbers into the above equations, and obtain that while Sedna’s orbit precesses at about 0.15 degrees per million years, 2014 SR349 precesses at 0.8 deg/Myr. Give it a few hundred million years, and the orbits will disband. Therefore, some kind of an external gravitational pull is actively keeping them confined.</span></div>
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<span style="font-kerning: none;">As discussed in numerous published papers (see here for a list (papers that cite BBa)), the above orbital anomalies collectively point to the existence of P9. Nevertheless, to date, the parameters of P9 have remained relatively poorly determined. In the new paper, we went to some lengths to remedy this problem. As an example of the type of calculations we carried out, consider one constraint that comes from matching the critical semi-major axis that corresponds to the transition point between randomized and clusters orbital distributions. In other words, if a planet is responsible for the structure that we see, how does it keep all the orbits aligned, and why does this alignment suddenly “turn on” at ~250AU? The simplest way to understand this analytically is to restrict the orbits to a common plane and to examine the functional form of their gravitational coupling. But to do so without resorting to simulations (which is important if we want to <i>understand</i> the dynamics rather than just model them), we have to rely on the so-called orbit-averaging procedure.</span></div>
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<span style="font-kerning: none;">Back in the late 1700’s, Joseph-Louis Lagrange and Pierre-Simon Laplace realized that over very long periods of time, gravitational interactions between planets can be approximated by smearing the planets along their respective orbits and computing the gravitational torques that the massive wires exert upon one another. This brilliant insight was better formalized in the mid-1800’s by Gauss, and forms the qualitative basis of secular perturbation theory. Employing this secular approximation, we can write down the total gravitational potential experienced by a KBO, under the influence of the known giant planets as well as Planet Nine, and it looks like this:</span></div>
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<span style="font-kerning: none;">Importantly, this expression is the <i>Hamiltonian</i> for the problem at hand, and acts like a stream-function (or a topographic map) for secular evolution of the KBO’s orbit. This means that the long-term changes in the KBO’s orbit will simply follow the contours of the above equation. Neat right? Now, mapping the level curves of this Hamiltonian on a eccentricity vs. longitude of perihelion (relative to P9) plane at different KBO semi-major axes reveals the emergence of a stable equilibrium at ∆w=π for a>250AU. Qualitatively, this is why only distant orbits are clustered — perihelion anti-aligned orbits are only stable beyond a critical semi-major axis, and this value depends on the assumed orbital parameters of P9.</span></div>
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The reason behind why the orbits all cluster to a common orbital plane can also be understood in this manner, but excitation of KBO orbits onto highly inclined/retrograde orbits is considerably more complicated. If you’re interested in learning more, check out section 4 of the manuscript.</div>
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<span style="font-kerning: none;">Analytical Intuition is important, but a thorough comparison between P9-sculpted synthetic Kuiper belt and real data requires a more detailed description of dynamics. Realistically, such a description can only come from N-body simulations. In this review, we did thousands of them, varying P9's mass and orbital parameters. Typical results from N-body simulations look like the fig below. Notice how in agreement with the above analytical formula, beyond a critical semi-major axis a~250AU, long-term stable KBOs - shown in this plot as blue points - cluster in longitude of perihelion:</span></div>
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In the simulations, the specific choices of P9 parameters directly translate to the characteristics of the distant Kuiper belt sculpted by P9’s gravity. For instance, the critical semi-major axis at which the transition from randomized to clustered orbits ensues, the actual degree of clustering, the mean tilt of the orbits, etc. all depend sensitively on P9 parameters. Although a little abstract, the most transparent approach to visualizing the relationship between simulation and data is in Poincare action-angle variables, and the figure below gives you a taste of the simulations success criteria that we used, as well as a representation of one example simulations<br />
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<span style="font-kerning: none;">In section 5 of the paper, we carried out a quantitative comparison between statistical properties of the synthetic data and the real objects for each one of our N-body sims. Intriguingly, it was this analysis that revealed that a comparatively low mass Planet Nine fits the data better than our original estimates for P9 in every respect. If you don’t believe me, feel free to examine the full ensemble of 5 Mearth simulations for yourself in the plot below.</span></div>
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<span style="font-kerning: none;">In principle, there is so much more that I would like to say, but at this point I think it’s becoming progressively clearer that my coffee supply ran out a couple paragraphs ago, and in an effort to prevent further degradation of the text, I will get straight to the final point: if Planet Nine is smaller, does that mean it's harder to find with a telescope? Counterintuitively, it's the opposite. The smaller distance from the sun more than makes up for the diminished surface area. Indeed, if we make naive baseline assumptions about P9’s albedo and adopt the interpolated <a href="https://iopscience.iop.org/article/10.1088/2041-8205/783/1/L6/pdf" target="_blank">exoplanet mass-radius relation</a> to estimate P9’s size, Planet Nine turns out to be about one magnitude brighter than we previously thought. Annoyingly, though, the aphelion is very close to (in?) the galactic plane, where confusion due to background stars can readily impede detection. Still, unless we are unlucky and P9 is unexpectedly small and/or dark, it should be within the reach of <a href="https://en.wikipedia.org/wiki/Large_Synoptic_Survey_Telescope" target="_blank">LSST</a> and comparable telescopes like <a href="https://en.wikipedia.org/wiki/Subaru_Telescope" target="_blank">Subaru</a>. The good news is that in the case of Planet Nine hypothesis, time truly will tell.</span></div>
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Konstantinhttp://www.blogger.com/profile/14245543234165152508noreply@blogger.com548tag:blogger.com,1999:blog-1052332993988376053.post-88073277855647985142019-02-26T22:34:00.000-08:002019-02-26T22:34:14.378-08:00Stories<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Helvetica Neue"; font-stretch: normal; line-height: normal;">
<span style="-webkit-font-kerning: none;">The history of Le Verrier’s mathematical discovery of Neptune is my favorite story, period. It’s literally got everything you’d want in a good novella - differential equations, integrals, telescopes, intrigue, you name it. Rather than try to rehash it here without doing it justice, I’ll point the interested reader to an excellent 2016 article by Davor Krajnović called “<a href="https://arxiv.org/pdf/1610.06424.pdf" target="_blank">The contrivance of Neptune.</a>” Here, I only want to call attention to what Le Verrier (and Adams) got right and what they got less right.</span></div>
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<span style="font-kerning: none;">It’s widely known that Neptune was discovered “with the tip of a pen.” Indeed, Le Verrier was able to derive Neptune’s location <i>on the sky</i> from orbital anomalies of Uranus with exquisite accuracy, such that Galle and D’Arrest’s observational campaign to discover this elusive planet took less than a single night. What is somewhat less well known is that Le Verrier and Adams’ calculations of Neptune’s <i>orbit and mass</i> were not as precise. The figure below shows the true orbits and locations of Uranus (gray) and Neptune (black) between 1830 and 1860, as well as the predicted orbits of Neptune (in purple).</span></div>
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<span style="-webkit-text-stroke-width: initial;">Notice that the inferred semi-major axis of Neptune was about 40 (rather than 30) AU and the derived mass (36 and 50 Earth masses for Le Verrier and Adams, respectively) also significantly exceeded that of Neptune. In light of the fact that the discovery of Neptune represents the only successful mathematical prediction of a planet to date, this level of uncertainty sets the gold standard for dynamically motivated planetary predictions. In other words, if we get Planet Nine to a similar level of precision, I’ll be satisfied. It is also useful to point out that the most significant quantity in perturbing the orbit of Uranus was the anomalous acceleration in the radial direction produced by the new body - GM/r^2 - a ratio that was calculated to higher accuracy than the individual values of mass and semi-major axis. As I will highlight later, the general framework of the Planet Nine hypothesis is characterized by comparable degeneracies between P9’s mass and orbital parameters.</span></div>
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<span style="font-kerning: none;">Following Le Verrier’s mathematical discovery of Neptune, the planet prediction business didn’t simply get a boost - it exploded. Jacques Babinet (1848), David P. Todd (1877), George Forbes (1880), Camille Flammarion (1884), William Pickering (1909-1932) all took turns predicting trans-Neptunian planets that later turned out to not be there. But no planetary prediction is quite as emblematic as Percival Lowell’s hypothesized “Planet X.” Briefly, the story goes as follows: despite the addition of Neptune to the solar system’s ledger of planets, small apparent discrepancies in the orbits of the giant planets remained, and pointed to the existence of a ~7 Earth mass planet beyond Neptune. The search continued well past Lowell’s death, and in 1930, a bright moving object was discovered by Clyde Tombaugh in the approximate location on the sky where Planet X was envisioned to be. Because Planet X was the object of the original search, the newly found body was initially considered to be the long-sought-after Planet X.</span></div>
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<span style="font-kerning: none;">Immediately, however, there was a problem. Planet X was supposed to be like Neptune, but Tombaugh’s new planet appeared dim and point-like, and therefore much much smaller. It soon became clear that the new member of the solar system could not be THE Planet X. The object was subsequently named Pluto, and its estimated mass steadily declined for the next 5 decades.</span></div>
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<span style="-webkit-text-stroke-width: initial;">Although Planet X - as originally formulated by Lowell - does not exist, the discovery of Pluto turned out to be the tip of an extraordinary trans-Neptunian iceberg called the Kuiper belt. The mapping and subsequent characterization of the Kuiper belt in the ‘90s and the ‘00s, generated a new wave of planetary proposals — check out Brunini & Melita (2002), Gladman & Chan (2006), Gomes et al. (2006), Lykawka and Mukai (2008), Trujillo and Sheppard (2014), Volk and Malhotra (2017) and many others that are referenced therein. All of these hypothetical planets were invoked to explain different observational puzzles, and attempt to do so through individual dynamical mechanisms. Stepping away from </span><i style="-webkit-text-stroke-width: initial;">specific</i><span style="-webkit-text-stroke-width: initial;"> predictions, however, it is worthwhile to examine the question of where still-undetected planets can hide in the solar system, from a completely model-independent perspective. As it turns out, the combination of ephemerides, orbital stability, and definition of a planet alone leave only a limited parameter space where additional solar system planets can hide (shown as the shaded region on the plot below):</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjp0ACW2pZ98IKtIJ4NLrSxM5XZkVAaDOmEgvifZT8mAfcHBZq62Tq0Fo4t-Rv7I2vd0N2HJd9kIm4Vz_F1wFhF8vEJmAkzBiIW0NmL0YQILEv2OGwBhJTo64pRc39E4cmyshyphenhyphen79PxUfwc/s1600/Screen+Shot+2019-02-26+at+6.05.01+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="877" data-original-width="906" height="386" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjp0ACW2pZ98IKtIJ4NLrSxM5XZkVAaDOmEgvifZT8mAfcHBZq62Tq0Fo4t-Rv7I2vd0N2HJd9kIm4Vz_F1wFhF8vEJmAkzBiIW0NmL0YQILEv2OGwBhJTo64pRc39E4cmyshyphenhyphen79PxUfwc/s400/Screen+Shot+2019-02-26+at+6.05.01+PM.png" width="400" /></a></div>
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<span style="-webkit-text-stroke-width: initial;">Remarkably, Planet Nine falls right in the center of that region.</span></div>
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Konstantinhttp://www.blogger.com/profile/14245543234165152508noreply@blogger.com65tag:blogger.com,1999:blog-1052332993988376053.post-26687705712266149172019-02-26T22:27:00.001-08:002019-02-26T22:37:52.021-08:00Progress<div style="font-family: "helvetica neue"; font-stretch: normal; line-height: normal;">
<span style="font-kerning: none;">The scientific process is, at its core, iterative. There is no such thing as a truly final/definitive answer - there are only solutions that are good enough <i>for now</i>. In a day-to-day sense, what this really means is that when you’ve been chugging away at some problem and you finally arrive at the result, you can be damn sure that you probably haven’t understood the Full Picture (even if in the moment it feels like you have). “Maybe there is a more elegant way to arrive at the solution? Maybe some approximation has introduced a hidden uncertainty? Maybe there’s a better way to look at the data?” Every step in the right direction is inevitably haunted by questions that fall along these lines. </span></div>
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<span style="font-kerning: none;">The Planet Nine story is no exception to this rule. Back when Mike and I published our <a href="https://iopscience.iop.org/article/10.3847/0004-6256/151/2/22/pdf" target="_blank">first P9 paper</a> three years ago, we didn’t worry that there might be a lot more work to be done on this problem - we were certain of it. Instead, what we worried about was that there exists a simpler, or perhaps more natural resolution to the anomalies we were seeing in the data, and that the Planet Nine hypothesis will be rendered irrelevant shortly after publication. That didn’t happen.</span></div>
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<span style="font-kerning: none;">To our joint relief (and to some extent surprise), thus far, the P9 hypothesis has fared the test of time rather well. Inevitably, questions have come up regarding <a href="https://iopscience.iop.org/article/10.3847/1538-3881/aa7aed/pdf" target="_blank">the role of observational biases</a> in shaping the orbital clustering we see in the distant Kuiper belt, but these concerns have been largely <a href="https://arxiv.org/pdf/1901.07115.pdf" target="_blank">put to rest</a>. <a href="https://arxiv.org/pdf/1804.06859.pdf" target="_blank">Alternative theories</a>, on the other hand, require the existence of a hidden, coherent, and massive belt of icy planetesimals at hundreds of AU - a scenario that suffers from a number of astrophysical drawbacks. The P9 story thus continues to be in pretty good shape. Nevertheless, we have always felt the need to drive our understanding of the Planet Nine hypothesis a little bit further (and then a bit further after that). So, in collaboration with Juliette Becker and Fred Adams from University of Michigan (as well as Elizabeth Bailey here at Caltech and Alessandro Morbidelli from Nice observatory on earlier works), we spent the last couple years characterizing P9-induced dynamics from <a href="https://iopscience.iop.org/article/10.3847/1538-3881/aa937c/pdf" target="_blank">analytical grounds</a> and trying to constrain the mass and orbit of Planet Nine to better precision.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggvHVdpfnkRmnfIsduBAypk1lLmnA3RB0vVstNySri5a8ntSV5jYqMwFalkdQaywwwkCOZga-Tv_8kyVDK22qHJpbZy35Cu1Ga8YCBxf5lrghCgF_CJ_XvT_68tYkGjQ3UhKOWTmtfhSA/s1600/Screen+Shot+2019-02-26+at+3.44.59+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="592" data-original-width="756" height="311" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggvHVdpfnkRmnfIsduBAypk1lLmnA3RB0vVstNySri5a8ntSV5jYqMwFalkdQaywwwkCOZga-Tv_8kyVDK22qHJpbZy35Cu1Ga8YCBxf5lrghCgF_CJ_XvT_68tYkGjQ3UhKOWTmtfhSA/s400/Screen+Shot+2019-02-26+at+3.44.59+PM.png" width="400" /></a></div>
<span style="font-family: "helvetica neue";">The results of these endeavors are compiled in our new review article entitled “</span><a href="https://arxiv.org/pdf/1902.10103.pdf" style="font-family: "helvetica neue";" target="_blank">The Planet Nine Hypothesis</a><span style="font-family: "helvetica neue";">,” published in Physics Reports today. Admittedly, in writing this manuscript, we ended up erring on the side of completeness over completion, so the paper is not exactly short. As a result, with an eye towards providing an “executive summary” of the results, in the next couple posts, I will highlight some of the main take-away points of the article, beginning with brief historical account of planetary predictions based on dynamical evidence.</span></div>
Konstantinhttp://www.blogger.com/profile/14245543234165152508noreply@blogger.com67tag:blogger.com,1999:blog-1052332993988376053.post-83736290969360300032019-01-22T10:33:00.000-08:002019-01-22T10:44:50.622-08:00Is Planet Nine just a ring of icy bodies?<div dir="ltr" style="text-align: left;" trbidi="on">
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<br />
<div class="MsoNormal">
We have just passed the three year anniversary of the
publication from Konstantin and I on our proposal for the existence of Planet
Nine. <span style="mso-spacerun: yes;"> </span>In those three years something
remarkable happened: not a single alternative hypothesis was proposed to
explain the observed alignment of the distant Kuiper belt objects that led to
the hypothesis. Instead, most of the discussion has centered about the critical
question of whether or not the alignment is really there or somehow an illusion
(the latest and definitive analysis, <a href="https://twitter.com/plutokiller/status/1087495838379651072" target="_blank">published yesterda</a>y, makes it clear that
the alignment is really there). It appeared that if the observations were real,
Planet Nine was the only explanation.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
A lack of alternative hypotheses is unusual. Astronomers are
extremely good at coming up with explanations for nearly anything. Usually the
problem is too many explanations with not enough data to discriminate between
them. The fact that no Planet Nine alternative was proposed for so long was a
testament to the fact that it is really really hard to explain the quite good
data in any other way.</div>
<div class="MsoNormal">
Finally, however, after three years, a new hypothesis has
been proposed which can at least explain the alignments without Planet Nine.
The basic trick is to take Planet Nine and split it up into a massive ring of
bodies on an eccentric inclined orbit like that of Planet Nine’s. Because
Planet Nine’s long distance gravitational effects are mostly caused by the long
term average position of Planet Nine (which is basically an inclined eccentric
ring!) this ring has more or less the same effects that Planet Nine has. (For the aficionados out there, read this as "Planet Nine's interactions are predominantly secular rather than resonant.")</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
I am happy that there is finally an alternative explanation,
even if that alternative is only Planet-Nine-ground-up-into-a-ring. </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
So, is Planet Nine really just an eccentric inclined ring of
icy bodies? </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
As happy as I am to see alternative hypotheses, and as
correct as I think the underlying physics of this paper is, I think it is utterly unlikely
that our solar system has a massive eccentric inclined ring of material. <span style="mso-spacerun: yes;"> </span>There are two major reasons why this seems somewhere
between implausible and impossible to me. First, the ring needs to contain
something like 10 times the mass of the Earth. Current estimates of the amount
of material in the Kuiper belt are about 100-500 times smaller than that. Could
we be wrong by a factor of 100-500? Sure. There are always ways to conspire to
hide things in the outer solar system, but that is an awful lot of mass to
hide.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Second, it is critical to ask: why would there be a massive
eccentric inclined ring of material in the distant solar system in the first
place?<span style="mso-spacerun: yes;"> </span>The new paper doesn’t address
this question at all. It simply shows that if such a carefully arranged ring is put into place by fiat it can stabilize itself (Konstantin doesn't think such a disk is stable over the age of the solar system, but that's beyond my pay grade; the new paper doesn't realistically address the question so it's hard for me to know) and can cause the same effects that Planet Nine
would. But I can’t think of any remotely plausible reason such a disk would be
there in the first place. Basically the answer to “why do we see a disk of distant
eccentric inclined Kuiper belt objects?” is “because there is a much more massive
disk of even more distant eccentric inclined Kuiper belt objects keeping it in
place.” To be fair, that doesn’t mean that there isn’t such a disk. There are
plenty of things in the universe that we originally thought were implausible
that turned out to be true. But it is by no means a simple, natural
explanation.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
The Planet Nine hypothesis, on the other hand, explains the
observations and is considerably simpler. One planet, scattered into the outer
solar onto a eccentric inclined orbit, explains a host of otherwise
unexplainable phenomenon. As breathtaking as the idea that there might be a new planet out there is, the steps to get there are really rather mundane. This new alternative is a much more complicated
answer to the same question. Usually in science we prefer the simpler solution.
Again, this doesn’t guarantee that it is true, but that there needs to be some
compelling reason to believe that the simpler explanation is wrong and the more
complicated one is correct. I can’t see any such reason.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
The good news, though, is that a ring of bodies is
significantly easier to find than a single planet. While I would argue that it
should already have been found it it existed, at least we can all agree that something
remains out there to be found and that continued exploration of the outer solar
system is the key to unraveling what is going on out there.</div>
<div class="MsoNormal">
<br /></div>
</div>
Unknownnoreply@blogger.com87tag:blogger.com,1999:blog-1052332993988376053.post-13203556743299361172018-09-21T15:10:00.004-07:002018-09-21T16:12:47.975-07:00Mean Motion Resonances and the Search for Planet Nine<div class="" style="font-family: Helvetica; font-size: 14.7px; font-stretch: normal; line-height: normal; margin-bottom: 12px;">
<span class="" style="-webkit-font-kerning: none;">Greetings! My name is Elizabeth Bailey, and I am a graduate student here at Caltech. As part of my work so far, I have addressed the ongoing search for Planet Nine, in particular the use of mean-motion resonances to infer its present-day location on the sky. </span></div>
<div class="" style="font-family: Helvetica; font-size: 14.7px; font-stretch: normal; line-height: normal; margin-bottom: 12px;">
<span class="" style="-webkit-font-kerning: none;">A <a href="https://en.wikipedia.org/wiki/Orbital_resonance" target="_blank">mean-motion resonance</a> occurs when two bodies orbiting a central body have orbital periods related by an integer ratio. A great example is Pluto and Neptune. Pluto’s orbit is not a perfect circle, but rather a little elongated (e ~ 0.25). It actually crosses Neptune’s orbit, which might lead one to ask if they are on a collision course with each other. Fortunately, the answer is a confident “no.” Neptune and Pluto will never collide, because they are in a 3:2 (pronounced “three-to-two”) mean motion resonance with each other. Meaning, for every three trips Neptune completes around the sun, Pluto completes exactly two. It’s as if they’re dancing with each other. Every three times Neptune steps into the intersection of their orbits, Pluto steps twice somewhere else, and they don’t step on each other. </span></div>
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<span class="" style="-webkit-font-kerning: none;">So what does this have to do with Planet Nine? If Planet Nine exists, the distant KBOs it shepherds may very well experience resonant interactions with it. In fact, this was already pointed out in Konstantin & Mike's <a href="http://iopscience.iop.org/article/10.3847/0004-6256/151/2/22/pdf" target="_blank">original Planet Nine paper</a>, and is at this point relatively <a href="https://arxiv.org/pdf/1710.01804.pdf" target="_blank">well understood</a>. As a result, we can reasonably expect that at least some of the observed KBOs are <a href="https://arxiv.org/pdf/1603.02196.pdf" target="_blank">currently locked</a> into resonances with Planet Nine, and if we can understand the machinery of these interactions, <a href="https://arxiv.org/pdf/1612.07774.pdf" target="_blank">perhaps we can infer the location of P9</a>.</span></div>
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<span class="" style="-webkit-font-kerning: none;">In a sense, the distant solar system is a lot like a giant cosmic nightclub. In this analogy, we are scanning the dance floor for Planet Nine, but it's hanging out in a dark corner somewhere in the back, while everyone is doing a P9-themed dance. So rather than looking for P9 itself, we are instead trying to figure out where it is by studying the KBO mosh-pit. This brings us to the key problem at hand: is this feasible </span>in practice<span style="font-size: 14.7px;">? We address this question in <a href="https://arxiv.org/pdf/1809.02594.pdf" target="_blank">our recent work</a>, published in the Astronomical Journal. </span></div>
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<span class="" style="-webkit-font-kerning: none;">The short answer is no - using resonances does not appear to be a feasible approach to find Planet Nine. Here's a figure from the paper comprised of seven histograms, corresponding to simulations with seven different eccentricities of Planet Nine (e_9 = 0.1, ..., 0.7) showing the count of objects occupying individual resonances. (The 2:1 resonance is located at "2" on the horizontal axis, and the 3:2 resonance is located at "1.5," and so forth.)</span></div>
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<span class="" style="-webkit-font-kerning: none;">The takeaway point from this figure is that although you do find a lot of KBOs at the big-name resonances like 3:2 or 1:1, there are many objects occupying other resonances with larger integers in their names, like 14:5 or 2:7. There is a disturbing consequence of the mathematical nature of the planetary disturbing function (yes, it is actually called "The Disturbing Function" in celestial mechanics literature) which, upsettingly, suggests that these so-called high-order resonances become increasingly important when dealing with eccentric planets like Planet Nine, and the results of computer simulations presented in this work confirm this. In summary, because Planet Nine is eccentric, it carries out very complicated dance moves with the KBOs. </span></div>
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<span class="" style="-webkit-font-kerning: none;">It's worth mentioning that the simulations used to make this figure were simplified in comparison to reality. The canonical giant planets Jupiter through Neptune were treated as a static ring of mass (this is often referred to as the “secular” approximation), and the solar system is treated as a flat 2-dimensional object even though Planet Nine is, in reality, inclined. Think of it as a best-case scenario of sorts: in this physical setup, Planet Nine is the only active perturber of the KBOs. In the real solar system, Neptune is also on the dance floor, behaving in a very disruptive fashion. When KBOs get too close to Neptune, it flings them around. Sometimes those KBOs resume dancing with Planet Nine, but other times they just head out the door into interstellar space. </span></div>
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<span class="" style="-webkit-font-kerning: none;">Suppose, despite these complications, you could determine which individual KBOs are indeed in mean motion resonances with Planet Nine at this time. Then, if this information were to be of any use, you would then need to know the specific resonance of each KBO. In 3-D simulations, there is no obvious concentration of objects at particular resonances (see figure below). Hence, no matter how long we wait for more KBOs to be observed, we have virtually no hope of using resonances to predict Planet Nine's current location along its orbit. </span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgH9sTiFtseTWOzEfTLd9ykdt8wCl6CxoN1v3iEt5ef-ISKD9j5LwNOOKphvHTAS2h8-3eJNf0hFK9DmbhlaVBuRrO7TiZUp_ELxIUnMPku5_b9y2m3Y6D3dIf0tz7_rxqN2t0cNTMdACk/s1600/F2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="468" data-original-width="636" height="293" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgH9sTiFtseTWOzEfTLd9ykdt8wCl6CxoN1v3iEt5ef-ISKD9j5LwNOOKphvHTAS2h8-3eJNf0hFK9DmbhlaVBuRrO7TiZUp_ELxIUnMPku5_b9y2m3Y6D3dIf0tz7_rxqN2t0cNTMdACk/s400/F2.png" width="400" /></a></div>
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<span class="" style="-webkit-font-kerning: none;">Although based on the results of this work it does not appear feasible to predict the present-day location of Planet Nine along its orbit, this does not by any means imply that Planet Nine is invisible to telescopes. There is still a well-defined swath of sky in which the search for Planet Nine continues. We have merely shown that mean-motion resonances with KBOs are not a useful tool for deciding where point the telescope, so we're back to systematically scanning the sky. Turns out that even in astronomy, the easy way is the hard way.</span></div>
Konstantinhttp://www.blogger.com/profile/14245543234165152508noreply@blogger.com71tag:blogger.com,1999:blog-1052332993988376053.post-82249182246526453992018-05-07T13:57:00.000-07:002018-05-07T13:57:49.103-07:00Planet Nine makes some KBOs go wild<div dir="ltr" style="text-align: left;" trbidi="on">
Hi, everyone! I’m Tali, an undergrad at the University of Michigan. Last summer, I worked on a Planet Nine project with Konstantin and Mike, and although we didn’t find Planet Nine (yet!), we did look further into the stability of objects in the presence of Planet Nine. Turns out, not everything is stable!
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In his <a href="http://www.findplanetnine.com/2017/10/theory.html" style="text-decoration: none;">last post</a>, Konstantin explained that the main cluster of anti-aligned objects is able to remain stable due to mean motion resonances with Planet Nine. Their orbits always cross Planet Nine’s orbit, but such resonances allow the objects to avoid collisions. Here’s an example of what the dynamics looks like: the green orbit is Planet Nine, and pink orbit is an anti-aligned Kuiper belt object. The little blue circle is Neptune’s orbit, and the star is the Sun (not to scale).</div>
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<img height="267" src="https://lh4.googleusercontent.com/0vWh3rttxPEhiBch1VyBdej95uamWVXnzi70q9NkOZ4EIVWHwb1Rh_hS4IT3jNgnvCQ3nB0DG7a71kt05-sQ9lc-4VnDu0z8nYbigGHGAGwC8dr6sfWFy8Ilhq6YsxrVZAj0qgVh" style="border: medium none; transform: rotate(0rad);" width="329" /></div>
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What we see here is that the anti-aligned object experiences librations (=bounded oscillations) in the direction its orbit points (the longitude of perihelion). Meanwhile, Planet Nine’s orbit slowly precesses and changes direction as well.</div>
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BUT, it turns out that being in resonance with Planet Nine is not enough for stability. That’s because Neptune is still in the picture. Let’s look back at the animation above. Notice that as the pink orbits wags back and forth, its perihelion distance (=the shortest distance from the orbit to the Sun) changes. The pink orbit stretches (and hugs Neptune’s orbit) and then circularizes (and detaches from Neptune). The wider the “wagging the tail” oscillations are, the more pronounced the in and out behavior becomes. If the object librates with too large of an amplitude, it comes suuuuuper close to Neptune. And when that happens, it either gets ejected from the solar system or its dynamics changes entirely, and its behavior is no longer relevant to Planet Nine.</div>
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SO, the stability of the anti-aligned objects can be summarized by the two gifs below. When the longitude of perihelion libration (tail-wagging) is mild, our object experiences small changes in perihelion distance, and thus remains at a safe distance from the inner solar system. But, if the librations become too wide (and too wild), the object goes unstable, thanks to Neptune.</div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><img height="400" src="https://lh3.googleusercontent.com/NthGP6PtOBE6_5J_qpl6r56ySAd2d3ndsbiU36OASpxajH3pzn_Yoxst-rhwIQ0kw1agWyZuSp3olib7wuS1MNy1e3mbJieSNkIfcsnSE2jKXsCWYCyzPsH2ClXVb83bV6p5PeZS" style="border: medium none; margin-left: auto; margin-right: auto; transform: rotate(0rad);" width="372" /></td></tr>
<tr><td class="tr-caption" style="text-align: center;">STABLE LIBRATIONS</td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: right;"><tbody>
<tr><td style="text-align: center;"><img height="261" src="https://lh5.googleusercontent.com/-xzl_2Lb9Owpx5F4BUFVOgz6Xya8uIE-a0l1vXfcAKL9TFanW0nCRYQ9e3AdFpJSZ1jhNdB-nJir_PO0CIJQPZE7sAJJJP1GUwBD2BEHB_G0RUhFouPKvqdUK0PD9gG9maGVpxgX" style="border: medium none; margin-left: auto; margin-right: auto; transform: rotate(0rad);" width="351" /></td></tr>
<tr><td class="tr-caption" style="text-align: center;">UNSTABLE BEHAVIOUR</td></tr>
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Now, the anti-aligned population is not the only one we looked at. Planet Nine carves out an aligned cluster of objects as well, which experience librations in longitude of perihelion, but this time, inside the orbit of Planet Nine:</div>
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<img height="285" src="https://lh6.googleusercontent.com/Pnf56KrRtgNBw_UPB6cAGDSUirCGNBdlC63inXnJAbth8XF_sZezcjeoR6b9wNB4wGkFUy89fPKptjsYt-G7xiie08-6doDhvQI2TxO_-zg3WBxggpBfrDGBU9boV1VG1rg-BrAK" style="border: medium none; transform: rotate(0rad);" width="310" /></div>
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As you can see this object is in the perfect stable location - it stays far away from Neptune (blue) AND doesn’t cross Planet Nine’s orbit, and just quietly librates in longitude of perihelion. This object is all set for life. Nothing will make it budge from this configuration.</div>
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BUT, there are objects that seem to be aligned at first, but suffer because their libration amplitudes are too large. Here’s an example of such an object:</div>
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<img height="281" src="https://lh3.googleusercontent.com/94CsNBwohxJrbKx-XOycUXx4eC0CV_CvRxuGSLJI27le2yAIQyI_4PaS0y8fthHifbGbcpluUK73cC8M8WbVdspLQqb2Qz7rEarlZ2sreKOA8k2SSd_phUOUiD9NNaTIAhYx83WH" style="-webkit-transform: rotate(0.00rad); border: none; transform: rotate(0.00rad);" width="288" /></div>
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In the animation above, the orbit spins too far and crosses Planet Nine’s orbit. This is not good for two reasons: (i) Planet Nine starts having collisions with this object and knocking it about, and, (ii) UNLESS the object is in a resonance with Planet Nine, it gets swept by Planet Nine into the Neptune scattering region. If you look at the animation carefully after the pink orbit crosses the green orbit, you’ll see that the perihelion distance of the object is slowwwly decreasing. When it gets small enough - when the object starts interacting strongly with Neptune - we get the same output as for the unstable anti-aligned objects (i.e. instability and a crazy jumping dog.)</div>
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So, what’s the bottom line? Not all anti-aligned objects are stable! And not all aligned objects are stable. And it all depends on their perihelion distance, which is closely tied with their librations in longitude of perihelion.</div>
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Moreover, it turns out that what kind of objects we find surviving through the end of our simulations depends on the initial conditions we put in. What do I mean by initial conditions? Well, for example, we expect that different scenarios of <a href="http://www.findplanetnine.com/2016/08/origins.html" style="text-decoration: none;">Planet Nine’s formation</a> would have affected the initial configuration of the Kuiper belt in different ways. So, suppose we start with two different initial conditions: a “narrow” Kuiper belt (objects initially within a narrow interval of perihelion distances) and a more widely spread “broad” Kuiper belt. And now we integrate these populations forward, in the presence of Planet Nine, in two separate simulations. Do these populations end up creating the same Kuiper belt?</div>
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In our recently accepted paper, we find that they don’t! In fact, the stable aligned population discussed above is completely missing from the “narrow” Kuiper belt. So, as the astronomy community continues to find more and more of these distant Kuiper belt objects, we might be able to start to tell which initial Kuiper belt we started with, and maybe how Planet Nine formed… </div>
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<a href="https://arxiv.org/pdf/1804.11281.pdf" style="text-decoration: none;">Read our paper here</a> to find out more about Planet Nine, initial conditions, and stability!</div>
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Unknownnoreply@blogger.com69tag:blogger.com,1999:blog-1052332993988376053.post-4373350367617362272017-10-10T19:56:00.000-07:002017-10-10T20:02:08.810-07:00Theory<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Helvetica Neue"; font-size: 11px; font-stretch: normal; line-height: normal;">
<span style="font-kerning: none;">Every die-hard fan of the scientific method knows that <a href="https://en.wikipedia.org/wiki/Karl_Popper" target="_blank">Karl Popper</a> was a baller. While his achievements clearly extend far beyond analysis of the scientific method alone, he is arguably best known for his work on <a href="https://en.wikipedia.org/wiki/Falsifiability" target="_blank">empirical falsification</a>. In essence, the idea behind his argument is that a theory is only any good if there exists a direct and clear experimental/observational way to demonstrate that it is incorrect. In other words, it is more important to point out avenues in which your theory can be wrong than to flaunt all the possible ways it could be right.</span></div>
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<span style="font-kerning: none;">Why am I writing about this? Mike and I just spent a week at 14,000ft on the Big Island directly searching for Planet Nine, and I’ve been thinking a lot about how Popper’s falsifiability criteria apply to the Planet Nine hypothesis… Obviously, if we search the entire sky at sufficient depth and don’t find Planet Nine, then we are plainly wrong. But I don’t think this is going to happen. Instead, I think we (or some other group) are going to detect Planet Nine on a timescale considerably shorter than a decade - maybe even this year if we/they get lucky. Which begs the question: if a planet beyond Neptune is found, how would we proceed to determine that the Planet Nine theory is actually right?</span></div>
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<span style="font-kerning: none;">Figure 1. Mike and I at the telescope - where colors don't exist.</span></div>
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<span style="font-kerning: none;">I’m sure this question sounds incredibly stupid, so let me back up a bit. The <a href="https://arxiv.org/pdf/1601.05438.pdf" target="_blank">Batygin & Brown 2016 AJ paper</a> is by no means the first to predict a trans-Neptunian planet with a semi-major axis of a few hundred astronomical units. That accolade goes to <a href="https://en.wikipedia.org/wiki/George_Forbes_(scientist)" target="_blank">George Forbes</a>, who in 1880 proposed a planet located at ~300AU, based upon an analysis of the clustering of the aphelion distances of periodic comets (sound familiar?). Since then, a trans-Neptunian planet has been re-proposed <a href="http://www.nature.com/nature/journal/v507/n7493/full/nature13156.html?foxtrotcallback=true" target="_blank">over</a> and <a href="https://arxiv.org/pdf/1704.02444v2.pdf" target="_blank">over</a> again, which brings us to problem at hand: whose trans-Neptunian planet theory is right and whose is wrong?</span></div>
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<span style="font-kerning: none;">In my view, there is a very clear and intelligible way to answer this question. Each proposition of a trans-Neptunian planet is uniquely defined by (i) the data it aims to explain and (ii) the dynamical mechanism that sculpts the observations. So in order to be deemed correct, the discovered planet must match both of these specifications of the theorized planet.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3y6HGXlTrwWh4ipyDyKEncBHDzlc4wenxONTjod0xHFnIe5Qj7gzoNLbdSkprPAhJrPqlH9jVBWHLzjf0ICNQZKKvM2dvetKwTmDwlIJKRKTJ0Shj3ytzraPxG4Jp3hz7lqHTD9iG1eQ/s1600/Screen+Shot+2017-10-10+at+6.53.12+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="778" data-original-width="956" height="260" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3y6HGXlTrwWh4ipyDyKEncBHDzlc4wenxONTjod0xHFnIe5Qj7gzoNLbdSkprPAhJrPqlH9jVBWHLzjf0ICNQZKKvM2dvetKwTmDwlIJKRKTJ0Shj3ytzraPxG4Jp3hz7lqHTD9iG1eQ/s320/Screen+Shot+2017-10-10+at+6.53.12+PM.png" width="320" /></a></div>
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<span style="font-kerning: none;">Figure 2. The current observational census of distant KBOs.</span></div>
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<span style="font-kerning: none;">When it comes to the Planet Nine hypothesis, point (i) is well-established: Planet Nine is invoked to explain (1) physical clustering of distant Kuiper belt orbits, (2) the perihelion detachment of long-period KBOs such as Sedna and VP113, as well as (3) the origin of nearly-perpendicular orbits of centaurs in the solar system. Embarrassingly, until recently our understanding of the “machinery” behind how Planet Nine generates these observational signatures has been incomplete. That is, although we have plenty of numerical <i>experiments</i> to demonstrate that Planet Nine can nicely reproduce the observed solar system, the <i>theory</i> that underlies these simulations has remained largely elusive.</span></div>
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<span style="font-kerning: none;">The good news is that this is no longer a problem. In a recently accepted <a href="https://arxiv.org/pdf/1710.01804.pdf" target="_blank">paper</a> that I co-authored with <a href="https://www-n.oca.eu/morby/" target="_blank">Alessandro “Morby” Morbidelli</a>, the theory of Planet Nine is characterized from semi-analytical grounds. So, for the first time, we not only know what Planet Nine does to the distant Kuiper belt, but we understand <i>how</i> it does it.</span></div>
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<span style="font-kerning: none;">The first lingering question that Morby and I tackled is that of stability: how do the distant Kuiper belt objects avoid being thrown out of the solar system by close encounters with Planet Nine, when their orbits intersect? Turns out, the answer lies in an orbital clockwork mechanism known as <i><a href="https://en.wikipedia.org/wiki/Orbital_resonance" target="_blank">mean motion resonance</a></i> (MMR). When a Kuiper belt object is locked into an MMR with Planet Nine, it completes an integer number of orbits per (some other) integer number of orbits of Planet Nine. This strict rationality of the orbital periods allows the bodies to exchange orbital energy in a coherent fashion, and ultimately avoid collisions.</span></div>
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<span style="font-kerning: none;">But how do such configurations arise in nature? Remarkably, the answer in this case is “by chance.” When the Kuiper belt first formed, a staggering number (roughly 30 Earth masses worth) of small, icy asteroid-like bodies were thrown out into the distant realm of the solar system by Neptune (for the interested reader, see papers about the Nice model <a href="https://arxiv.org/pdf/0712.0553.pdf" target="_blank">here</a> and <a href="https://arxiv.org/pdf/1111.3682.pdf" target="_blank">here</a>). Most of these objects were not fortunate enough to accidentally land into mean motion resonances with Planet Nine and were ejected from the solar system. However, the few that were, survive in the distant Kuiper belt to this day, and comprise the anti-aligned cluster of orbits that we observe. As a demonstration of this point, check out the simulated orbital period distribution of surviving Kuiper belt objects in one of our idealized simulations, and note that all distant bodies have rational orbital periods with that of Planet Nine:</span></div>
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<span style="font-kerning: none;">Figure 3. Orbital distribution of long-term stable KBOs in an idealized P9 simulation.</span></div>
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<span style="font-kerning: none;">All of this said, the full picture is of course not as clear-cut. Within the context of our most realistic calculations of distant Kuiper belt evolution, the clustered KBOs chaotically hop between resonances, instead of staying put. Still, the qualitative framework provided by analysis of isolated resonances holds well, even in our most computationally expensive simulations.</span></div>
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<span style="font-kerning: none;">Ok so this resolves the question of how Kuiper belt objects survive, but it leaves open the question of why their orbits are clustered together. Intriguingly, a qualitatively different dynamical mechanism - known as <i>secular</i> interactions (see <a href="https://arxiv.org/pdf/0811.2812.pdf" target="_blank">here</a> for a neat discussion) - is responsible for the orbital confinement that we see. Plainly speaking, over exceedingly long periods of time (e.g. hundreds of orbits), Planet Nine and the Kuiper belt objects it perturbs will see each-other in almost every possible configuration along their respective orbits. Thus, their long-term evolution behaves as if the mass of Planet Nine has been smeared over its orbital trajectory, and its gravitational field torques the elliptical orbit of the test particle. The plot below shows the eccentricity-longitude of perihelion portrait of this secular dynamic inside the 3:2 mean motion resonance, where the background color scale and contours have been computed analytically and the orange curve represents a trajectory drawn from a numerical simulation. </span></div>
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<span style="font-kerning: none;">Figure 4. Eccentricity-perihelion diagram showing the secular trajectories of stable KBOs trapped in a 3:2 MMR with P9.</span></div>
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<span style="font-kerning: none;">Indeed, the fact that the semi-analytic theory predicts looped trajectories that cluster around a P9 longitude of perihelion offset of 180 degrees implies that the raising of perihelion distances (i.e. lowering of eccentricities) of long-period KBOs and anti-aligned orbital confinement are actually the same dynamical effect. In other words, the reason that objects such as Sedna and VP113 have orbits that are not attached to Neptune is because they are entrained in the peculiar anti-aligned secular dynamic with Planet Nine. </span></div>
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<span style="font-kerning: none;">Finally, there is the puzzle of the highly inclined orbits. Whenever one sees cycling of orbital inclination and eccentricity, there is a temptation to invoke the <a href="https://en.wikipedia.org/wiki/Kozai_mechanism" target="_blank">Kozai-Lidov</a> mechanism as the answer. In the case of Planet Nine, however, the high-inclination dynamics are keenly distinct from those facilitated by the Kozai-Lidov effect. Perhaps the most obvious reason why the dynamics we observe in numerical simulations is not the Kozai-Lidov effect is that in our calculations, highly inclined KBOs develop the highest eccentricities when their orbits are perpendicular to the plane of Planet Nine’s orbit, in direct contrast with perpendicular and circular orbits entailed by the Kozai-Lidov effect. </span></div>
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<span style="font-kerning: none;">So if it’s not the Kozai-Lidov resonance, then what is it? As it turns out, the high-inclination dynamics induced by Planet Nine is characterized by the bounded oscillation of a octupole-order secular angle which is equal to the difference between the longitude of perihelion of the KBO relative to that of Planet Nine and twice the KBO argument of perihelion. How could we have ever thought it was anything else?… The plot below shows the high-inclination secular resonant trajectories executed by test-particles in our simulation plotted in canonical action-angle coordinates, with the observed objects shown in orange. Examining this plot closely, one detail that I’m reminded of is the fact that the few high-inclination large semi-major axis centaurs that we know of are actually the “freaks” of the overall population, since they all have perihelia on the order of ~10AU. Certainly, detecting a sample of these objects with perihelia well beyond 30AU would be immensely useful to further constraining the parameters of the model.</span></div>
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Figure 5. High-inclination dynamics, depicted in action-angle variables.</div>
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<span style="font-kerning: none;">With the above rambling in mind, I will admit that all I’ve mentioned here is an introductory account of the paper. As such, it represents a considerable simplification of our actual calculations, so if you want to better understand the full picture, I can only urge you to read the <a href="https://arxiv.org/pdf/1710.01804.pdf" target="_blank">paper itself</a>. Importantly, however, the work presented in this manuscript not only provides us with a better understanding of how the observed census of distant KBOs has been sculpted by Planet Nine, it finally places the P9 hypothesis within the framework of Popper’s demand for falsifiability, and sincerely allows for the confrontation of the Planet Nine theory with the observational search. The final step is now to find it.</span></div>
Konstantinhttp://www.blogger.com/profile/14245543234165152508noreply@blogger.com237tag:blogger.com,1999:blog-1052332993988376053.post-66315750020954393312017-09-21T10:15:00.000-07:002017-09-21T13:14:20.572-07:00Planet Nine: where are you? (part 1)<div dir="ltr" style="text-align: left;" trbidi="on">
We haven’t found Planet Nine yet, in case you were
wondering. To date, the telescopic searches have really just begun to scratch the
surface of the area that needs to be scanned, and, while clever new projects to
find Planet Nine with different techniques have been proposed, most of these
efforts are just getting underway. But don’t worry: the new season of Subaru searching starts tonight! With
good weather, we should be able to scan a significant part of our search
area. Stay tuned.<br />
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To get ready for this new season of searching for Planet Nine, we have spent most of the last year developing our understanding of the way that Planet Nine interacts with the rest of the solar system. Much of this has involved large amounts of analytic and computational work to figure out what the orbit
of Planet Nine looks like and where in its orbit Planet Nine is. If we could
figure that out perfectly, we could simply go out tonight and point our
telescopes right at it, as was done for the discovery of Neptune in 1846.
Sadly, we have less information on Planet Nine than Le Verrier did for Neptune
in 1846, so we’re not able to pinpoint it just yet, but we are able to
constrain what the orbit looks like and, thus, where we should look.
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I suspect that most people don’t really care to know the
details of how we’re trying to figure out where Planet Nine is. But one group
cares a lot: the other astronomers actively looking for Planet Nine. Since our
first prediction of the existence of Planet Nine, we’ve tried hard to keep
anyone who wanted to know up to date on where we think the best places to
search are. The more people who are involved in looking in the more different
ways, the more quickly Planet Nine will be detected, so part of our work of
trying to figure out the orbit of Planet Nine is for the sake of all of these
other groups.</div>
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To understand where we think Planet Nine might be right now,
we need a long digression on orbits (if you’re intimately familiar with
Keplerian orbital elements or simply don’t want to know, please skip ahead!).
All objects in the solar system travel on elliptical paths around the sun, with
the sun at one of the foci of the ellipse. If you’re on the Earth looking at the
sky, however, the path of the orbit doesn’t look like an ellipse, it simply
looks like a great circle across the sky with you at the center (on Earth, a
great circle is like a line of longitude, or like the equator; lines of
latitude that are not the equator are not great circles; it works the same in
the sky). If I want to describe the orbital <i style="mso-bidi-font-style: normal;">path</i>
of Planet Nine, then, I need to tell you where this great circle is. To describe
any great circle, you only need to know two numbers. There are many different
ways to define these two numbers, but we will use (1) the longitude where the
great circle crosses the equator (which on the sky we just define to be the
extension of the Earth’s equator) when it crosses from south to north (all
great circles cross the equator twice 180 degrees apart, so we had best specify
which of the two we mean), and (2) the angle that the orbit makes with respect
to the equator when it crosses the equator. In celestial mechanics, these two
numbers are called the longitude of the ascending node (ascending =
south-to-north; get it?) and the inclination. If we knew these two numbers
perfectly we would know the exact path that Planet Nine takes across the sky. (The
motion of the Earth complicates things a little, but because Planet Nine is so
far away we can mostly ignore those details.) If we wanted to point a telescope
directly at Planet Nine, all we would need to know are the <b style="mso-bidi-font-weight: normal;">longitude of ascending node</b> (which I’ll just call “node” from now
own), the <b style="mso-bidi-font-weight: normal;">inclination</b>, and (3) where
within the orbit the planet is. We’ll call this last parameter the <b style="mso-bidi-font-weight: normal;">orbital longitude</b> and simply define it
as the longitude in the sky where the object is (this definition is not the norm
of celestial mechanics, where instead you’ll get mean anomaly or eccentric
anomaly or other more complicated things; we’ll stick with this easier to
understand version).<br />
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While the first three parameters tell the path across the
sky and where the object is, they don’t tell you anything about the shape of
the orbit or how far away the planet is (which we care about because that helps
us estimate how bright it should be and whether or not it should have already
been spotted in parts of its orbit). We know that Planet Nine goes in an
ellipse around the sun. The shape of the ellipse is completely specified by (4)
knowing the average distance of the object from the sun and by (5) a number
from 0 to 1 which defines how elongated the object is (zero means it is a
circle, 1 means it is so elongated that it never closes back in on itself). We
call these <b style="mso-bidi-font-weight: normal;">semimajor axis</b> and <b style="mso-bidi-font-weight: normal;">eccentricity</b>.<br />
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You need one last number. While we now know the shape of the
orbit and the orbital plane, we are still don’t know how the orbit is oriented
within its plane. We can specify that by (6) determining the longitude when the
orbit comes the closest to the sun. We call this last parameter the <b style="mso-bidi-font-weight: normal;">longitude of perihelion</b> (this is a bit
of a simplification, but an unimportant one). The figure below illustrates what
it means to keep (1)-(5) fixed and only change the longitude of perihelion. The
shape and orbital plane of the planet are fixed, and we are simply spinning the
orbit around on its axis.<br />
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<i>(If you skipped the details about Keplerian orbital elements,
come back now!)</i></div>
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Those are a lot of things to learn if we want to find Planet
Nine. Here’s how we’re making progress.</div>
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The easiest orbital parameter for us to extract is the
longitude of perihelion of Planet Nine. Why? Because the main observable effect
of Planet Nine is to capture distant eccentric Kuiper belt objects into orbits
which are what we call anti-aligned with Planet Nine (see the illustration at
the top of the page!). “Anti-aligned” means, precisely, that the longitude of
perihelion of the Kuiper belt objects is (on average) 180 degrees away from
that of Planet Nine. We now know of about 10 of these anti-aligned objects, so
can look at their longitudes of perihelion and get a direct estimate of the
longitude of perihelion of Planet Nine (if you care about the details: we
actually exclude<span style="mso-spacerun: yes;"> </span>the two most recently
detected objects as they came from the OSSOS survey which has been shown to
have <a href="https://arxiv.org/abs/1706.05348" target="_blank">striking biases</a> in the objects that it finds). When we do this, we find a
value of 235 with an uncertainty of 12 degrees. This is a great start, but we
have 5 more parameters to go (and longitude of perihelion doesn’t actual help
tell us the orbital path through the sky).<br />
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In our <a href="https://arxiv.org/abs/1603.05712" target="_blank">second paper about a year ago</a>, we used a suite of
computer simulations to see how Planet Nine would affect eccentric objects in
the Kuiper belt if we varied all of the other parameters. We found some key
results. If Planet Nine comes too close it tears up the Kuiper belt. If it
stays too far away it does too little. If Planet Nine is too inclined it has
only a small effect. Those constraints help on everything except for the node
of Planet Nine and the actual longitude of Planet Nine. Without the node,
though, we really have no constraint on the orbital path at all! We made some
estimates by using a different quantity, but those estimates were the least satisfying
part of the analysis. Nonetheless, those led to our best estimates of where to
look, and the picture that you have all seen here.</div>
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<br /></div>
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Since that last paper, though, we have learned a lot more
about the physics of how the gravity of Planet Nine affects the orbits of
distant objects in the Kuiper belt. Luckily, one of the things we now
understand much better is how to constrain the node of Planet Nine.<span style="mso-spacerun: yes;"> </span>Early on, we recognized that all of the
distant eccentric Kuiper belt objects had similar longitudes of ascending node,
and it seemed clear that these must be related to that of Planet Nine somehow.
With some even more realistic follow-on computer simulations we realized that
what we had surmised was right: the distant eccentric Kuiper belt objects have
the same average node as Planet Nine. Planet Nine partially pulls these distant
objects into its own orbital plane. But only partially. The distant objects, on
average, do not have the same inclination as Planet Nine. The distant objects
live in an average orbital plane that is close to midway between that of the 8
other planets and Planet Nine. Though this result is simple to state, a lot of
work (or perhaps a lot of electricity for computers) went in to that statement!
And the good news is that can now estimate the node much more precisely. If we
take those same eccentric distant Kuiper belt objects and look at their nodes,
we find that Planet Nine has a longitude of ascending node of ~94 degrees. The
average inclination of those objects, by the way, is 18 degrees, so we know
that the inclination of Planet Nine is higher than this, but not much higher,
because otherwise, as we found earlier, it doesn’t make an anti-aligned
population.<br />
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I know, I know, saying that we now know the longitude of
ascending node of Planet Nine does not sound exciting to most people. But we
have reduced the uncertainty on this parameter by a factor of 5, which is
essentially as good as having done a search of 80% of the relevant sky! OK.
Sort of.</div>
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Now, if you’ve been paying close attention, you know what I
want to know next. We only have general constraints on the inclination of
Planet Nine, and we have no real constraints on the longitude. How are we going
to find those? I think the solution is doing the same sorts of computer
simulations but sort of in reverse. We have been doing new computer simulations
where we take the ~20 known objects whose orbits are thought to be affected by
Planet Nine and we have put them into their current positions in the solar
system today. We then put a Planet Nine in and watch what happens. Sometimes
the simulated Planet Nine sends everything flying. Sometimes after a billion
years the solar system looks close to the same as it does today. We learn
general things: large inclinations are bad, having Planet Nine too far away
doesn’t make a powerful enough effect. How exactly to balance these constraints
is not yet obvious, but through about a 100 trillion cumulative years of
simulating the real objects in the outer solar system I think we’re getting
close.<br />
<br /></div>
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In my perfect fantasy world these latest simulations will
tell us more or less where Planet Nine is and we will simply go look and it
will be there as Neptune was. Probably that is asking too much of reality. But
we’re going to give it a try. In the mean time, we are slowly narrowing down the region of the sky in which we need to search. If you're looking for Planet Nine, go look there!</div>
</div>
Unknownnoreply@blogger.com277tag:blogger.com,1999:blog-1052332993988376053.post-30647816902226031052017-07-02T10:39:00.002-07:002017-07-03T09:08:51.429-07:00Status Update (Part 2)<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: Helvetica; font-size: 11px; line-height: normal;">
<span style="font-kerning: none;">I ended the last post by pointing out that the Planet Nine hypothesis, as currently formulated, entails a theoretical solution to five seemingly-unrelated observational puzzles: (i) orbital clustering of a>250AU KBOs, (ii) dynamical detachment of KBO perihelia from Neptune, (iii) generation of perpendicular large-semi-major axis centaurs, (iv) the six-degree obliquity of the sun, and (v) pollution of the more proximate Kuiper belt by retrograde orbits. Virtually all of the discussion surrounding the new OSSOS dataset to date has focused on long-period orbits and the statistical significance of perihelion clustering beyond ~250AU - a concern relevant exclusively to point (i). Breaking with this trend, in this post I want to examine a shorter-period component of the new data, and discuss how it relates to arguably the most unexpected consequence of P9-driven evolution: generation of retrograde orbits with semi-major axes smaller than ~100AU (i.e. aforementioned point (v)).</span></div>
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<span style="font-kerning: none;">Those of you who have been following the P9 saga for more than a year might remember the article by <a href="https://arxiv.org/pdf/1608.01808.pdf"><span id="goog_2108570534"></span>Chen et al.<span id="goog_2108570535"></span></a> from last August, which reported the detection of <i>Niku</i>, a ‘rebellious’ Kuiper belt object that orbits the sun in the retrograde direction (see news coverage <a href="http://www.popularmechanics.com/space/deep-space/a22293/niku-weird-object-beyond-neptune/" target="_blank">here</a> and <a href="https://www.space.com/34479-niku-weird-objects-orbit-puzzles-scientists.html" target="_blank">here</a>). While the orbit of Niku itself is in some sense unremarkable (because it is acutely similar to the orbit of Drac - another retrograde object that was <a href="http://iopscience.iop.org/article/10.1088/0004-637X/697/2/L91/pdf" target="_blank">detected</a> back in 2008), this discovery did successfully reinvigorate the community’s interest in the high-inclination population of the trans-Neptunian region. </span></div>
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<span style="font-kerning: none;">Here is a look at all objects within the current dataset with inclinations greater than 60 degrees, semi-major axes in the range of 30AU to 100AU, and perihelion distance in excess of Jupiter’s orbit:</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBtohOv7JQzj-hVTBdwVMaOC1Whd4Ww-MR1YR3kFs6nnM7r5IaTvvBxtnrd6J-klSplxQeLcrO_rfg4NOdb6CqaMHglGWIDGYj6pMU5M8MbNPxfbN0HyYRS1IXr7eiV5wBnEzzWI1PxX8/s1600/Screen+Shot+2017-07-02+at+7.00.11+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1154" data-original-width="1322" height="348" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBtohOv7JQzj-hVTBdwVMaOC1Whd4Ww-MR1YR3kFs6nnM7r5IaTvvBxtnrd6J-klSplxQeLcrO_rfg4NOdb6CqaMHglGWIDGYj6pMU5M8MbNPxfbN0HyYRS1IXr7eiV5wBnEzzWI1PxX8/s400/Screen+Shot+2017-07-02+at+7.00.11+AM.png" width="400" /></a></div>
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<span style="font-kerning: none;">For scale, Neptune’s orbit is shown here as a blue circle, and the orbits of Niku and Drac are emphasized in gray. Generally speaking, these bodies trace out an apparently-random orbital structure and raise an important question regarding the physics of their origins, since none of them can be reproduced by conventional simulations of the <a href="http://iopscience.iop.org/article/10.1088/0004-6256/150/3/73/pdf" target="_blank">solar system’s early evolution</a>.</span></div>
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<span style="font-kerning: none;">Unlike objects such as Sedna and 2012 VP113, Niku and Drac are currently quite close to Neptune itself, and have semi-major axes that are much too small to interact with Planet Nine directly. Nevertheless, in a <a href="https://arxiv.org/pdf/1610.04992.pdf" target="_blank">paper</a> published last October, we showed that Planet Nine naturally leads to their production. The crux of our result is that the current orbits of these bodies are very different from their primordial ones. Specifically, in our simulations we noticed that Kozai-Lidov type oscillations experienced by distant Kuiper belt objects due to Planet Nine can drive them onto highly inclined, Neptune crossing orbits. Subsequently, close encounters with Neptune shrink the orbit, freezing it onto a retrograde state. <a href="https://twitter.com/marksubbarao" target="_blank">Mark Subbarao</a> from Adler Planetarium has kindly created this visualization of one of our simulated particles, that ends up on an orbit that is almost an exact replica of Niku and Drag (grab the video <a href="https://caltech.box.com/s/zvi1m8tj6uarnenft9p6gvv9xs35cmjb" target="_blank">here</a> if the player below does not work):</span></div>
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dyABtmOTQiNS2xQWO0BpLERj4_QIS0x5sHlhauDiXxWpdtyjyFoz0bUUdwHZfkvncq4OXtm50B5TYk0KBY6wg' class='b-hbp-video b-uploaded' frameborder='0'></iframe><br />
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<span style="font-kerning: none;">Despite a rather complicated and genuinely chaotic evolution, our P9-facilitated generation mechanism of these objects predicts a rather specific orbital distribution in (semi major axis a) - (inclination i) - (perihelion distance q) space. This prediction is shown below as a background green/gray grid, with observed data over-plotted as purple/black points.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQKam5CSGg16v33Y9Pedcy8PaklIMxqIX3rZu1i9284aGhZ5YCoYVvHxUPFQyrajmBlWilgWBpbjgyjaPU8mGJ39DZWuFI-VJ5kJoyX9isHFiriS_FbvUcvWOoIWdmXIP-T6IGChTQTJo/s1600/Screen+Shot+2017-07-01+at+2.21.23+PM.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="765" data-original-width="1600" height="305" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQKam5CSGg16v33Y9Pedcy8PaklIMxqIX3rZu1i9284aGhZ5YCoYVvHxUPFQyrajmBlWilgWBpbjgyjaPU8mGJ39DZWuFI-VJ5kJoyX9isHFiriS_FbvUcvWOoIWdmXIP-T6IGChTQTJo/s640/Screen+Shot+2017-07-01+at+2.21.23+PM.png" width="640" /></a></div>
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<span style="-webkit-text-stroke-width: initial;">In addition to the observed objects that were already known back in October of last year, this plot shows two new data points that also fit the simulated pattern beautifully. Thus, the predictions of the Planet Nine hypothesis have held up very well within the more proximate part of the trans-Neptunian region, where the planet’s direct influence is minimal. </span><span style="font-kerning: none;"></span></div>
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<span style="font-kerning: none;">So where does the new data leave us? Let’s summarize: while the membership of the primary perihelion cluster has gone from six to ten, the distant belt now also has some objects that do not belong to the apsidally anti-aligned population of long-period KBOs. Despite worries of Planet Nine’s immediate demise, it is pretty clear that these bodies fit well with other dynamical classes predicted by the model, so there’s no real conflict there. Closer to Neptune, we’ve picked up a couple high-inclination objects that also agree well with the model. Sigh…</span></div>
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<span style="font-kerning: none;">Cumulatively, I can’t help but feel an uneasy combination of relief and disappointment. On one hand, the agreement between simulations and data implies that the theoretical model remains on solid footing. As we head into upcoming P9 observing season, this is important and reassuring. On the other hand, we haven’t learned anything genuinely new from the expanded dataset, and P9’s precise location on its orbit as well as a well-founded qualitative description of P9-induced dynamics remain somewhat elusive. Clearly, much work - both theoretical and observational - remains to be done. So back to research.</span></div>
Konstantinhttp://www.blogger.com/profile/14245543234165152508noreply@blogger.com225tag:blogger.com,1999:blog-1052332993988376053.post-67188604279808261532017-06-30T18:28:00.001-07:002017-06-30T18:32:33.473-07:00Status Update (Part 1)<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: 'Helvetica Neue'; font-size: 12px; line-height: normal;">
<span style="font-kerning: none;">It has been an exciting and turbulent couple of weeks in Planet Nine land. The OSSOS survey has released their full data set, which in addition to over 800 garden-variety Kuiper belt objects, contains four little worlds with semi-major axes beyond 250AU. Together with the previously published data, this brings the count of distant bodies relevant to the P9 hypothesis up to 13 - a whopping 117% increase in the census of long-period KBOs, compared with what we had back in early 2016.</span></div>
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<span style="font-kerning: none;">When viewed from above, the orbits of the objects look like this:</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiCwTBIwKVtOPX0GOcIwjuMwCcUNZiTZHhYN3IvBga9Oqo05CJPSOSQf5EJTm8nw2n1F2GTqBYbnOKR-MpdYKp8oUpSuEuhTARW-oCJKCzolDju_4742KlVDzJLde10_nD5GWoocbmDhE/s1600/Screen+Shot+2017-06-29+at+11.51.31+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="782" data-original-width="998" height="312" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiCwTBIwKVtOPX0GOcIwjuMwCcUNZiTZHhYN3IvBga9Oqo05CJPSOSQf5EJTm8nw2n1F2GTqBYbnOKR-MpdYKp8oUpSuEuhTARW-oCJKCzolDju_4742KlVDzJLde10_nD5GWoocbmDhE/s400/Screen+Shot+2017-06-29+at+11.51.31+PM.png" width="400" /></a></div>
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So what story does the newly updated data foretell? Let’s look at the dry facts first. The membership of the primary orbital cluster that we pointed out in the first paper (shown in purple) has grown to ten. Meanwhile, two of the objects (shown in green) have orbits that are diametrically opposed to the primary cluster. Finally, there is also a single outlier, 2015 GT50, shown in gray. Cumulatively, this is a somewhat more complex picture than what we had a couple years ago.</div>
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<span style="font-kerning: none;">If you look at the OSSOS data in isolation, it contains two objects that are in the purple camp, one green orbit, and the gray outlier. You need to know exactly zero statistics to conclude that these four points DO NOT form a pattern. And this is what the OSSOS team concludes as well, after carrying out a sophisticated account for the observational biases inherent to their survey. Indeed, from the independent OSSOS dataset alone, a random underlying distribution (as opposed to a clustered distribution) cannot be ruled out.</span></div>
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<span style="font-kerning: none;">When you look at the full dataset, however, the propensity for orbital clustering is clear. <a href="https://arxiv.org/pdf/1706.05348.pdf" target="_blank">Shankman et al.</a> argue that this clustering is unlikely to be real, and is merely apparent. That is, in their view, observational biases conspire to make certain parts of the night sky more observable than others, leading to the discovery of orbits that share a common orientation more frequent. In striking contrast, <a href="https://arxiv.org/pdf/1706.04175.pdf" target="_blank">a recent paper</a> that Mike put together shows exactly the opposite to be true for the non-OSSOS dataset: observational bias cannot account for orbital clustering beyond 250AU.</span></div>
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<span style="font-kerning: none;">Perhaps the resolution lies in that observational surveys that discovered non-OSSOS objects share very little in their design with OSSOS, leading to staggeringly different biases between the OSSOS and non-OSSOS datasets. But one way or another, the likely take away message here is that although the data shows a statistically significant tendency for clustering, the emergent story is not as simple as that of all orbits with periods longer than ~4000 years (or equivalently, semi-major axes greater than 250AU) sharing a common orientation. Rather, the primary orbital cluster is accompanied by a diametrically opposed population of orbits, and is contaminated by an outlier.</span></div>
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<span style="font-kerning: none;">Let’s now compare this picture with theory. Numerical simulations of solar system dynamics that include P9 </span>(e.g. <a href="https://arxiv.org/pdf/1601.05438.pdf" target="_blank">BB16a</a> <a href="https://arxiv.org/pdf/1603.05712.pdf" target="_blank">BB16b</a>) predict that beyond semi-major axis of 250AU, there will be a strong, long-term stable cluster of bodies with orbits that are anti-aligned with respect to the major axis of P9 as well as a weaker, metastable cluster of objects that are aligned with the orbit of P9. From an evolutionary point of view, objects belonging to the anti-aligned cluster are those that were scattered into distant orbits billions of years ago and were locked into an immutable, resonant pattern of anti-aligned perihelion libration. On the other hand, aligned orbits are those that were scattered out by Neptune (from a lower semi-major axis region) comparatively recently (e.g., ~ hundreds of millions of years ago), and due to mean-field interactions with Planet Nine will be ejected from the solar system as soon as their orbits precess out of alignment with that of P9.</div>
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<span style="font-kerning: none;">Within the context of this theoretical expectation, the purple and green orbits depicted in the above picture are readily interpreted as members of the anti-aligned and aligned clusters respectively. To this end, here is a plot of orbital orientation (longitude of perihelion relative to the major axis of Planet Nine) vs. particle semi-major axis where the data are color-coded in the same way as in the above graphic, while blue and orange points show dynamical footprints of the long-term stable and metastable simulated particles respectively:</span><br />
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If we adopt this interpretation, the purple data points are drawn from the distribution of simulated objects shown in blue, while the green points belong to the orange population of test-particles. Although this explanation is comforting, we pretty much knew this already. So there is nothing particularly surprising here.<span style="font-kerning: none;"></span></div>
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<span style="font-kerning: none;">The data point I got considerably more intrigued by is the outlier, 2015 GT50. As already mentioned previously, this object does not belong to either the aligned or anti-aligned cluster, so naively speaking it simply doesn't fit the model. A more cursory inspection of the above plot however, brings to light the existence of a string of specific orbital radii that correspond to resonances with Planet Nine, where the simulated objects circulate through the full 0-360 degree range of orbital orientations. Remarkably, the outlier (2015 GT50) falls *exactly* on one such orbit (i.e. note on the plot above that the gray point falls on a vertical blue line). </span></div>
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<span style="font-kerning: none;">This is kind of staggering. Without changing the Planet Nine parameters at all (to make this plot I’ve adopted the same a=700AU e=0.6 m=10Mearth P9 configuration as in the original Batygin & Brown 2016 AJ <a href="https://arxiv.org/pdf/1601.05438.pdf" target="_blank">paper</a>), the model manages to fit all the data, including the supposed outlier. Of course, the fact that the observed object fits so well with theory might be a coincidence, but this correspondence nevertheless emphasizes that the mere existence of a small number of apsidally unconfined objects that do follow the overall pattern exhibited by the data, does not constitute strong evidence against the Planet Nine hypothesis. Instead, mapping out this comparatively uncommon population of unconfined objects might lend important constraints on P9’s semi-major axis.</span></div>
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<span style="font-kerning: none;">There is one other crucial aspect here, which is that the clustering of a>250AU orbits constitutes only one line of evidence for Planet Nine. If that were the entire story, the P9 hypothesis would have never made it to publication, because we would not have submitted the paper. Instead, what makes the theoretical case for Planet Nine compelling is its capacity to simultaneously explain (i) orbital clustering, (ii) dynamical detachment of KBO perihelia from Neptune, (iii) generation of perpendicular large-semi-major axis centaurs, (iv) the six-degree obliquity of the sun, as well as (v) pollution of the more proximate Kuiper belt by retrograde orbits. In my view, it is only when these pieces of the puzzle are put together that Occam’s razor begins to cut in Planet Nine’s favor. But in the end, time will tell - unlike many theoretical questions, the existence of Planet Nine has a well-defined observational resolution, and we’ll know the answer in less than a decade. </span></div>
Konstantinhttp://www.blogger.com/profile/14245543234165152508noreply@blogger.com78tag:blogger.com,1999:blog-1052332993988376053.post-70252946217390709022017-05-04T17:17:00.000-07:002017-05-04T17:21:17.789-07:00Planet Nine: the score card<div dir="ltr" style="text-align: left;" trbidi="on">
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Last year, just after Konstantin and I announced our hypothesis that a
distant massive planet in an eccentric orbit was corralling distant
Kuiper belt objects into peculiar orbits, I wrote a post explaining why
it might all be wrong. Not that it I thought was all wrong – I was and
still am quite convinced that Planet Nine is out there waiting to be
found – but it’s always good to understand how a hypothesis might be
wrong, particularly when it’s one of your own.<br />
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The biggest worry with the original evidence for Planet Nine was that we
might have stared at our own data for so long that patterns were
appearing out of the randomness. This sort of pattern finding is what
leads to people discovering faces on Mars or deities in burnt toast or,
sometimes, giant planets in the void of space. As you remember, the
evidence for the existence of Planet Nine was that the six most distant
know objects in the Kuiper belt were all swept off in one direction and
also systematically tilted in the same direction (see the top of this
page!), contrary to how they should be. We calculated a probability that
such an alignment should occur due to chance, and we came up with
something like one-in-a-million. This calculation is one place our
hypothesis could go wrong. Though I think we did this calculation in a
sensible way, these sorts of after-the-fact calculations should always
be looked at a little suspiciously. A much better approach is to use
your hypothesis to predict what will happen in new data. We did exactly
this when we predicted the presence of objects with orbits perpendicular
to the solar system and then realized these objects indeed existed. For
Konstantin and I this prediction was what changed Planet Nine from
being a cute idea to a solid and viable hypothesis. Even that successful
prediction, however, was less central to the main observation of an
aligned set of distant objects. What I really wanted to see was whether
or not future discoveries would live up to our specific predictions.<br />
<br />
It’s been a year now. How has the hypothesis fared?<br />
<br />
First, let’s review the specific predictions.<br />
<br />
(1) Newly discovered distant Kuiper belt objects (specifically those
with semimajor axis beyond 230 AU, for the sticklers out there) will
continue to have orbits the sweep off in the opposite direction of the
hypothesized orbit of Planet Nine<br />
<br />
(2) These objects will be systematically tilted the same way as the original 6 objects.<br />
<br />
Our second paper, a few months later, made a third prediction:<br />
<br />
(3) In addition to all of the distant objects swept in the opposite
direction, there should be a small population of distant objects with
orbits in the same direction as Planet Nine. No such objects were known
but they must also exist in the Planet Nine hypothesis is true.<br />
<br />
Finally, in a talk at a scientific conference in October, after some
even more detailed computer simulations, we made one last prediction, or
perhaps we should call it a modification of the second prediction:<br />
<br />
(4) Newly discovered objects will have orbital planes that are, on
average, tilted in the same direction, but there will be a systematic
spread in that tilt.<br />
<br />
This last prediction is difficult to explain but easy to show. Every
object orbiting the sun has an orbital north pole. Objects which are
tilted exactly the same will all have the same north pole. We can
represent the tilt of the orbit of an object by the position of its
north pole on a top-down view of its latitude and longitude. In this
plot, the degree of the tilt of the orbit of the object is the distance
from the center of the plot, which the direct of the tilt of the orbit
of the object is the direction from center to the point. Any objects in
the exact orbit plane of the solar system will have a pole latitude of
90 degrees, and will plot right in the center of the plot. Our latest
round of computer simulations showed us to expect a cluster of pole
positions all tilted off in one direction, but with a larger spread than
we had anticipated in prediction (2). The comparison of the computer
simulations of the expected pole positions with the real pole positions
of the six distant objects was good, but that’s not surprising, as we
designed the computer simulations to match the known objects. The
question will be: where do future discoveries lie? Note that it is
pretty easy for any one object to satisfy this prediction, as the
predicted pole positions cover a pretty wide swatch of the sky, but in
general they cluster more strongly off in one direction.<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihXMGWvATzAKewQVycY637B6LypukRGLZg2Qtc09Mv-5Cj5_SN5Nvow6OGb0bP7rptZz5Xr6q8kSOUcD2qWLRLLZsHsSVChuSNHNGkKCprU1_j4bxz9SO9PyS4k9YcN1IId40OIl28ewQ/s1600/poles1.PNG" style="margin-left: auto; margin-right: auto;"><img border="0" height="375" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihXMGWvATzAKewQVycY637B6LypukRGLZg2Qtc09Mv-5Cj5_SN5Nvow6OGb0bP7rptZz5Xr6q8kSOUcD2qWLRLLZsHsSVChuSNHNGkKCprU1_j4bxz9SO9PyS4k9YcN1IId40OIl28ewQ/s400/poles1.PNG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Poles of distant
Kuiper belt objects. The original six objects all had poles tilted
approximately in the same direction, as can be seen by the red points.
The small black dots show the poles found in computer simulations. While
they concentrate near where the red dots are, they cover a much wider
range of space.</td></tr>
</tbody></table>
<br />
<br />
Since then we’ve been waiting to see what might be discovered. It’s slow
going. From 2000 until 2013 only six distant objects had been found.
Happily, astronomers have been busy, and 4 new distant objects have been
announced just in the past nine months. Where are they? Let’s take a
look.<br />
<br />
The most interesting set of objects came from Scott Sheppard and Chad
Trujillo – the same group that realized early on that something fishy
was going on in the outer solar system and that inspired us to try to
figure it out. Sheppard and Trujillo found 3 distant objects. Two of
them fit right into the pattern of the previous 6 objects. They are both
swept off in the correct direction, and their orbital poles fit within
the range of our computer simulations (again, though, this is a large
range to fit into. Sorry. Blame Planet Nine). The third new distant
object, though, is my favorite. It is swept into an orbit exactly
opposite of all of the rest. This object was precisely the type
predicted for the new population we had predicted, and it was in exactly
the right spot. How exciting was it to see this newly predicted
population? Let’s just say I did a little dance in my office when I saw
the orbit.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIJ6MCnzkyN9z9bEVBXH2nokcy7nJJN8LulLYf6aCf4k7C5a7NniNjroYxP_MCJxC-BocthAoWePXm_OtlvMK8l1uXEfoXELh7OseUEOKjINaghB54Q9MPXY6SYTlsA4CHa9h69okGCU8/s1600/orbs.PNG" style="margin-left: auto; margin-right: auto;"><img border="0" height="560" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIJ6MCnzkyN9z9bEVBXH2nokcy7nJJN8LulLYf6aCf4k7C5a7NniNjroYxP_MCJxC-BocthAoWePXm_OtlvMK8l1uXEfoXELh7OseUEOKjINaghB54Q9MPXY6SYTlsA4CHa9h69okGCU8/s640/orbs.PNG" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The orbits of the
most distant Kuiper belt objects. The red objects are the original six,
the green are the Sheppard & Trujillo discoveries, while the blue
is the OSSOS discovery. </td></tr>
</tbody></table>
<br />
<br />
Most recently, the OSSOS team announced the discovery of a single
distant object. If you look where its orbit lies and then you look at
its pole, you will not be surprised to learn that the announcement of
this discovery again had me doing a little dance in my office. Four for
four! But then you might also be surprised that the astronomers making
the announcement claimed that it showed that there was probably no
Planet Nine, partially based on the fact that the pole is not tilted
enough. What? Ah, it’s because they’re looking at the rather simple
prediction (2) and not taking into account the refined understanding
that led to prediction (4). That’s OK. The discussion of prediction (4)
took place at a scientific conference, and the paper describing it,
though submitted for publication, has not yet come out. It’s always
hard for scientific authors to know how to acknowledge these sorts of
things, and so, though the authors knew about the prediction, they
hadn’t had the opportunity to read a detailed paper describing it, so
they chose to not mention it. We’ll still count it.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDAkSdeGOiW8Jp7Llw0cfu02zvgTGDkwaHKIkA2yEq-pjMt1bhbcqswcv55VN37D47QUW_Nyk6lJ_p94pFIWDHvBFX969gYHF9OmoDsGCOFdSsZBlRZDizNDghDeSfs8gKyYuUfq7MGjo/s1600/poles2.PNG" style="margin-left: auto; margin-right: auto;"><img border="0" height="373" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDAkSdeGOiW8Jp7Llw0cfu02zvgTGDkwaHKIkA2yEq-pjMt1bhbcqswcv55VN37D47QUW_Nyk6lJ_p94pFIWDHvBFX969gYHF9OmoDsGCOFdSsZBlRZDizNDghDeSfs8gKyYuUfq7MGjo/s400/poles2.PNG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The newly discovered objects (green = Sheppard & Trujillo, blue = OSSOS) fit nicely into the predicted pole positions. </td></tr>
</tbody></table>
<br />
<br />
We now have a score card! Originally there were six objects. Now there
are ten. That’s a 66% increase, which is good work, mostly thanks to
Sheppard & Trujillo’s efforts. And every single discovery fits a
true prediction perfectly. By “true prediction” I mean an authentic
prediction about something not yet seen, rather than an after-the-fact
explanation. Those are hard. Those are the things that we give serious
credence to, as a fun idea turns into a compelling hypothesis turns into
a rigorous theory. <br />
<br />
Are we there yet? No. I would put us about halfway between compelling
hypothesis and rigorous theory. There are still a few details about
Planet Nine and its effect on the outer solar system that we can’t yet
explain. But we’re close. When (or, to be fair, I should say “if”) those
details are nailed down, I will be happy to put Planet Nine into the
category of rigorous theory. Of course, we might get lucky and actually
find it first. Then it will simply be confirmed fact.<br />
<br />
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<br />
The season for hunting Planet Nine is coming upon us soon (we predict
that Planet Nine will most likely be discovered near the constellation
Taurus, which starts to rise in the fall). With all of these new
discoveries and, significantly, with our improved understanding of the
way in which Planet Nine gravitationally effects the objects of the
outer solar system, it’s time to update our predicted positions for all
of those searching for Planet Nine. The next two posts will be a bit
technical, but will give the most detailed information for anyone out
there trying hard to find Planet Nine. Good luck, and, um, tell me if
you find it.</div>
</div>
Unknownnoreply@blogger.com153tag:blogger.com,1999:blog-1052332993988376053.post-89372865869588121882017-03-03T15:43:00.000-08:002017-03-03T15:43:37.245-08:00Planet Nine: the movie<div dir="ltr" style="text-align: left;" trbidi="on">
When I am not searching for Planet Nine, I am teaching classes here at Caltech and throughout the world. The most fun class is my online class <a href="https://www.coursera.org/learn/solar-system" target="_blank">The Science of the Solar System</a>. It is a 100% free online class hosted at Coursera for anyone in the world. I've been running the class for several years now, and I finally got around to updating the class to include a short lecture on Planet Nine. For fun I thought I would post a copy here just to keep everyone up to date on my favorite yet-unseen planet. It's about 20 minutes long, and extra amusing if you watch it at double speed. <a href="https://youtu.be/v-ktWBtt7sc" target="_blank">CLICK HERE</a> to watch it on Youtube,<br />
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If you enjoy this lecture, you might enjoy the whole class. Give it a try. It is, after all, entirely free.</div>
Unknownnoreply@blogger.com156tag:blogger.com,1999:blog-1052332993988376053.post-64164088246424827832016-08-02T16:44:00.002-07:002016-08-02T16:44:15.766-07:00Origins<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: Helvetica;">
If I was to pick a single characteristic of daily (academic) life that never ceases to amaze, it would be the rate at which time flies. It has been a little over six months since the publication of the original P9 paper, and the number of follow-up studies that have been unveiled since then edge on thirty. A subset of these studies have, rather than attempting to further characterize Planet Nine’s present-day state, considered the intriguing question of Planet Nine’s <i>origins</i>. Having finished teaching a class on the formation and evolution of planetary systems last quarter, this question has been on my mind as well. </div>
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In essence, there are three potential scenarios for the formation of Planet Nine that have been discussed in the literature. They are (I) <a href="http://arxiv.org/pdf/1603.08010v1.pdf" target="_blank">outward scattering</a> (II) <a href="http://arxiv.org/pdf/1603.07247v2.pdf" target="_blank">external capture</a> and (III) <a href="http://arxiv.org/pdf/1603.08008v1.pdf" target="_blank">in-situ formation</a>. Within the framework of the first picture, P9 forms alongside other solar system planets, but is perturbed onto a highly elliptical, long-period orbit after the dissipation of the solar nebula. In other words, the extreme orbit of Planet Nine is generated through the honest labor of gravitational planet-planet interactions (with a bit of work done at the end by passing stars; see below). </div>
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: x-small;">Orbit of an outward-scattered planet. Made with Super Planet Crash (http://www.stefanom.org/spc/).</span></td></tr>
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External capture, on the other hand, paints the solar system in a more conniving light. In this story, Planet Nine is kidnapped by the Sun’s gravitational pull from an unsuspecting passing star, rendering P9 a bonafide exoplanet. Finally, the in-situ formation scenario simply envisions that the solar system’s protoplanetary disk extended to ~1000AU, and over time a distant annulus of material coalesced into a ~10 Earth mass body.</div>
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Although I’m a fan of the theory of <a href="http://arxiv.org/pdf/1511.09157.pdf" target="_blank">in-situ formation of giant planets in the inner nebula</a>, in-situ formation of P9 seems to be the least likely of the three aforementioned alternatives. If we extend the classical minimum mass solar nebula to ~1000AU with a Mestel-like surface density profile, we obtain a disk mass of Mdisk ~ (2 pi) (1700 g/cm^2) (1AU) (1000AU) ~ 1.2 solar masses. In addition to being straight-up gnarly, such a disk severely violates the <a href="https://en.wikipedia.org/wiki/Toomre%27s_Stability_Criterion" target="_blank">gravitational stability criterion</a>, and with its sub-Jovian mass, P9 is probably not a product of direct gravitational collapse. </div>
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So if P9 didn’t form in place, it was either scattered outwards or it was stolen. Interestingly, both of these processes require the solar system to be embedded within its birth cluster to operate successfully. This is because in the capture scenario, a dense stellar environment is necessary for stars to get close enough to exchange planets, and in the outward scattering scenario, perturbations from passing stars are needed to lift Planet Nine’s perihelion from q ~ 5AU (i.e. Jupiter’s orbit) to its present-day value of q ~ 250 AU. </div>
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<tr><td class="tr-caption" style="text-align: center;">The solar system embedded within a very dense birth cluster (a snapshot from a movie created by A. M. Geller http://faculty.wcas.northwestern.edu/aaron-geller/visuals.php)</td></tr>
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<span style="-webkit-text-stroke-width: initial;">The dynamics of interactions between Planet Nine and passing stars were addressed in a </span><a href="http://arxiv.org/pdf/1602.08496v2.pdf" style="-webkit-text-stroke-width: initial;" target="_blank">paper</a><span style="-webkit-text-stroke-width: initial;"> by Li & Adams. In short, Li & Adams find that external capture (despite being dramatic and esthetically satisfying) is a fundamentally low-probability event: capture cross-sections are much smaller than ejection cross-sections in the birth cluster. Thus, the capture scenario can likely be ruled out on probabilistic grounds. </span></div>
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Intriguingly, the outward scattering story (the only remaining option) is not immune to external kicks either. If left alone in the birth cluster for ~100 million years, the same gravitational perturbations from passing stars that act to lift P9’s perihelion can also strip the planet away all together. Although the exact limits depend on detailed parameter choices, these calculations imply a particular timing for the successful generation and retention of Planet Nine. Specifically, Planet Nine probably formed within the first 1-10 million years of the solar system’s lifetime and acquired its orbit a few 10s of millions of years later, towards the end of the birth cluster’s lifetime. </div>
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From here, we can speculate a bit. On one hand, this timing seems inconsistent with early scattering as envisioned for example by <a href="http://arxiv.org/pdf/1506.03029v1.pdf" target="_blank">Izidoro et al (2015)</a>, because any objects acquiring long-period orbits while the gas is still present would be stripped away by passing stars. But the nebular epoch is not the only time when the solar system could have conceivably ejected planets. The other reasonable instance is the era of transient dynamical instability associated with <a href="https://en.wikipedia.org/wiki/Nice_model" target="_blank">the Nice model</a>. After all, N-body modeling shows that the solar system could have harbored an additional ice giant that would have been expelled at this time (see <a href="http://arxiv.org/pdf/1111.3682v1.pdf" target="_blank">here</a>, <a href="http://arxiv.org/pdf/1109.2949v1.pdf" target="_blank">here</a> and <a href="http://arxiv.org/pdf/1208.2957v1.pdf" target="_blank">here</a>). To this end, here is a simulation that starts out with an extra Neptune that ejects after about ten million years.</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5JDWrF1Hc-K0iXrM5MfKR35GMyhSRTElSnHyr0XaAKEfa-9_9zsR-QJr7Ex84lOE8azFvm0UkMa_pYOdhziGPXm81TPyMPejnX_-XfnsQ9L00300Bidc0AwMn5w0X6l1O6SiUyLpCeqQ/s1600/Screen+Shot+2016-08-02+at+4.12.59+PM.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="270" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5JDWrF1Hc-K0iXrM5MfKR35GMyhSRTElSnHyr0XaAKEfa-9_9zsR-QJr7Ex84lOE8azFvm0UkMa_pYOdhziGPXm81TPyMPejnX_-XfnsQ9L00300Bidc0AwMn5w0X6l1O6SiUyLpCeqQ/s400/Screen+Shot+2016-08-02+at+4.12.59+PM.png" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: x-small;">Dynamical evolution of an initially 5-planet outer solar system (from Batygin et al 2012)</span></td></tr>
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<span style="-webkit-text-stroke-width: initial;">If we subscribe to this point of view, then Planet Nine is the solar system’s original <a href="https://en.wikipedia.org/wiki/Five-planet_Nice_model" target="_blank">fifth giant planet</a>. Pretty neat. But wait - by fixing the onset of giant planet instability to sometime before ~100 million years after the Sun’s birth, we have broken an attractive feature of the Nice model: the <a href="https://en.wikipedia.org/wiki/Late_Heavy_Bombardment" target="_blank">late heavy bombardment</a>. The large-scale instability represents a natural trigger for the avalanche of debris that scarred our Moon’s surface, and this very notion served as the main motivation for <a href="http://iopscience.iop.org/article/10.1088/0004-6256/142/5/152/pdf" target="_blank">rethinking</a> how the instability gets activated in the first place. Bummer.</span></div>
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Now, terrestrial planets themselves require ~100 million years to <a href="http://arxiv.org/pdf/1312.1689v4.pdf" target="_blank">form</a> (seriously, why couldn’t all these timescales be a little more distinct from one another?!!), so in order to bombard the Moon, the instability would have had to happen after that. Moreover, a recent <a href="http://arxiv.org/pdf/1603.02502v1.pdf" target="_blank">analysis</a> linked Mercury’s weirdly excited orbit to a sweeping secular resonance that is associated with changes in system’s architecture during the dynamical reformation. But at the same time, another <a href="http://arxiv.org/pdf/1510.08448v1.pdf" target="_blank">study</a> that came out earlier this year pointed out that the terrestrial planets are unlikely to survive the Nice-model instability in the first place. So perhaps the fact that we exist to even ask these questions is evidence in itself that the instability proceeded before the formation of the terrestrial planets was complete?</div>
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<span style="-webkit-text-stroke-width: initial;">At this point, my head is spinning and I want to stop speculating. With Planet Nine in the mix, the solar system’s origin story has once again began to resemble a jig-saw puzzle with pieces that don’t quite snap into place perfectly. But this is probably due to the fact that the piece that represents P9 has not yet been directly imaged, and one can only speculate as to what kind of additional constraints on the solar system’s early evolution will come to light once Planet Nine’s physical and orbital properties are revealed. But like I said, for now I want to stop speculating.</span></div>
Konstantinhttp://www.blogger.com/profile/14245543234165152508noreply@blogger.com65tag:blogger.com,1999:blog-1052332993988376053.post-51858676995632017342016-03-17T15:40:00.000-07:002016-03-17T15:40:21.818-07:00Where is Planet Nine?<div dir="ltr" style="text-align: left;" trbidi="on">
At the time we published our paper on Planet Nine, we were working on a companion paper, that we had hoped to finish that same day, that would tell you where to look for Planet Nine. Finally, only two months later than anticipated, we have finally finished the paper.<br />
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I'll be writing in more depth about where we think Planet Nine is, how we constrain it, and how we're going about trying to find it, but, first, I want to simply put in a link to the paper, so you can go read it yourself:<br />
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<a href="http://www.gps.caltech.edu/~mbrown/papers/ps/findp9.pdf" target="_blank"><b>Observational constraints on the orbit and location of Planet Nine in the outer solar system</b></a><br />
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Michael E. Brown & Konstantin Batygin <b><br /></b><br />
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<i> Abstract: We use an extensive suite of numerical simulations to constrain the mass and orbit of Planet Nine, the recently proposed perturber in a distant eccentric orbit in the outer solar system. We compare our simulations to the observed population of aligned eccentric high semimajor axis Kuiper belt objects and determine which simulation parameters are statistically compatible with the observations. We find that only a narrow range of orbital elements can reproduce the observations. In particular, the combination of semimajor axis, eccentricity, and mass of Planet Nine strongly dictates the semimajor axis range of the orbital confinement of the distant eccentric Kuiper belt objects. Allowed orbits, which confine Kuiper belt objects with semimajor axis beyond 230 AU, have perihelia roughly between 200 and 350 AU, semimajor axes between 300 and 900 AU, and masses of approximately 10 Earth masses. Orbitally confined objects also generally have orbital planes similar to that of the planet, suggesting that the planet is inclined approximately 30 degrees to the ecliptic. We compare the allowed orbital positions and estimated brightness of Planet Nine to previous and ongoing surveys which would be sensitive to the planet's detection and use these surveys to rule out approximately two-thirds of the planet's orbit. Planet Nine is likely near aphelion with an approximate brightness of 22<V<25. At opposition, its motion, mainly due to parallax, can easily be detected within 24 hours.</i></div>
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The key figure is at the very end, as it answers WHERE SHOULD I BE LOOKING FOR PLANET NINE???? Here is that figure in a much larger form so you can see it better:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPGasHAGhyphenhyphenH3oCTQ7i4k7yPhfvO_NlDt0fQ3MiKoMp3BzFOGJ9q2sdvaHLPAK9PTsopRIU1nbf-v1KoEFTv9wYM3XzvEDKeiqY5VZVSFcp4AgEVgaTOKM6ZSblc6uVpJS1gs0hpOpx7IY/s1600/fig10.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPGasHAGhyphenhyphenH3oCTQ7i4k7yPhfvO_NlDt0fQ3MiKoMp3BzFOGJ9q2sdvaHLPAK9PTsopRIU1nbf-v1KoEFTv9wYM3XzvEDKeiqY5VZVSFcp4AgEVgaTOKM6ZSblc6uVpJS1gs0hpOpx7IY/s640/fig10.png" width="498" /></a></div>
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You can read the paper for details on what the colors all mean, but the quick version of the story is this: in the black regions no current or ongoing survey can detect Planet Nine through its full predicted range. Amazingly, the black region is pretty small! Each color represents a survey that should have or will detect Planet Nine if it is in that position in the sky. Light blue is earlier work of mine from a large all sky survey, dark blue is ongoing work I am doing using Pan-STARRS transient data, green is the Pan-STARRS moving object key project (with an extension, in red), yellow is the Dark Energy Survey. My favorite constraint is orange, which shows where the lack of perturbations to the position of Saturn as measured by the Cassini spacecraft rules out Planet Nine.<br />
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So now you know. Now, please, go find Planet Nine.</div>
Unknownnoreply@blogger.com220tag:blogger.com,1999:blog-1052332993988376053.post-35124711308018639042016-02-12T19:34:00.002-08:002016-02-12T19:36:30.866-08:00A Stranger at Home<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: Helvetica;">
An interesting consequence of being asked the same question repeatedly, is that you stop thinking about the answer. Instead, you find yourself reciting a variant of the same prefabricated response that you gave the previous twelve times. Naturally, in this mode of operation, your brain is susceptible to being stumped by otherwise trivial inquiries, simply because you haven’t heard them before and they don’t automatically register in the existing database. Recently, I found myself in exactly this situation. </div>
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A recurrent question about which Mike and I have thought extensively is “what if you’re wrong?” For an extended discussion about this possibility, scroll down to the previous post. But the perplexing question, posed to me by a reporter some time ago, was a different one: “what if you are right?” In all honesty, my first reaction was “huh? What does this even really mean?” Of course, we <i>hope</i> that we are right! We <i>hope</i> that the dynamical mechanism connecting the alignment of the distant Kuiper belt orbits, the detachment of Sedna-type ellipses from Neptune and the mysteriously inclined trajectories of large semi-major axis Centaurs, is a chaotic web of mean-motion resonances facilitated by Planet Nine. Moreover, we <i>hope</i> that Planet Nine will be observationally detected, like, as soon as possible, ya know what I’m sayin’?… </div>
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But on second thought, it is evident that I was being dopey. This question has considerable depth. If we are right, the clockwork of our solar system is about to acquire a very aberrant new gear, and this has profound implications for how our strange cosmic home fits into its extrasolar context. More specifically, the detection of Planet Nine would render our solar system a slightly less abnormal member of the Galactic planetary census.</div>
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In order to understand just how unusual the architecture of the known solar system is, it is useful to dial the clock back to late November of 1995 - that is, to the discovery of the first <a href="http://adsabs.harvard.edu/abs/1995Natur.378..355M" target="_blank">planet around another sun-like star</a>. With a mass slightly larger than that of Saturn, this object (dubbed 51 Peg b) is bonafide giant planet. However, unlike Jupiter and Saturn, that require more than a decade to finish a single revolution around the sun, 51 Peg b completes its orbital trek in a little over four days. Indeed, the first proof that planets around other main-sequence stars are extant also provided the first hint that orbital architectures of extrasolar planets can be very different from that of solar system’s planets.</div>
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Observational characterization of more expansive giant planet orbits during the subsequent decade and a half continued to yield surprises. Evidently, long-period giant planets tend to occupy eccentric, rather than circular, orbits. <span style="-webkit-text-stroke-width: initial; text-align: center;">The figure below shows the semi-major axis - eccentricity distribution of well-characterized extrasolar planets. While the solar system giants would be found scraping the bottom of this figure, exoplanets clearly occupy the the entire eccentricity range, with a nearly parabolic orbit of HD 20782 b at the helm of the population.</span><span style="-webkit-text-stroke-width: initial; text-align: center;"> </span></div>
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<span style="-webkit-text-stroke-width: initial; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhg4BgchHk3dyZ34EFcFP_yidwPwOEqQ5DACe5W4jLq21LXtDKZCd6Jr_87LoHB0jIEJZziygMTb_g4xDAH4lIBJcdbjBJYI7HdPpVmXXHwEVVmp1z74Jc8iP1B9KqcFVAUt_JDAFeMFV8/s1600/Screen+Shot+2016-02-12+at+10.20.02+AM.png" imageanchor="1"><img border="0" height="303" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhg4BgchHk3dyZ34EFcFP_yidwPwOEqQ5DACe5W4jLq21LXtDKZCd6Jr_87LoHB0jIEJZziygMTb_g4xDAH4lIBJcdbjBJYI7HdPpVmXXHwEVVmp1z74Jc8iP1B9KqcFVAUt_JDAFeMFV8/s400/Screen+Shot+2016-02-12+at+10.20.02+AM.png" width="400" /></a></span></div>
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<span style="font-size: x-small;">Figure 1: semimajor axis - eccentricity distribution of well-characterized extrasolar planets. The predicted orbit of Planet Nine is shown as well.</span></div>
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<span style="-webkit-text-stroke-width: initial;">More recently, the <a href="http://arxiv.org/pdf/1501.07286v2.pdf" target="_blank">triumphant success of the Kepler mission</a> showed that the default mode of planet formation in the galaxy generates objects that are somewhat smaller than Uranus and Neptune, but are substantially more massive than the Earth. In other words, planetary masses of order ~10 Earth masses are not only prevalent in the exoplanet catalog, they are dominant. Although the transit technique limits the observational window of Kepler to orbits inside ~1AU, there is little reason to suggest that more distant orbits should be devoid of such planets.</span></div>
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<span style="font-size: x-small;">Figure 2: the catalog of planetary candidates detected by Kepler. The sizes of the depicted points are representative of the corresponding planetary radii. The semi-major axes are shown on a logarithmic scale. Figure from <a href="http://arxiv.org/pdf/1503.06945v2.pdf" target="_blank">Batygin & Laughlin 2015</a>.</span></div>
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Cumulatively, a distinct picture of the Galactic planetary census is beginning emerge, wherein the ordered orbits of the known planets of the solar system are starting to appear increasingly abnormal. On the other hand, with a characteristic mass approximately 10 times greater than the Earth and an eccentricity of ~0.6, Planet Nine fits into this extrasolar planetary album seamlessly. Intriguingly, this yet-unseen world may provide the closest link between our solar system, and the extrasolar realm. Indeed, Planet Nine may constitute the closest thing to the solar system’s very own extrasolar planet.</div>
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Konstantinhttp://www.blogger.com/profile/14245543234165152508noreply@blogger.com95tag:blogger.com,1999:blog-1052332993988376053.post-3687704082079839312016-02-12T10:46:00.001-08:002016-02-12T15:22:24.350-08:00Why I believe in Planet Nine.<div dir="ltr" style="text-align: left;" trbidi="on">
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In my last post I went into detail on ways in which our
Planet Nine hypothesis could be wrong, and I suggested for you, if you’d like
to be a Planet Nine skeptic, which you’re encouraged to be, what new
observations you should be looking for before you start to believe it yourself.
Here, I’m going to tell you why I already am a believer in Planet Nine and why
maybe you should be too.</div>
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As we’ve discussed, the Planet Nine hypothesis was initially
developed to explain one simple phenomenon: the alignment of the most distant
objects in the Kuiper belt. The existence of that alignment looks pretty
compelling, but even when you calculate things like a 0.007% chance that it
could happen due to chance you still worry about the fact that there are only 6
objects that you’re talking about. Still, Konstantin and I worked on this for
about a year until, by about late last summer, we had a nice comprehensive
theory which could explain how a massive planet on an elongated orbit could
capture equally orbitally-elongated Kuiper belt objects into protected
mean-motion resonances. It was a fun result with some cute physics to it, as no
one had really considered the effect of such extreme planetary eccentricities
on populations of small objects before. It’s always a good day when you learn
something new about the ways in which planetary physics can work.<br />
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<tr><td class="tr-caption" style="text-align: center;">The whole point of Planet Nine was to explain the orbital alignment of these six objects. The number of other phenomena that Planet Nine also explains -- essentially by accident -- is astonishing.</td></tr>
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A particularly satisfying aspect of the hypothesis was that
it neatly and eloquently explained the peculiar orbit of Sedna.<span style="mso-spacerun: yes;"> </span>I have <a href="http://www.mikebrownsplanets.com/2010/10/there-is-something-out-there.html" target="_blank">written elsewhere</a> on what is peculiar
about Sedna’s orbit and why it demands an explanation, and I have spent 12
years searching for solutions to Sedna’s peculiar orbit, and here was an
explanation where we hadn’t even been looking for one. In short, Sedna is
peculiar because it has been pulled away from the Kuiper belt by something. And
to be pulled away from the Kuiper belt there needs to be something beyond the
Kuiper belt to do the pulling. Back when we discovered Sedna, we proposed that
perhaps that something was a planet! Or a passing star! Or the cluster of stars
that the sun was born in! We didn’t really know. With only a single object
there were more possibilities than answers. But as we continued surveying the
outer solar system and found no new bright planets out there, we gradually
settled into the view point that the most likely explanation was that Sedna had
been pulled away from the Kuiper belt by the combined effect of the nearby
stars that formed along with the Sun 4.5 billion years ago. This proposition
was exciting: Sedna would be a fossil record of the birth of the Sun itself,
and finding more of them which teach us about that time period.</div>
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Now, however, we have a simpler explanation. If a planet is
forcing the most distant objects into alignment, it will also take these most
distant objects and periodically pull them away from the Kuiper belt before
pushing them back in. In fact, the Planet Nine hypothesis <i style="mso-bidi-font-style: normal;">demands</i> that objects like Sedna, and also 2012 VP113, a more
recently discovered by similarly odd object, exist. After 12 years of searching
for the explanation for Sedna we found it by trying to explain something else
entirely. <span style="mso-spacerun: yes;"> </span></div>
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<i style="mso-bidi-font-style: normal;">Interesting side note:
As I was writing this post I noticed something that I hadn’t before. It’s not
just Sedna and 2012 VP113: </i>all<i style="mso-bidi-font-style: normal;"> of the
distant objects which are pulled </i>even a little bit<i style="mso-bidi-font-style: normal;"> away from the Kuiper are in our cluster (specifically, if you look at
all objects with semimajor axis>100 AU and perihelion > 42 AU).<span style="mso-spacerun: yes;"> </span>Wow. </i></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
That’s not bad. As a scientist, you would love to form a
hypothesis that makes predictions that turn out to be true. That makes you
begin to believe in your hypothesis. In this case, we didn’t predict the existence
of Sedna and then go find it, but rather we knew about Sedna and accidentally
came up with a solution. That’s more of a two-birds-with-one-stone situation
than a prediction, I think. Still, we were quite pleased.<span style="mso-spacerun: yes;"> </span>While previous speculation about planets
beyond Neptune had struggled to find viable explanations for even single
phenomena, we had come up with a relatively rigorous theory which naturally
explained two seemingly unrelated phenomena. </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
At this point I think that Konstantin and I were mentally
ready to publish a paper with a conclusion something like “here’s a nice theory
which explains two different things and hey it’s even quite plausible!”</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
What happened next is what made me go from finding the
explanation plausible to finding the explanation likely. While sitting in my
office looking at the outputs of our gravitationally simulations, Konstantin
and I realized that Planet Nine had another major effect that we hadn’t
anticipated. Some of the objects with very distant elongated orbits had their
orbits twisted so that instead of being more or less oriented along with the
disk of the rest of the solar system, they were essentially perpendicular to
it. And, when they happened, instead of being lined up with the other distant
objects, their orbits swung off to the left or to the right by nearly 90
degrees. I described these orbits as “wings” because that’s how they looked in
the simulations. </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Objects with perpendicular orbits? I remember when one was
discovered a few years ago. It was so unusual that it was nicknamed “Drac,” in
honor of Dracula’s ability to climb on walls. Or something like that. I was
quite excited to quickly look up the orbital parameters of Drac and see if its
orbit corresponded to the location of the wings, but, to my chagrin, Drac was
the wrong sort of object. I had remembered correctly that Drac was
perpendicular, but its orbit did not go nearly far enough from the sun to be
affected by Planet Nine. And it was not even pointing in the right direction. The
origin of Drac was still a mystery, but it didn’t seem connected to Planet Nine
(oh but it is; more later!). </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
While Konstantin and I were still sitting in my office,
disappointed by Drac, I thought to look at the complete database of all of the
object discovered in the outer solar system, and, to my surprise, there was a
collection of objects that were <i style="mso-bidi-font-style: normal;">not</i>
part of the Kuiper belt that we had overlooked. These were object which, though
though were quite elongated and went to great distances, traveled far <i style="mso-bidi-font-style: normal;">inside</i> the orbit of Neptune – coming
nearly to the orbit of Jupiter in some cases – before swinging back out to the
distant reaches of Planet Nine. We had ignored these objects previously because
we knew that when objects came into the giant planet region their orbits would
be modified by interactions with the planets. What we hadn’t anticipated is
that objects coming in on perpendicular orbits would have much less of a chance
to have their orbits modified. Our simulations showed that objects with distant
elongated perpendicular orbits which came close to the giant planets still
maintain their alignment to the wings.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
When we realized this, Konstantin stay riveted in his chair
in my office while I plotted the locations of these objects which we had
overlooked. There are 5 of them. I told him, “If these are right where we
predict they should be my head is going to explode.” I plotted them. Four are
on one of the wings, the fifth is on the other wing. Right as predicted. My
head did not actually explode, I think, but it is possible that my jaw hit the
floor. We were both silent for a minute, and Konstantin said, in a semi-amazed
voice, “This is actually real, isn’t it?”<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoTVbLzxRrIk8QJTYxXLWqxapb0TIVivBSXkMSf_zE_giGheTHY51w51nyceFQ_xbsAPckPSsA4MffR65hw3xfjVDqEI16HKzD8NsllJ9YXRacpnqI4IYdbbWw5fhhLA5Q64u-FY9qY_s/s1600/P9_KBO_extras_orbits.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoTVbLzxRrIk8QJTYxXLWqxapb0TIVivBSXkMSf_zE_giGheTHY51w51nyceFQ_xbsAPckPSsA4MffR65hw3xfjVDqEI16HKzD8NsllJ9YXRacpnqI4IYdbbWw5fhhLA5Q64u-FY9qY_s/s640/P9_KBO_extras_orbits.jpg" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The distant objects with orbits perpendicular to the solar system were predicted by the Planet Nine hypothesis. And then found 5 minutes later.</td></tr>
</tbody></table>
</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Yeah. I think it’s real. As Konstantin later said, “It’s
like killing two birds with one stone and not even realizing there was a third
in the tree and killing it, too.” The existence of the elongated perpendicular
Centaurs – as those objects are called – was a pure prediction that was
dramatically confirmed. Sadly, the rest of the world didn’t get to participate
in the drama, as it all took place over the course of about five minutes in my
office last fall, but trust me on this one: the drama was there. </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
And Drac, which had been such a disappointment? Once we
started looking we realized that our gravitational simulations create Drac,
too. Sometimes, when the elongated perpendicular Centaurs <i style="mso-bidi-font-style: normal;">do</i> get too close to giant planet, that planet pulls their orbit a
little close, and also swings the orbit around randomly. Another Drac is born.
The Planet Nine hypothesis <i style="mso-bidi-font-style: normal;">requires</i>
the existence of objects with orbits like Drac, which otherwise had no
plausible explanation.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Does that make four (<i style="mso-bidi-font-style: normal;">five?</i>)
birds yet? Hard to keep count.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Here, then, is the summary of my reactions to each of the
four (<i style="mso-bidi-font-style: normal;">now five) </i>things explained by
Planet Nine</div>
<ol style="text-align: left;">
<li><span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="mso-list: Ignore;"><span style="font: 7.0pt "Times New Roman";"></span></span></span>A distant massive eccentric planet can capture
eccentric Kuiper belt objects into elongated anti-aligned orbits like the ones
we see: <i style="mso-bidi-font-style: normal;">Hey, that’s cool! </i></li>
<li><span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="mso-list: Ignore;"><span style="font: 7.0pt "Times New Roman";"></span></span></span>The Planet Nine hypothesis explains Sedna, and
requires Sedna to exist: <i style="mso-bidi-font-style: normal;">Wow. That’s a
really nice hypothesis that sounds pretty plausible!</i></li>
<li> <span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="mso-list: Ignore;"><span style="font: 7.0pt "Times New Roman";"></span></span></span>The existence of Planet Nine predicts the
existence of elongated distant perpendicular Centaurs in specific locations and
they are then found to exist. <i style="mso-bidi-font-style: normal;">Holy cow.
Planet Nine is real!?!?!</i></li>
<li><span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="mso-list: Ignore;"><span style="font: 7.0pt "Times New Roman";"></span></span></span>The Planet Nine hypothesis explains the unusual
orbit of Drac and requires that objects with orbits like that will exist: <i style="mso-bidi-font-style: normal;">Of course it does.</i></li>
<li><span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="mso-list: Ignore;"><span style="font: 7.0pt "Times New Roman";"></span></span></span>The Planet Nine hypothesis explains why all of
the distant objects which have been pulled away from the Kuiper belt are
equally clustered: <i style="mso-bidi-font-style: normal;">Any vestigial doubts
have vanished.</i></li>
</ol>
<i style="mso-bidi-font-style: normal;"> </i>At this point my main question is “what unusual phenomenon
in the Kuiper belt does Planet Nine <i style="mso-bidi-font-style: normal;">not </i>explain?”
(We have, regretfully, come to the conclusion that Planet Nine cannot account
for the parting of the Red Sea or the waning of the ice ages, though both of
those possibilities have been suggested to us multiple times). <br />
<div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
So I believe. But it’s OK if you’re not ready to believe.
Unlike some hypotheses, this one has a definite proof. We have to go find it.
We will. I have very little doubt that we will. </div>
</div>
</div>
Unknownnoreply@blogger.com482tag:blogger.com,1999:blog-1052332993988376053.post-22250315270475068862016-01-25T16:45:00.000-08:002016-01-25T16:46:23.162-08:00Why Planet Nine might not exist<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="MsoNormal">
<i>[or: what keeps me up at night] </i><br />
<br />
As you will see in the next post, I think Planet Nine is really
out there. But that doesn’t mean you should think it is out there. You might be
skeptical. In fact, I would prefer that you were skeptical. I would prefer that
you read the scientific paper, looking for potential flaws, caveats, and places
where we might have been led astray. But, OK, I understand that the actual
scientific paper is on the weighty side, so, rather than make you wade through
it finding the potential piutfalls, instead, I will give you my top list of
things that might be wrong. </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
First, though: what is <i style="mso-bidi-font-style: normal;">not</i>
wrong.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<i style="mso-bidi-font-style: normal;">If </i>there is an
approximately 10 Earth mass planet on an extremely elliptical orbit in the
outer solar system, it would definitely line up the orbits of Kuiper belt
objects with similarly elongated orbits, it would create Kuiper belt objects with
orbits twisted by 90 degrees to the planets of the solar system, and it would
make objects, like Sedna, which have elongated orbits which don’t ever come
close to the rest of the Kuiper belt. These effects we now know from a general
mathematical analysis and from detailed computer simulations to double-check
the mathematical analysis. This analysis, I am confident to say, is iron-clad.
Astronomers will try to reproduce it (I hope), and they will get the same
results (I know). There truly is no wiggle room here. A 10 Earth mass planet
does exactly all of the things that we are trying to explain.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
If I am so confident of this, how could Planet Nine possibly
not exist? Just because Planet Nine can explain all of these effects, it
doesn’t not mean that there is no other possible explanation. We tried to think
of everything that we could, and systematically ruled out alternatives, but
that doesn’t mean that someone else won’t come up with an idea that works.
Again, I hope that there are skeptical astronomers working <i style="mso-bidi-font-style: normal;">right now</i> to come up with alternatives. I am confident that they
will not come up with them (because I do actually think we considered
everything that could possibly be out there), but, unlike my statement above, I
will definitely not say that this one is iron-clad. Aluminum-clad, maybe.
Stainless steel, perhaps. I’d be willing to bet a lot of money against the idea
that someone will find an alternative explanation for all of the effects that
we are seeing. But it is possible I could lose.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
There is one insidious way in which we may have been fooled
into thinking that Planet Nine exists, however, and it is a problem that
permeates all of experimental science. My single biggest worry is that perhaps –
just perhaps -- we have been fooled into seeing a pattern where none exists.
Humans excel at recognizing patterns, even when they are not there (see:
everything single face-on-Mars claim ever, for example). Could we have been
similarly fooled? Absolutely (again: I don’t think we have been, for reasons
detailed in that next post, but is it possible? Of course). Here’s how:</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
In our analysis, we show that the six most distant objects
that have orbits extending outward from the Kuiper belt all line up within a
100 degree quadrant and all have orbital planes which are tilted away from the plane
of the planets by about 20 degrees (and within 6 degrees of each other). From
some very simple calculations we can show that the probability of these
alignments happening due to chance is only about 0.007%. You could also say
that there is a 99.993% chance that the alignments we are seeing in the outer
solar system are real, and that we are not simply being fooled into seeing a
pattern where none exists.</div>
<div class="MsoNormal">
But, really, if you said that, you’d be wrong. Real
statistics don’t work that way. You can’t, for example, flip 100 coins, realize
that 10 of them in the far upper right corner all turned up heads and then say
“wow; the chances of 10 heads in the far upper right corner is only one in 1024
so something must be happening up there.” And if you flipped all of the coins
again, chances are you wouldn’t get 10 heads in the far upper right corner (in
fact, chances are 1 in 1024). The real statistical question that you should be
asking at the first coin flip is more like “what is the probability that
something that seems anomalous will appear just due to chance?” That question
is essentially impossible to answer, because it relies on knowing what a human
who is looking for anomalous patterns would call anomalous.</div>
<div class="MsoNormal">
There are two good ways to combat these sorts of flawed
statistics. The first I just mentioned above: replicate the experiment and look
for the same result. Your eye and brain might pick out a random pattern from
the noise one time, but the same pattern will not occur again. You might see
different patterns, but that just shows you how easy it is to find patterns in
data.</div>
<div class="MsoNormal">
How do we replicate the finding that the most distant
objects in the outer solar system are unusually aligned? We find more of them.
If the alignment was just random pattern finding by easily fooled humans, it
will quickly go away when the next half dozen objects are discovered. And while
it took 12 years to discover the first 6 aligned objects, the next few should
be much faster, as telescopes and surveys continue to get bigger and more
powerful. One caveat: our computer simulations do not predict that 100% of the
most distant objects will be clustered. Just the vast majority. So finding one
or two outside of the cluster is not the end of Planet Nine. But finding the
next six objects randomly distributed around the sky would be a pretty clear
indication that we fell into the pattern-matching trap and that Planet Nine is
a fantasy. The Planet Nine hypothesis makes strong predictions, and these can
be used to show that the hypothesis is wrong, if it is.</div>
<div class="MsoNormal">
The second way to combat the flawed statistics of pattern
matching is to use your explanation for the pattern that you see to predict
something entirely unrelated to the pattern. In our example of the coins above,
you could hypothesize that the explanation for all of the coins coming up heads
in one spot on the table is that there is a powerful magnetic field in that one
location of the table (ok, I’m not sure how that could make things come up all
heads, but work with me on this one). You could then make predictions. Perhaps
you would predict that a set of ball bearings placed on the table would
systematically roll towards that location. Or something. The key is that the
prediction is something that you don’t know the answer to ahead of time, is not
directly related to your original observation, and has a low probability of
occurring on its own. Here you are not replicating the experiment but are
instead performing a different experiment and predicting a very specific
answer.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Our hypothesis passed this test with flying colors – in my
opinion – with the prediction and subsequent realization of the existence of
what we call the distant twisted orbits (maybe we need a better term for these;
definitely we need a better term for these). But maybe it’s all just a bigger
case of pattern matching? Such an explanation begins to get unlikely, but now
we have a second set of objects that can be replicated, and we’ll all be
watching the results come in.</div>
<div class="MsoNormal">
There is one other more mundane in which we can be “wrong.”
Given the small number of objects and our, currently, limited number of
computer simulations (“limited” here still means ~6 months of super computer
time, but we haven’t had time to precisely explore all of the possible
parameters of Planet Nine), it is possible that our estimates are not precisely
correct. Maybe Planet Nine js 20 times the mass of the Earth instead of 10.
Maybe it is actually a giant terrestrial planet instead of a small gas giant.
Maybe it is slightly further away or tilted into a slightly different plane.
These tweaks are OK.<span style="mso-spacerun: yes;"> </span>We would still say
that the Planet Nine hypothesis is correct.</div>
<div class="MsoNormal">
If, however, a planet is found beyond Neptune and it is
totally different from what we have described, if it exists, but it fails to
cause the basic gravitational interactions that we have discussed, then, quite
simply, we are wrong. We are not predicting that there is <i style="mso-bidi-font-style: normal;">some</i> planet beyond Neptune, we are predicting that there is <i style="mso-bidi-font-style: normal;">this</i> planet beyond Neptune and it is
causing <i style="mso-bidi-font-style: normal;">these</i> effects on the outer
solar sytem.</div>
<div class="MsoNormal">
Now, finally, is what you can tell your friends and family
to impress them by your informed skepticism of the Planet Nine hypothesis:</div>
<div class="MsoNormal">
“I worry that they have underestimated the likelihood of
finding an intriguing pattern in the orbital data and that they have just been
fooled into finding a pattern where there is none. I am waiting for the next
few discoveries of distant object to see if they, too, have aligned and twisted
orbits like the theory demands. And, for now, I am also running some computer
simulations to check some ideas I have about other ways that the patterns can develop.
Ask me again in six months.”</div>
</div>
Unknownnoreply@blogger.com101tag:blogger.com,1999:blog-1052332993988376053.post-12791914416841633772016-01-24T08:12:00.000-08:002016-01-24T09:04:41.973-08:00The long and winding history of Planet X<div dir="ltr" style="text-align: left;" trbidi="on">
Standing up in public and claiming that you have found evidence for a new planet in the solar system almost certainly means that you are about to join a century-long list of people who have been wrong. I mean, look, le Verrier and Adams did it in 1846 when they predicted the existence of Neptune, sure, but since then there have been dozens (hundreds?) of similar claims (including le Verrier himself, who thought he had found a Planet Vulcan inside the orbit of Mercury) which have all lead to absolutely nothing.<br />
<br />
For most of the 160 years, astronomers tried to use the positions of the planets themselves to infer the existence of another planet (amusingly: it was the search for this alleged planet that led to the inadvertent discovery of Pluto, which is why the New York Times headline on the day of the Pluto announcement suggests that the planet might be bigger than Jupiter, which it is not). This idea was finally put to rest in 1993, when a <a href="http://adsabs.harvard.edu/full/1993AJ....105.2000S2002" target="_blank">careful analysis of modern data showed that all of the planets are exactly where they are supposed to be </a>(links to papers here may lead to irritating pay walls, but you can at least read the abstracts, I think).<br />
<br />
When it was clear that the planets were where they were supposed to be, astronomers moved on to the comets, which traverse the regions where Planet X might be, and could be effected by them. A suggestions was made that Planet X <a href="http://www.nature.com/nature/journal/v313/n5997/abs/313036a0.html" target="_blank">causes comet showers </a>and <a href="http://www.sciencedirect.com/science/article/pii/001910358690062X" target="_blank">modulates the positions of incoming comets,</a> but these suggestions have <a href="http://mnras.oxfordjournals.org/content/335/3/641.short" target="_blank">rarely been given much credibility</a> when <a href="http://link.springer.com/article/10.1134/S1063773706050094" target="_blank">more detailed analyses</a> are performed.<br />
<br />
The idea of trying to detect Planet X by its gravitational effects was re-picked up soon after the discovery of the Kuiper belt. Early on, astronomers proposed a <a href="http://www.sciencedirect.com/science/article/pii/S0019103502969356" target="_blank">Mars-like planet at ~60 AU</a> to explain an apparently abrupt outer edge to the Kuiper belt, but then <a href="http://www.sciencedirect.com/science/article/pii/S0019103504001708" target="_blank">quickly ruled it out.</a> But the idea kept floating around, and many papers suggested some sort of variant.<br />
<br />
Things began to get interesting with the <a href="http://iopscience.iop.org/article/10.1086/422095/meta" target="_blank">discovery of Sedna</a>, which was the first object discovered in the solar system whose orbit could only be explained by interaction with <i>something</i> besides the known planets (I have a whole series on this <a href="http://www.mikebrownsplanets.com/2010/10/there-is-something-out-there.html" target="_blank">over on my blog</a>. Also, now I know how to end the series). In the discovery paper, I suggested, among other possibilities, a new planet. But a ~Earth sized one around 70 AU. Really, though, for the past 12 years I have been convinced that Sedna's strange orbit is a left over relic from the formation of the sun in a cluster of stars 4.5 billion years ago. Others suggested a <a href="http://iopscience.iop.org/article/10.1088/0004-6256/135/4/1161/meta" target="_blank">~Mars mass planet a little further out</a> as the culprit, or even <a href="http://iopscience.iop.org/article/10.1086/505214/meta" target="_blank">a planet that was once in the outer solar system</a>, but is now gone. Planets are popular things to propose when you see some gravitational effect that you cannot otherwise explain.<br />
<br />
After Sedna, the most interesting developments in the Planet-X-ology came from two papers over the past few years. First, <a href="http://www.nature.com/nature/journal/v507/n7493/abs/nature13156.html" target="_blank">Chad Trujillo and Scott Sheppard </a>noted some unusual orbital alignments among distant Kuiper belt objects (arguments of perihelion appeared clustered around zero, to be specific). They proposed a ~2 earth mass planet at a few hundred AU organizing these objects through a mechanism called a Kozai resonance, though they pointed out in their own paper that they couldn't make the idea work out. And <a href="http://adsabs.harvard.edu/abs/2015DPS....4721109S" target="_blank">detailed simulations</a> showed that their proposed planet did not have the hoped for effect and thus could not be real. Once again. Though this time, critically, the <i>data</i> looked good, just not the explanation.<br />
<br />
<br />
A more recent study also had important clues about Planet Nine. In September, <a href="http://www.sciencedirect.com/science/article/pii/S001910351500264X" target="_blank">Rodney Gomes</a> and colleagues proposed that an entirely separate set of objects were being influenced by some sort of distant planet. While they were not able to use the observations to say much about the planet, they concluded that it was likely that these objects were being pushed around by something large and far away.<br />
<br />
So by this last September, then, if you were paying extremely close attention, you might have been clued in that <i>something</i> was going on in the outer solar system and that a large planet might well be a good explanation, but no one could figure out exactly what was going on. Was there some way to connect Sedna, the strange alignments of Trujillo and Sheppard, and the distant objects of Gomes et al?<br />
<br />
<br />
This moment reminds me of the time right after the discovery of Uranus. In 1783, Anders Johan Lexell published the first calculation of the orbit of Uranus (proving that it was on an elliptical, rather than parabolic orbit, and thus not a comet). Lexell found that, while the orbit of Uranus was elliptical, it also appears to be being perturbed by an external body, presumably a planet. More detailed calculations of the orbit of Uranus in 1821 by Alexis Bouvard confirmed the orbital irregularities and reinforced the idea that there must be an eighth planet out there. These calculation are the ones that led Adams and le Verrier to separately try to see if they could figure out not just <i>if</i> there was a planet out there, but <i>where </i>there was a planet.<br />
<br />
This point is where Konstantin and I started. We could tell that the data from Trujillo and Sheppard was right: <i>something</i> was happening in the outer solar system, but no one could quite figure out what (the paper by Gomes et al. hadn't been published yet, but would eventually be a critical part of the story). We quickly re-confirmed that the Kozai resonance hypothesis of Trujillo and Sheppard didn't work, so what was it? At this point you can read <a href="http://www.findplanetnine.com/2016/01/premonition.html" target="_blank">Konstantin's account</a> of how we got to the answer. Are we right this time? After all of these years? We think so. The data are good, the understanding of how the gravitational forces push everything around is good. We think that, this time, we've actually identified something real out there. We're confident enough to stand up in public and say that we think we have found evidence for a new planet in the solar system.<br />
<br />
And we think it is time to retire the long and winding history of Planet X, and start anew with Planet Nine.<br />
<br />
<br />
<br /></div>
Unknownnoreply@blogger.com88tag:blogger.com,1999:blog-1052332993988376053.post-84506035142195420382016-01-19T17:55:00.000-08:002016-01-19T22:54:08.004-08:00Premonition<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: 'Helvetica Light';">
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There is an uneasy exhilaration in announcing that the solar system might contain a dim, massive, and as-yet unseen planet.</div>
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Certainly, nearly every attempt to predict the existence of a “<a href="https://en.wikipedia.org/wiki/Planets_beyond_Neptune" target="_blank">Planet X</a>” has ended in failure, but history does contain one shining success. LeVerrier and Adams’ <a href="https://en.wikipedia.org/wiki/Discovery_of_Neptune" target="_blank">theoretical predictions</a> of the existence of Neptune, based on observed irregularities in Uranus’ orbit, are hailed as one of the all-time success stories of astronomy. And as history shows, the issues with post-1846 claims of Planet X have had more to do with erroneous interpretation of the observational data, than anything else. In other words, every time the observations seemed to call for an introduction of a putative additional planet, further analysis has revealed that the apparent anomalies could be fully reconciled within the framework of the known solar system.</div>
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Remarkably, the solar system in 2016 tells a very different story. Beginning with the 2003 detection of Sedna (a discovery I remember learning about from a guy cautiously trying to hide his lit cigarette in his backpack during high school lunch break), it has been clear that the solar system still has some tricks up its sleeve. Unlike the rest of the Kuiper belt, Sedna traces out an orbit whose origin cannot be explained by perturbations from the known giant planets alone. And while Sedna’s isolated orbit could in principle be attributed to a dynamical perturbation that occurred during the solar system’s infancy, the 2014 <a href="http://www.nature.com/nature/journal/v507/n7493/full/nature13156.html" target="_blank">paper</a> by Trujillo and Sheppard demonstrated that there is in fact, much more to the story. It was with this very paper in hand, and a facial expression showing a combination of excitement and concern, that Mike Brown walked into my office a year and a half ago.</div>
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Prompted by their discovery of 2012 VP<span style="font-size: x-small;">113</span>, a second object residing on a Sedna-type orbit, Trujillo and Sheppard pointed out that all Kuiper belt objects with orbits that do not veer into inter-planetary space and spend longer than approximately 2000 years to complete a single revolution around the Sun, tend to cluster in the argument of perihelion. As it turns out, this clustering represents only a part of the full picture. A closer look at the data shows that six objects that occupy the most expansive orbits in the Kuiper belt (including Sedna and 2012 VP<span style="font-size: x-small;">113</span>) trace out elliptical paths that point into approximately the same direction in physical space, and lie in approximately the same plane. </div>
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Mike and I were genuinely perplexed. Could the confinement of the orbits be due to an observational bias or a mere coincidence (after all, we are talking about six objects here - not exactly “big data”)? Thankfully, the probability of the observed alignment being fortuitous can be assessed in a statistically rigorous manner, and clocks in at right around 0.007%. Not a <a href="http://www.quickmeme.com/img/aa/aa702842c77416a1e630d386827c1dbe6fc41526aa60717bff5260d7133fcc65.jpg" target="_blank">great gamble</a>. Moreover, application of simple perturbation theory (or direct numerical integration) demonstrates that if allowed to evolve under the gravitational influence of Jupiter, Saturn, Uranus and Neptune, the orbits would become randomly oriented on timescales much shorter than than the multi-billion year lifetime of the solar system. So the dynamical origin of the peculiar structure of the Kuiper belt cannot be outsourced to the distant past - something is holding the orbits together <i>right now</i>.</div>
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Our progress was initially anything but rapid. Coming from observational and theoretical backgrounds respectively, Mike and I don’t always speak the same language, and would spend hours arguing profusely, only to later realize that we are in fact, saying the exact same thing. Then there were all the ideas that did not pan out. Ideas crowding out our outtakes reel range from models where the self-gravity of the Kuiper belt itself keeps the observed structure intact (see a recent <a href="http://arxiv.org/abs/1509.08920" target="_blank">paper</a> by Madigan & McCourt on this topic) to a scenario where the orbit of a distant planet cradles the orbits of Kuiper belt objects from the outside, maintaining the same average orientation. Each hypothesis failed when confronted with the data.</div>
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Last summer brought our first glimpse of hope. Through a series of numerical experiments (wherein an initially axisymmetric disk of planetesimals occupying eccentric, Neptune-hugging orbits, was allowed to evolve under the gravitational influence of a distant perturber) we began to note that planetesimal swarms could be sculpted into collinear groups of spatially confined orbits by “Planet Nine". Intriguingly, this would only occur if Planet Nine was chosen to be substantially more massive than the Earth, and to reside on a highly eccentric orbit. More unexpectedly, the confined orbits would cluster in a configuration where the long axes of their obits are anti-aligned with respect to Planet Nine, signaling that the dynamical mechanism at play is <a href="http://adsabs.harvard.edu/abs/1992IAUS..152..153K" target="_blank">resonant</a> in nature.</div>
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Surprising and unforeseen results suddenly began to accrue. Upon a cursory examination of the simulation data, we noticed that gravitational torques exerted onto the Kuiper belt by Planet Nine would induce long-period oscillations in the perihelion distances of the confined KBOs. This naturally generated detached orbits, such as those of Sedna and 2012 VP<span style="font-size: x-small;">113</span>. Moreover, the evolutionary calculations suggested that if we were to revisit the Kuiper belt in a hundred million years, objects like Sedna and VP would look like conventional garden variety KBOs, while some of the more typical objects would acquire detached orbits. </div>
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And finally, there was a weird, crazy twist. Even in simulations where Planet Nine was chosen to reside in approximately the same plane as the rest of the solar system, the model consistently generated orbits that are nearly perpendicular with respect to the nominal plane of the Kuiper belt. Imagine our surprise when we realized that such a population of objects actually exists! (See also this <a href="http://www.sciencedirect.com/science/article/pii/S001910351500264X" target="_blank">paper</a> by Gomes et al) Ultimately, some additional effort is needed to understand the process by which KBOs acquire perpendicular orbits, but our bets are placed onto the Kozai effect inside mean-motion resonances. </div>
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In the end, our model ties together three elusive aspects of the Kuiper belt (namely, physical alignment of the distant orbits, generation of detached objects such as Sedna and the existence of a population tracing our perpendicular orbital trajectories) into a single, unifying picture. As a dynamical model, this appears compelling. But it is simultaneously important to keep in mind that until Planet Nine is caught on camera, it remains a theoretical prediction. In the mean time, however, we hope that our calculations trigger an observational hunt for Planet Nine, and we will one day wake up to learn that solar photons that have reflected off of planet nine’s frigid surface, have landed onto the aperture of a terrestrial telescope. </div>
Konstantinhttp://www.blogger.com/profile/14245543234165152508noreply@blogger.com50tag:blogger.com,1999:blog-1052332993988376053.post-73748712491367475942016-01-19T11:23:00.003-08:002016-01-19T12:53:08.527-08:00Is Planet Nine a "planet"?<div dir="ltr" style="text-align: left;" trbidi="on">
In 2006, when the International Astronomical Union codified what we mean when we say the word "planet," I was quoted multiple times saying something like, "That's it. That's the end of planets. We get eight in this solar system and that will have to be enough. Since 1845 there have been no new ones to discover."<br />
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I was wrong.<br />
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We think that Planet Nine is between 5 to 10 times the mass of the Earth (some evidence that we are continuing to examine suggests that it might even be closer to 20 times the mass of the Earth; Konstantin is optimistic; I'm skeptical; such tensions are what keep collaborations like ours honest). That puts it at a little smaller than Neptune.<br />
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But is it a planet? The IAU definition of planet includes the clunky phrase that it has to "clear its orbit." Really, this phrase is just an attempt to explain the concept that planets are the gravitational dominant things of planetary system and that one of the ways they display their gravitational dominance is by pushing around everything in their path. Overly literal critics of the IAU definition will insist that because Jupiter has asteroids which co-orbit with it (the Jupiter Trojans) that Jupiter is not a plane by this definition, etc. etc., but that is simply a problem with the clunkiness of the statement of the definition, not of the underlying concept.<br />
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Is Planet Nine gravitationally dominant? I think it is safe to say that any planet whose existence is inferred by its gravitational effects on a huge area of the solar system is gravitationally dominant.<br />
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If that is not good enough for you, though, astronomer Jean-Luc Margot at UCLA has recently written a<a href="http://arxiv.org/pdf/1507.06300" target="_blank"> nice paper </a>finally quantifying what the phrase "clear its orbit" really means. To clear an orbit, an object has to be a certain size, given its distance. I've taken the key figure from his paper, which shows the planets of the solar system and compares them to the "planet" criterion (note that all of the planets are <i>well</i> above the planet line, while the 3 dwarf planets are <i>well </i>below it; this wide separation between planets and dwarf planets is another indicator of how solid the concept of gravitational dominance in the solar system is). If we extend this figure out to the distance and mass of Planet Nine, we find that it, too, is above the planet line for all of our considered cases.<br />
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(technical note: Margot has several different criteria for clearing; we prefer the "clear the feeding zone in 4.5 billion years" criterion, which is the line that we have extended).<br />
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For for much of the predicted range and size of Planet Nine it is comfortably above the line, at its most distant possible orbit and its smallest possible mass, Planet Nine just barely scrapes by as a planet by this calculation. However, we believe that if it really is on the most distant of possible orbits it is probably on the more massive side. Why? Because if it is going to have the effects that we have seen, it needs to be even more massive if it is further away. In short: no matter where it is, the one thing we know for sure about Planet Nine is that it is dominating the outer edge of the solar system. That is enough to make it a planet by anyone's calculation.</div>
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