Thursday, September 21, 2017

Planet Nine: where are you? (part 1)

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.


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.


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.


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 path 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 longitude of ascending node (which I’ll just call “node” from now own), the inclination, and (3) where within the orbit the planet is. We’ll call this last parameter the orbital longitude 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).

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 semimajor axis and eccentricity.
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 longitude of perihelion (this is a bit of a simplification, but an unimportant one). The figure here 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.


(If you skipped the details about Keplerian orbital elements, come back now!)

Those are a lot of things to learn if we want to find Planet Nine. Here’s how we’re making progress.

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  the two most recently detected objects as they came from the OSSOS survey which has been shown to have striking biases 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).

In our second paper about a year ago, 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.

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.  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.

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.
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.

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!

Sunday, July 2, 2017

Status Update (Part 2)

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)).

Those of you who have been following the P9 saga for more than a year might remember the article by Chen et al. from last August, which reported the detection of Niku, a ‘rebellious’ Kuiper belt object that orbits the sun in the retrograde direction (see news coverage here and here). 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 detected back in 2008), this discovery did successfully reinvigorate the community’s interest in the high-inclination population of the trans-Neptunian region. 

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:


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 solar system’s early evolution.

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 paper 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. Mark Subbarao 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 here if the player below does not work):

video

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.


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. 

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…


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.

Friday, June 30, 2017

Status Update (Part 1)

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.

When viewed from above, the orbits of the objects look like this:


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.

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.

When you look at the full dataset, however, the propensity for orbital clustering is clear. Shankman et al. 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 recent paper 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.

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.

Let’s now compare this picture with theory. Numerical simulations of solar system dynamics that include P9 (e.g. BB16a BB16b) 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.

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:


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.

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). 

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 paper), 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.

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. 

Thursday, May 4, 2017

Planet Nine: the score card


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.

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.

It’s been a year now. How has the hypothesis fared?

First, let’s review the specific predictions.

(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

(2) These objects will be systematically tilted the same way as the original 6 objects.

Our second paper, a few months later, made a third prediction:

(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.

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:

(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.

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.
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.


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.

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.
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.


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.
The newly discovered objects (green = Sheppard & Trujillo, blue = OSSOS) fit nicely into the predicted pole positions.


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.

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.

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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.

Friday, March 3, 2017

Planet Nine: the movie

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 The Science of the Solar System. 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. CLICK HERE to watch it on Youtube,


If you enjoy this lecture, you might enjoy the whole class. Give it a try. It is, after all, entirely free.

Tuesday, August 2, 2016

Origins

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 origins. Having finished teaching a class on the formation and evolution of planetary systems last quarter, this question has been on my mind as well. 

In essence, there are three potential scenarios for the formation of Planet Nine that have been discussed in the literature. They are (I) outward scattering (II) external capture and (III) in-situ formation. 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). 

Orbit of an outward-scattered planet. Made with Super Planet Crash (http://www.stefanom.org/spc/).

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.

Although I’m a fan of the theory of in-situ formation of giant planets in the inner nebula, 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 gravitational stability criterion, and with its sub-Jovian mass, P9 is probably not a product of direct gravitational collapse. 

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. 

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)

The dynamics of interactions between Planet Nine and passing stars were addressed in a paper 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. 

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. 

From here, we can speculate a bit. On one hand, this timing seems inconsistent with early scattering as envisioned for example by Izidoro et al (2015), 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 the Nice model. 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 here, here and here). To this end, here is a simulation that starts out with an extra Neptune that ejects after about ten million years.

Dynamical evolution of an initially 5-planet outer solar system (from Batygin et al 2012)

If we subscribe to this point of view, then Planet Nine is the solar system’s original fifth giant planet. 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 late heavy bombardment. 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 rethinking how the instability gets activated in the first place. Bummer.

Now, terrestrial planets themselves require ~100 million years to form (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 analysis 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 study 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?

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.

Thursday, March 17, 2016

Where is Planet Nine?

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.

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:


Observational constraints on the orbit and location of Planet Nine in the outer solar system

Michael E. Brown & Konstantin Batygin


 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.






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:

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.


So now you know. Now, please, go find Planet Nine.