how did the Solar System form?

I saw a very nice talk today by Philippine Griveaud (MPIA) about how the Solar System formed. The idea is that the giant planets formed in an accretion disk. Their formation opened gaps and caused migration (first Type I and then Type II, if you must know :). That migration pulled them into a resonant chain. That is, if the giant planets formed the way we think they formed, they must have been in a resonant chain. But they aren't in such a chain now; what gives?

The idea is that when the gas is expended (or blown out by winds), the remaining planetestimals (think: asteroids, comets, Kuiper Belt objects) interact with the planets such that they get moved from orbit to orbit and eventually ejected. These dynamical interactions break the resonant chain, migrate the giant planets to their current locations, and scatter rocks and ice balls into the interstellar regions.

It was a great talk, but also led to a lot of interesting questions, such as: How does this all fit in with the formation of the rocky planets? And how does this square with our observations (growing rapidly, apparently) of interstellar asteroids? Oh and: How does all this connect to observations of debris disks, which I now (officially) love.

Gothamfest

Once a year (and differently every year), we get together as much of the astronomical community in New York City as we can and have them give fast talks. Today was great! I learned a huge amount, and no highlight reel would do. But here are some examples: Amanda Quirk (Columbia) has great data on M33 stars that maybe we could use to build images of the orbital toruses using technology that Price-Whelan and I developed over the last few years? Marc Huertas-Company (Paris) said (confidently?) that many of the star-forming galaxies found by JWST at very high redshift are likely prolate. Michael Higgins (CUNY) and Keaton Bell (CUNY) have a beautiful system to separate sources of variability out in NASA TESS data using structure in frequency space. Kate Storey-Fisher (NYU) showed results from Giulio Fabbian cross-correlating her ESA Gaia quasar sample with the ESA Planck lensing map, with better error bars than any previous survey! Ben Cassese (Columbia) showed a moving-object pipeline with NASA TESS imaging that detects outer Solar System objects, much like old work by Dustin Lang and myself.

patches of imaging

I am discussing with Sean Ku (NYU) and Victor Kuang (NYU) the NASA Cassini imaging of Saturn. We want to make (from the data) a high-quality face-on picture of the rings. This is a problem (from my perspective) in computer vision, so we need a camera model (and a lot of other things). One thing I hypothesized about this problem today is the following (am I right?):

Any sufficiently small patch of a camera image can be modeled with a pinhole-camera-like camera model, provided that we give the camera model the freedom to make the image plane not perpendicular to the line from the pinhole to the patch of the image plane. Is this correct? We are about to find out, the hard way.

I'm wrong about HORIZONS

The JPL HORIZONS system is amazing! You can compute the position of anything in the Solar System, at any time. With Weichi Yao (NYU) and others, I have been looking at Halley's Comet, with the thought of making a machine-learning benchmark data set (this is an idea from Soledad Villar, JHU). When we look up Halley in HORIZONS, we find many Halleys, not just one. I hypothesized that this is because there are different solutions for Halley on different apparitions. But somehow I am sort-of wrong: That's true for most of the Halleys in the system. But then today in our meeting Yao showed that there's one that seems to do well at all epochs. Huh? Anyway, HORIZONS is better on content than documentation!

astrology: Yes, it's true

Today Paula Seraphim (NYU) and I extended our off-kilter research on the possibility that we live in a simulation to off-kilter research on whether astrology has some basis in empirical fact. It does! There are birth-season correlations with many things. The issue with astrology, oddly, is not the data! It is with the theory that it is all related to planets and constellations. And if you think about the causes of birth-season effects on personality and capability, most of them (but not all of them) would have been much stronger 2000 years ago than they are today!

frequencies and resonances

My day had a twitter (tm) component in which I asked about the correspondences between gaps in Saturns rings and low-integer-denominator resonances with Saturns moons (and, I learned, planetary seismic modes). This led me to Jason Hunt (Flatiron), who I asked about resonances in the Milky Way disk: Can the gaps in velocity space in the local disk be associated cleanly with particular resonances with the bar or spiral structure or Sagittarius? He thought yes, for some, and made some nice plots of the three orbital frequencies as a function of velocity in the local neighborhood. These are all steps towards (in my mind) figuring out the frequencies of disk perturbations more-or-less directly from the data.

periodograms and posteriors; also barycentric astrometry?

Winston Harris (MTSU) and I looked at the output of The Joker and the Lomb-Scargle periodogram on his fake exoplanet radial-velocity data. They maybe look similar. It makes sense, since they are both doing a simple likelihood-based linear fit of periodic functions.

I spent some time putting together a notebook to test the idea that Josh Winn (Princeton) had that the Solar System barycentric radial-velocity correction could be indicative of the stellar astrometry for the very brightest stars, where precise astrometry is (strangely) hard. It should be possible at some level, since the barycentic correction does depend on the astrometry! I love the idea of doing astrometry by taking radial-velocity measurements.

finding outer Solar System objects in TESS

Ben Montet (UNSW) put up the bat symbol for a project to find outer Solar System objects using NASA TESS data. It was the scale of problem I wanted: A stack of postage stamps from eleanor and a reflex angular velocity vector (really parallax vector) for Sedna. The issue is all those other pesky stars, and asteroids on closer orbits! I did some exploratory data analysis, in which I detrended each image using a PCA of all the images. But at the same time, others did pixel-based detrending like in CPM and others did more traditional image differencing with a reference image. It's nice: In all methods, Sedna sticks out beautifully! The question is: What methods will be best for finding objects further out in the Solar System? These are harder because they are fainter, but also because they don't move as far relative to the stars in a month!

calibrating spectrographs; volcanic exo-moons

I had a conversation with Ana Bonaca (Harvard) early today about the sky emission lines in sky fibers in Hectochelle. We are trying to understand if the sky is at a consistent velocity across the device. This is part of calibrating or really self-calibrating the spectrograph. It's confusing though, because the sky illuminates a fiber differently than the way that a star illuminates a fiber. So this test only tests some part of the system.

At the Brown-bag talk, Bob Johnson (Virginia) spoke about exo-moons and in particular exo-Ios. Yes, analogs of Jupiter's moon Io. The reason this is interesting is that Io interacts magnetically and volcanically with Jupiter, producing an extended distribution of volcanically produced ions in Jupiter's magnetic field. It is possible that transmission spectroscopy of hot Jupiters is being polluted by volcanic emissions of very hot moons! That would be so cool! Or hot?

#GaiaSprint, day 2

After playing with visualization yesterday, Christina Eilers (MPIA) and I got the idea that perhaps the radial-velocity variations we see in the Milky Way disk might indicate density variations. In particular, does the radial-velocity field converge on high-density regions in the disk (spiral arms, say) and diverge on low-density regions (inter-arm gaps, say)? Sarah Pearson (Flatiron) came to our rescue with a nice visualization of the density and velocity fields, in which she could smoothly go from showing one to the other. And indeed, our intuitions were justified, at least qualitatively.

In the evening check-in, Paolo Tanga (Côte d'Azur) showed some beautiful results on the ESA Gaia coordinate systems relative to other catalogs. He calls these differences "zonal corrections" for historical reasons! I asked him how he knows which of the coordinate systems is best, and he said: In the best frame, the asteroids will travel on calculable trajectories. (I would say gravitational trajectories, but for asteroids, radiation pressure and other forces are relevant too!) So the best coordinate system will be Newtonian in the Solar System! Of course given frame dragging, and strictly speaking, Newtonian for the Solar System will not be Newtonian for the Galaxy! I asked about that and it led to some discussion with Larry Widrow (Queen's). I have much to say about all this, but I'm not yet ready to say it out loud.

Math+X Houston, day 2

Today was day 2 of the 2019 Math+X Symposium on Inverse Problems and Deep Learning in Space Exploration at Rice University in Houston. Again I saw and learned way too much to write in a blog post. Here are some random things:

In a talk about provably or conjectorally effective tricks for optimization, Stan Osher (UCLA) showed some really strange results, like that an operator that (pretty much arbitrarily) smooths the derivatives improves optimization. And the smoothing is in a space where there is no metric or sense of adjacency, so the result is super-weird. But the main takeaway from his talk for me was that we should be doing what he calls “Nesterov” when we do gradient descent. It is like adding in some inertia or momentum to the descent. That wasn't his point! But it was very useful for me.

There was a great talk by Soledad Villar (NYU), who showed some really nice uses of deep generative models (in the form of a GAN, but it could be anything) to de-noise data. This, for a mathematician, is like inference for an astronomer: The GAN (or equivalent) trained on data becomes a prior over new data. This connects strongly to things I have been trying to get started with Gaia data and weak-lensing data! I resolved to find Villar back in NYC in February. She also showed some nice results on constructing continuous deep-learning methods, which don't need to work in a discrete data space. I feel like this might connect to non-parametrics.

In the side action at the meeting, I had some valuable discussions. One of the most interesting was with Katherine de Kleer (Caltech), who has lots of interesting data on Io. She has mapped the surface using occultation, but also just has lots of near-infrared adaptive-optics imaging. She needs to find the volcanoes, and currently does so using human input. We discussed what it would take to replace the humans with a physically motivated generative model. By the way (I learned from de Kleer): The volcanoes are powered by tidal heating, and that heating comes from Io's eccentricity, which is 0.004. Seriously you can tidally heat a moon to continuous volcanism with an eccentricity of 0.004. Crazy Solar System we live in!

In the afternoon, Rob Fergus (NYU) talked about the work we have done on exoplanet direct detection with generative models. And he has done the same (more-or-less repeated our results but with Muandet and Schölkopf) with discriminative models too. That's interesting, because discriminative models are rarely used (or rarely power-used) in astronomy.

phase-space volume; Oort dynamics

The research highlights of the day were a call with Matt Buckley (Rutgers) and a Physics Colloquium by Scott Tremaine (IAS). In the former, we discussed the design of a first paper about Buckley's work on measuring phase-space volumes of bound and disrupting dynamical objects in the Milky Way halo. He has some great results! But we don't understand the sensitivities to noise yet, or the in-practice issues of making robust measurements. And I mean “robust” here in the statistical inference sense.

In the latter, Tremaine answered most of the questions we formulated a few weeks ago about the origin and properties of the Oort cloud. My loyal reader may know that I am suspicious about many of the things that are said about the Oort cloud, but Tremaine showed numerical results that seem to back up most of the lore. He then switched to talking about interstellar asteroid 'Oumuamua. Aside from the usual loose talk of aliens, Tremaine said something remarkable: The pre-Solar-System velocity vector of the object is very close to current consensus on the Local Standard of Rest (something else of which I doubt the existence). Tremaine noted that it might conceivably represent an amazingly accurate measurement of the LSR! Too early to tell yet.

Trojans, Oort Cloud, greedy algorithm paradox

Early in the day, undergraduate Mitchell Karmen (NYU) blew me away by showing a possible Trojan satellite hiding in the Kepler false-positive bin. It probably has some other explanation, but damn it's exciting! I discussed this with Rodrigo Luger (Flatiron) who dampened my excitement (for good reasons).

At stars meeting, Michele Bannister (Belfast) spoke about ways in which we might use the properties of the outer Solar System (and especially the things past the Kuiper Belt and including the Oort Cloud) to constrain the birth environment and subsequent dynamical environment of the Sun at formation. It appears that these structures could be created early and are strongly modified by nearby stars and close passages. One implication is that different stars should have very different Oort Clouds. That's a great prediction; now how to test it?

Mike Blanton (NYU) showed some very cool results from the work being done on SDSS-V robot fiber positioners. As you might guess, the positioning of fibers on a focal plane by robot arms that can collide is an intractable problem in general—it's like traveling salesman. But you might also know that most NP problems are pretty well-served by sensible greedy algorithms. That is, you can usually do something akin to the simplest thing and still succeed most of the time.

Blanton showed the interesting thing (worked out by Conor Sayres at UW) that if they do a greedy algorithm to take the robot arms from the "home" state to the configuration they want, it is very slow and hard, and it still fails in many cases. But if they do the exact same greedy algorithm the other way—that is, to take the arms from the configuration they want back to the home state—it works fine! So they do that and then run the result backwards!

Crazy talk. And cool. And worthy of a lot more thought. And something about entropy? After all, the home state is like a crystal.

planetesimals!

Today Michele Bannister (Belfast) gave a great talk about the outer Solar System. She was very clear that her observations do not rule out in any way the existence of Planet 9. But they do discredit every single shred of evidence in its favor! And she gave many other mechanisms that could explain the same data. That is, there really doesn't seem to be any reason to believe that there is an unknown planet hanging out in the outer Solar System. Lots of what she said relies on the following theoretical observation: When a planetesimal is perturbed by a massive body on an orbit interior to its perihelion, it tends to preserve its perihelion but change its semi-major axis. And the same but opposite when the massive body is outside it's aphelion. All planetesimal migration scenarios must respect these constraints.

Before that, Kate Storey-Fisher (NYU) and I had a long conversation in which we re-discovered our confusions about the differences between the continuous Fourier transform (which never exists in any real-data context) and the discrete Fourier transform (which is what's appropriate when the data are treated as a patch of a periodic function. We got confused and then un-confused, but I am still somewhat confused!

asteroids and dark-matter halos

Today Michele Bannister (Belfast) showed up. We spent time talking about how asteroids are characterized in time-domain imaging surveys. The idea is to make a fictitious absolute magnitude, which is what the asteroid would look like if it was simultaneously 1 AU from the Sun and 1 AU from the Earth, and observed with the Sun and Earth both getting it from the same angle. That's not real! We discussed how we might improve that situation.

I also spoke with Lauren Anderson (Flatiron) about how we might reduce the dimensionality of cosmological simulations of galaxies to a small parameterization of what's possible. The idea is to get a not-too-complex parameterization of the triaxiality of galaxy dark-matter halos and their dependences on time. I have a vision here, but it isn't clear it is possible to execute. We discussed the issues of using existing simulations or running our own.

making the angle distribution uniform

Years ago, Jo Bovy (now Toronto) and I wrote this crazy paper, in which we infer the force law in the Solar System from a snapshot of the 8 planets' positions and velocities. Because you can't infer dynamics from initial conditions in general, we had to make additional assumptions; we made the assumptions that the system is old, non-resonant, and being observed at no special time. That led to the conclusion that the distribution function should depend only on actions and not on conjugate angles.

But that's not enough: How to do inference? The frequentist solution is orbital roulette, in which you choose the force law(s) in which the conjugate angles look well mixed or uniformly distributed. That's clever, but what's the Bayesian generalization? (Or, really, specification?)

It turns out that there is no way to generate the data with a likelihood function and also insist that the angles be mixed. In Bayesian inference, all you can do is generate the data, and the data can be generated with functions that don't depend on angles. But beyond the generative model, you can't additionally insist that the angles look mixed. That isn't part of the generative model! So the solution (which was expensive) was to just model the kinematic snapshot with a very general form for the distribution function, which has a lot of flexibility but only depends on actions, generate the angles uniformly, and hope for the best. And it worked.

Why am I saying all of this? Because exactly the same issue came up today (and in the last few weeks) between Rix (MPIA) and me: I have this project to find the potential in which the chemical abundances don't vary with angle. And I can make frequentist methods that are based on minimizing angle dependences. But the only Bayesian methods I can create don't really directly insist that the abundances don't depend on angle: They only insist that the abundance distribution is controlled by the actions alone. I spent the non-discussion part of the day coding up relevant stuff.

the very local neighborhood

Today Jackie Faherty (AMNH) gave the astro seminar at NYU. She got us fired up about Gaia even before her talk, at lunch, where she said that on April 25 the curtains would finally open and we would get to see the Milky Way for the first time! Her seminar didn't disappoint: She pointed out that of the five closest stars to the Sun, three were discovered in 2014! And it appears that the Solar Neighborhood still has lots of secrets for us to discover. She also showed us a star that passed within 60,000 AU of the Sun some 70,000 years ago. That's interesting! If it disturbed comets onto elliptical orbits, we won't see their infall for a few million years! (Just a free-fall argument there.) That observation, combined with things people have found in Gaia DR1, suggests that we have a close encounter like that about once per million years.

#siRTDM18, day 5

Armin Rest (STScI) gave a nice talk about time-domain astronomy, with stuff about finding Earth-impactors and also light echoes. After his talk, I told him the insane project conceived by Rix, Schölkopf, and me about modeling the whole Milky Way as a set of flickering light sources and a three-dimensional map of dust, using time-domain imaging at very low brightness. That's probably not possible! Rest is part of a big new sky survey for near-earth asteroids, which will also do a lot of variable-star science.

After that, Sarah Richardson (Microbyre) talked about automating various aspects of phylogeny for various kinds of microbes. I was impressed by the robotics setups available to biologists! Her talk also contained a lot of biology-101 content for the physicists and engineers; I learned a lot (and felt, once again, my regret that I didn't take more biology in college!).

Late in the day, Josh Bloom (Berkeley) and I did some real-time decision-making at the Emoryville card room.

data predicting data; bad Solar System

First thing in the morning, I met with Judy Hoffman (Berkeley) to discuss her computer-vision and machine-learning work. She suggested that machine-learning methods that are auto-encoder-like could be repurposed to make predictions from one kind of data to another kind of data on the same object. For instance, we could train an encoder to predict exoplanet RV signal, given Kepler light curve. Or etc! This appeals to me because it uses machine learning to connect data to data, without commitment to latent quantities or true labels for anything. She pointed me (relatedly) to a new kind of model called ADDA, for which she is responsible.

In the afternoon, Chiara Mingarelli (Flatiron) gave the NYU Astro Seminar about pulsar timing and gravitational radiation, expressing the hope and expectation that this method will deliver signals soon. She told a very interesting story about a false-positive detection that nearly went to press when they figured out that it was resulting from residuals in the Solar System ephemerides. The SS comes in because you have to correct Earth-bound timings to a frame that is at rest (or constant velocity with respect to) the SS barycenter.

This isn't the first time I have heard this complaint. The astronomical community really needs an open-source and probabilistic SS ephemeris, so we can use the SS model responsibly inside of inferences. Freedom-of-information act time?

SPHEREx workshop, day 2

I got up at 0530 and looked at the participants and schedule for the SPHEREx workshop. I realized that I had prepared precisely the wrong talk yesterday! So I threw away my slides and made completely new slides. It was rushed. I forgot things. But it was still an improvement. I switched from saying things about scientific goals to saying things about technical improvements or extensions that could make the project more capable in respects that would serve the needs of (among other things) stellar science.

I then headed in to the workshop; I could only make it to the second day. I learned so much today. I can't do it justice. Here are some random facts: A lot could be learned about exoplanets if we could get bolometric fluxes for the stars.
I knew this already, I guess, but the prospects for SPHEREx here are excellent, if the project can deliver absolutely calibrated flux densities. There is a mass–metallicity relationship inside the Solar System! The Solar System contains Trojan satellites/asteroids around Neptune, not just Jupiter! There is no model for the zodiacal light in the Solar System that matches the observations to the level of precision that an infrared survey would need to remove or avoid it. The zodiacal light is consistent with being made up of ground up asteroids and evaporated comets! ALMA has observed many debris disks around nearby stars; some of these are angularly huge. The poster child is Fomalhaut, which has a thin, elliptical ring. It's a crazy thing. I learned these things from a combination of Dan Stevens (OSU), Jennifer Burt (MIT), Carey Lisse (JHU), and Meredith MacGregor (Harvard), but that's just a tiny sampling.

At the end of the day there was discussion of calibration, led by Doug Finkbeiner (CfA) and me. I very much enjoy the technical challenges for SPHEREx and the enthusiasm of the team taking them on.