Dr Tomer Yavetz

Today Tomer Yavetz (Columbia) defended his PhD, which was in part about the dynamics of stellar streams, and in part about macroscopically quantum-mechanical dark matter. The dissertation was great. The stellar-stream part was about stream morphologies induced by dynamical separatrices in phase space: If the stars on a stream are on orbits that span a separatrix, all heck breaks loose. The part of the thesis on this was very pedagogical and insightful about theoretical dynamics. The dark-matter part was about fast computation of steady-states using orbitals and the WKB approximation. Beautiful physics and math! But my favorite part of the thesis was the introduction, in which Yavetz discusses the point that dynamics—even though we can't see stellar orbits—does have directly observable consequences, like the aforementioned streams and their morphologies (and also Saturn's rings and the gaps in the asteroid belt and the velocity substructure in the Milky Way disk). After the defense we talked about re-framing dynamics around this idea of observability. Congratulations, and it has been a pleasure!

snail models; platykurtic galaxies

Suroor Gandhi (NYU) made me in real time some really nice plots today of what a swarm of stars in phase space do over time. Her plots are for the vertical dynamics of the disk. The very exciting thing is that she can reproduce the qualitative properties of The Snail (the phase-space spiral in the local Milky Way disk). Now we have to look at dependence on initial conditions, time of evolution, and potential parameters.

Dustin Lang (Perimeter) and I spoke for a bit about our old project modeling simple galaxy profiles with mixtures of concentric Gaussians. He is trying to build a truly continuous, interpolate-able model for all Sersic indices, and of course (well it wasn't obvious to me before today) at Sersic index of 0.5, the galaxy profile is exactly a Gaussian, so a mixture of Gaussians makes no sense. And then at indices less than 0.5, the distribution becomes platykurtic, so it can't be fit with a concentric mixture of positive Gaussians. What to do there. Lang wants to add in negative Gaussians! I want to say “don't go there”.

data science for stars; phase space

Our weekly Stars meeting at Flatiron was a pleasure today, as it usually is. Angus (Columbia) and Contardo (Flatiron) are looking at the possibility that we might be able to deblend binary and overlapping stars in the TESS data by their light curves alone. That's crazy, but just crazy enough that I love it! We discussed different ways they might get a training set for this. Luger (Flatiron) asked whether it might be possible to figure out the ell and em (spherical-harmonic order) of the asteroseismic modes by using projections onto transits. That also led to some good discussions about possible methods; many of the crowd liked the ideas that look like lock-in amplification. Marchetti (Leiden) gave us a nice discussion of the high-velocity star results from Gaia DR2. It's too early: The really exciting results will come in data releases 3 and 4 when the magnitude limit for the RVS data gets fainter.

Matt Buckley (Rutgers) showed Adrian Price-Whelan (Princeton) and me his results on measuring phase-space volumes of bound and disrupted objects. The idea is that you might be able to reconstruct the mass of a disrupted object, and say whether it was dark-matter dominated. And get all the attendant dark-matter-theory consequences of that. He showed (unsurprisingly) that observational noise increases the phase-space volume that you naively measure. So we discussed how to approach this. If we are frequentists, maybe we can just ”greedily“ correct the measurements in the direction that lowers the phase-space volume? If we are Bayesians, we have to make more assumptions, I think!

dynamics and chemistry

Today Kathryn Johnston (Columbia) test-drove a group meeting at Flatiron on Dynamics, to which I was honored to be invited. We went around the table and described our current dynamics-related projects. After that, it was Stars Meeting, which was its usual hugeness. At the suggestion of its (rotating) organizers, we are experimenting with different ways of making sure many voices are all involved in the conversation. That's a hard problem!

As Stars meeting many interesting things happened. A highlight for me was Adrian Price-Whelan (Princeton) describing work done at Aspen in the last few weeks on the Orphan stream. It looks for dynamical and chemical reasons like a disrupted dwarf galaxy, and it may fully wrap the Galaxy. Another highlight was a contribution from Victor Debattista (UCLAN) looking at chemical abundances in toy (that is, non-cosmological) simulations of star-forming disk galaxies. He has a new explanation for the bimodality between alpha-rich thick disk and alpha-poor thin disk, and his explanation is general, so it implies (as he explicitly predicts in his new paper) that the bimodality will be observed in all disk galaxies! That's exciting. Of course it is hard to observe.

In other news, Matthew Buckley (Rutgers) showed me really beautiful results, in which he can measure the mass of a globular cluster by using phase-space density or volume information, even in the presence of real data issues. The reason it is hard is that the data quality is extremely anisotropic in phase space. It looks extremely promising. I want to figure out how this relates to old-school methods, like virial methods and caustic methods.

evidence for dark-matter in (exceedingly large) colliders

Today Ana Bonaca (Harvard) showed beautifully that the features seen in the GD-1 stellar stream are very well described by an encounter in the past (collision, if you will) with a dark-matter substructure. Her argument is fundamentally qualitative, but so many aspects of the data are matched by the toy model she has made that it is hard to see how to get around the conclusion. This could be huge! We discussed the scope of the paper she could write (or really the content of the abstract).

gravitational clustering, gravitational interferometry

Today Michael Joyce (LPNHE) gave a great talk about analytic and conceptual directions towards understanding nonlinear gravitational growth of structure in the Universe. He focused on the stable-clustering approximation, which dates back to Peebles, is very predictive over a range of scales, and can be used to test simulations. At lunch afterwards, we discussed the great importance of studying gravity analytically, a point made often and well by Roman Scoccimarro (NYU).

Prior to the seminar, Ellie Schwab-Abrams (AMNH) and I discussed self-calibration for pulsar timing arrays, which we think and hope could lead to a new era of gravitational interferometry and enormously increase the sensitivity to long-term gravitational-wave signals. We decided to start by solving the radio-astronomy problem, which has yet to be solved in the literature, because no radio telescope has the problem that the relative velocities of it's elements are unknown!

6-volume, myspace, rules, tellurics

Too many things today for one blog post! So just a rapid-fire list. Matt Buckley (Rutgers) and Adrian Price-Whelan (Princeton) and I discussed whether we could, in practice, measure phase-space six-volumes given a point-set in Gaia or a future data set. It isn't clear, so we started by designing some extremely simple simulations to test.

Price-Whelan and I discussed our myspace project to find the nonlinear transformation of the phase-space data near the Sun to make the phase-space structure as compact or informative as possible. We have a plan for implementation of the data-science side of the project, but we have no idea whether anything we find will be interpretable!

We had our first Stars Meeting under the new rules that we established last week. The objectives are, more-or-less: We want the presenters to be less prepared and we want the audience to be more engaged. We created some rules or guidelines to help achieve these objectives. And the meeting went well! Among other things that happened in this meeting, Price-Whelan showed a forming star cluster he found in the Milky Way halo, possibly connected to the Magellanic gas stream, and John Brewer (Yale) showed micro-tellurics (tiny atmospheric absorption lines) found in some of the very first R=150,000 EXPRES spectra.

On that last point: Brewer found these tellurics by observing a B star, which has no narrow lines (and almost no lines at all), so the narrow absorption lines must be intervening. Megan Bedell (Flatiron) has a data-driven method for finding tellurics even in very featured, narrow-lined spectra, by exploiting the causal structure: Star lines move with the star, atmosphere lines move with the atmosphere! She confirms at least qualitatively, at least some of Brewer's lines. I expect that we have some nice points to make in the comparison.

Oh, and: Unmodeled telluric absorption might be the limiting systematic in exoplanet RV surveys, right now or in the near future.

ergodic stars; blinding and pre-registration

In the Stars group meeting, Nathan Leigh (AMNH) and Nick Stone (Columbia) spoke about 4-body scattering or 2-on-2 binary-binary interactions. These can lead to 3-1, 2-2, and 2-1-1 outcomes, with the latter being most common. They are using a fascinating and beautiful ergodic-hypothesis-backed method (constrained by conservation laws) to solve for the statistical input–output relations quasi-analytically. This is a beautiful idea and makes predictions about star-system evolution in the Galaxy.

In the Cosmology group meeting, Alex Malz (NYU) led a long and wide-ranging discussion of blinding (making statistical results more reliable by pre-registering code or sequestering data). The range of views in the room was large, but all agreed that you need to be able to do exploratory data analysis and also protect against investigator bias. My position is we better be doing some form of blinding for our most important questions, but I also think that we need to construct these methods to permit people to play with the data and permit public data releases that are uncensored and unmodified. One theme which came up is that astronomy's great openness is a huge asset here. Fundamentally we are protected (in part) by the availability of the data to re-analysis.

paper submitted!

Today I presented out chemical-tagging results at Blanton–Hogg group meeting. We show that (now that we can see them with The Cannon) overdensities in chemical space appear also to be overdensities (or at least oddities) in phase space. I followed the meeting by making final edits to the paper, submitting it to the Astrophysical Journal and the APOGEE Collaboration, and putting it on the arXiv. I also sent it to friends and colleagues. This led to an email battle with Charlie Conroy (CfA), who believes our results are somewhere between trivial and wrong!

confusion in angle-spectrum space, and search

At Galaxy Coffee, Trevor Mendel (MPE) showed discussed resolved stellar populations as observed with the MUSE integral-field spectroscopy instrument. They extract spectra using spatial priors based on HST imaging, which is not unlike the forced photometry we did with WISE. This is obviously a good idea in confused fields. That led to a bus conversation with Mendel about the confusion limit as applied to spectroscopic (or multi-band imaging data). The confusion limit is a function (in this case) of the spectral diversity, as well as spatial resolution; indeed a band with low angular resolution but in which there is strong spectral diversity could help enormously with confusion. This is a fundamental astronomy point which (to my limited knowledge of the literature) may be unexplored. We also discussed what the data-analysis problems would look like if we had models of stellar spectra that we believed.

In the afternoon, Price-Whelan and I pair-coded a search algorithm for stellar structures that hew close to one orbit, given noisy phase-space measurements. We chased the problem for a while and then decided we have to suck it up and do some real engineering. Brute-force search is slow! Our usual mode is play first, profile later, but this problem is slow enough that we need to profile before playing. In particular, we have to apply some engineering know-how to the discretization of our model (computed) orbits and to our comparison of data to models (where we probably need a kd-tree or the like).

Kepler, uncertainties, inference

Bernhard Schölkopf showed up for the day today. He spent the morning working with Foreman-Mackey on search and the afternoon working with Wang on self-calibration of Kepler. In the latter conversation, we hypothesized that we might improve Wang's results if we augment the list of pixels he uses as predictors (features) with a set of smooth Fourier modes. This permits the model to capture long-term variability without amplifying feature noise.

Before that, in group meeting, Sanderson told us about the problem of assigning errors or uncertainties to our best-fit potential in her method for Milky Way gravitational potential determination. She disagrees with the referee and I agree with the referee. Ultimately, we concluded that the referee (and I) are talking about precision, but the accuracy of the method is lower than the precision. I think we understand why; it has something to do with the amount of structure (or number of structures) in phase space.

At lunch, we met up with David Blei (Columbia) and shot the shih about data science and statistics. Blei is a probabilistic inference master; we convinced him that he should apply his super-powers towards astrophysics. He offered one of our party a postdoc, on the spot!

use all the data!

I spent the day up at Columbia, with the Stream Team, which is Marla Geha (Yale), Kathryn Johnston (Columbia), me, and parts of our research groups. We discussed just-finished papers, next papers, and things that have come up in the literature. On that last point, we spent some time discussing this paper by Gibbons et al on the Sagittarius stream. The paper makes potential inferences based on data, which is Good, but takes as its "data" a very limited set of measurements—a precession angle (between apocenters), two apocenter distances, and a progenitor 6-d position—and nothing else, which is Bad. We discussed the point that the limited set of measurements they used is not even close to a set of sufficient statistics; in particular, Price-Whelan has shown that you can get multiple potentials for any precession angle, and that the overall shape of the stream and the radial velocities of the stars in the stream will distinguish these options. When your data set contains many measurements (as theirs does) and when your model can predict those measurements (as theirs can), you only hurt yourself by using subsets of the data or limited, derived quantities! (I said all of this to Evans and Belokurov a couple months ago.) I don't want to harsh them out too much, though, because the stream literature has been rife with theory papers that don't confront data at all; this paper is a step in the right direction.

model-free or badly modeled?

Robyn Sanderson (Groningen) is in town to finish our paper (with Helmi) on inferring gravitational potentials using information theory. Our method looks for generic clustering in action-space; it is "model-free" in the sense that it doesn't specify a model; it doesn't even assume the stars are on streams (and it doesn't need to know how many streams, or which stars are in which streams, or whether the streams are really shells, etc). The flip side of this is that it must, therefore, be (implicitly) a bad model.

One way of looking at it is that our method provides an estimator (a point estimate) of the potential. That estimator is either efficient or not. If it is efficient, it is the maximum-likelihood estimator for some model that we have never specified and therefore don't know. That can't be good! Indeed we can see that the estimator is biased, and the bias is bigger than the variance.

However, all that said, the point of this project is to explore the possibility that phase-space is structured, and be agnostic about that structure. This is complementary to my usual kinds of approaches, that make explicit assumptions about the causal or generative process of any structure we are using for inference. The method is (fairly) fast and seems to work, so we are writing.

phase-space structure

Today Robyn Sanderson (Groningen) arrived at MPIA for three days of sprint on a paper about inferring the Milky Way Halo potential by optimizing the information (negative entropy) in the phase-space distribution function. This project involves the horror of transforming the observables to the actions (something I railed against a few days ago), but the method is promising: It permits identification of potentials given phase-space information without requiring that we identify related stars or specific structures at all. The method only requires that there be structure. And of course we are looking at how it degrades as the observational errors grow.

In addition to working on this, we attended the Rix-group Milky-Way group meeting, where (among other things), Wyn Evans (Cambridge) told us about using the apocenter information we have about the Sagittarius tidal stream to infer Halo potential parameters. He gets a low mass for the Milky Way (in accord with other stellar kinematic methods, but in conflict with Leo I's high velocity; is it bound?). I had a bit of a problem with how Evans and his collaborators join up the stream to the progenitor, but that may just be a detail. Hoping to learn more later this week.

NRFG, day 2

It turns out we are still Not Ready for Gaia. Binney (Oxford) opened the day with a strong argument that we should be thinking in terms of action–angle variables, and also a spirited explanation of his torus methods that do their best to approximate any potential with an explicitly integrable potential built from a quasi-optimal foliation of tori. His argument was good. That said, I am very against doing science by transforming the data to action–angle variables and then asking questions there. The transformation (often called sloppily a "projection") is highly non-linear and wrecks intuition about uncertainty. Besides, it depends on having a good potential model, which (I thought) was the whole point! Now Binney is not making this mistake: He wants us to do inference in the space of the observations, but there are certainly projects that transform to action–angle variables and say "look at the structure!" but don't note that the structure might be totally gone if either errors get finite or else the potential model is wrong (and both problems are unavoidable, always).

After Binney, Bovy spoke about his work with Rix modeling mono-abundance populations and getting the mass density in the Milky Way disk as a function of radius (near the Solar Circle). It is a monster project, with beautiful results. It brought to fruition quite a few things, some of which I was involved in, years past.

writing retreat

I spent the week traveling (hence no posts) and writing. I wrote text about the structure function and Gaussian processes for Bovy and Kasper Schmidt (MPIA). I wrote text about fitting a curve to a set of points in phase space for Jagannath. Next week it is back to Heidelberg and back to work.

cusp hypothesis testing

I finally wrote down in detail how we can do a hypothesis test for an ultra-faint galaxy between the cusp-in-projected-phase-space and self-gravitating-blob models. Zolotov is working on the execution.

Johnston

Kathryn Johnston (Columbia) spent the day at NYU, and we talked about many things. We both agree that streams—cold structures in phase space—are the future for constraining the Milky Way potential. We didn't accomplish much, but she encouraged me to finish up our various cold-structure projects!

stream perturbations

Spent time with Johnston today at Columbia and she encouraged me to dust off my manuscript on perturbations of cold streams by compact substructures. We realized that there are already morphological features in the known streams that could be analyzed, at least roughly, in terms of perturbations by substructures. I started to get her to agree that the smoothness and straightness of streams like GD-1 already make them interesting for the dark-matter model. But we both agreed that we can't be quantitative about that until we understand how the disruption of streams by substructure affects their detectability.

cosmic-ray anisotropy, regularization and convergence

I had the privilege of serving on the PhD thesis committee for the defense of Brian Kolterman's (NYU) PhD thesis today. He performed a set of very careful statistical tests of the angle and time distributions of about 10¹¹ few-TeV cosmic rays incident on the Milagro experiment. He finds an anisotropy to the distribution in celestial coordinates, he finds a time dependence to that anisotropy, and he finds the (expected, known) effect of the orbit of the Earth around the Sun. The most surprising thing is the time dependence of the (very small but very high significance) anisotropy. After the very nice defense, Gruzinov and I spent some time arguing about whether the anisotropy and its time derivative were reasonable in the context of any simple model in which the cosmic ray population is fed by supernovae events throughout the disk of the Galaxy. I think I concluded that his results must put a strong constraint on the coherence or large-scale structure of the local magnetic field.

Bovy and I discussed the convergence and regularization of the mixture-of-gaussians model that he is fitting to the error-deconvolved velocity distribution in the disk in the Solar Neighborhood. We read some of the literature on EM and it was very instructive. Now Bovy has some serious coding to do. If he succeeds with all these enhancements, he will be hitting this problem with a very large hammer.