AstroFest, day 3

Today was the third and final friday of the Gotham AstroFest series, in which we have a very large fraction of the entire astrophysics community in New York City give short talks. This was at NYU, and had contributions from NYU, AMNH, and CUNY scientists. There were a huge number of interesting results in the day. One of the most remarkable things about the day is that fully one quarter of the talks were about black holes. Between NYU and CUNY, there is a lot of research going on related to black holes: Their formation, primordial black holes, their binary dynamics, gravitational-wave signatures, and so on. That's excellent.

A few random highlights for me included: Evidence for weather on brown dwarfs as a function of temperature and gravity by Vos (AMNH), and (relatedly) comparisons between planet and brown-dwarf spectra by Popinchalk (CUNY). It really does appear that there are no strong differences between brown dwarfs and planets (something I discussed with Oppenheimer, AMNH, at lunch). Gandhi (NYU) showed some chemistry and orbits work she has done with Ness (Flatiron) before coming to NYU; that's very related to my interests! Williamson (NYU) visualized a linear SVM, which is beautiful (and old-school). MacFadyen (NYU) convinced us beautifully that his models of the NS—NS merger are really the best!

There was lots on dark-matter detection and dark-matter candidates, including even baryonic and black-hole types. And Tinker (NYU) showed beautiful satellite-galaxy statistics that he got by stacking and background-subtracting galaxy counts in the Legacy Survey imaging for DESI.

If you want to see the full slide deck for the event, it is here.

how to write a discussion section

In a low-research day, a highlight was a long conversation with Bonaca (Harvard) about the writing of her paper on the GD-1 stream interaction. We discussed structure, and especially the discussion. In a discussion, I like a humble sandwich on proud bread: Start by saying what's most impressive about what we've done, then go into caveats, limitations, approximation wrongness, and the consequences of all that. And then end on a positive note about what kinds of great new things this work will enable going forward.

Late in the day, Alex Kusenko (UCLA, IPMU) spoke about a very wide range of subjects. He claims to have a full explanation for why we don't see the cutoff in the gamma-ray occurrence rate required by photon–photon interactions with the infrared background. He claims that the gamma rays we see from blazars are really reprocessed from cosmic rays. Plausible! But I would need to know a lot more. He also claims to have a way to naturally make primordial black holes in the end stages of inflation, and make all of the dark matter that way. That's interesting. Unfortunately it was such a long and tiring day I couldn't get it together to really check either of these ideas carefully.

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!

structure of all models, ever; correlation-function representation

Early in the day I had a long conversation with Leistedt (NYU) about the philosophy of our machine-learning projects. We refined further our view that the machine learning should be part of a larger causal structure that makes sense. My position is that you can think of most (hard) physics problems as having some kind of generalized graphical model with a three high-level boxes. One is called “things I know well but don't care about”, which is things like noise model, instrument model, and calibration parameters. Another is called “things I don't know and don't care about” which is things like foregrounds, backgrounds, and other nuisances. And the last is called “things I don't know and deeply care about”. This last one is our rigid physics model. And the middle one is where the machine learning goes! If we could build models like this very generally, we would be infinitely powerful.

At mid-day, Storey-Fisher and I talked about all the things we could do if we had a correlation function that is not values-in-bins, but was a linear combination of functions. We could look for cosmological gradients. We could do clustering multipoles at small scales, we could estimate the correlation function and power spectrum simultaneously, we could extract Fisher-optimal summary statistics for cosmological parameter estimation. And all these things are possible with our new correlation-function estimator. Next step: Getting the code fast enough to do non-trivial tests.

In the astro seminar at NYU, Savvas Koushiappas (Brown) showed us weak but very interesting evidence that maybe there is a dark-matter annihilation signature in the NASA Fermi data on the Reticulum II dwarf galaxy. Obviously this is incredibly important if it holds up as more data and better calibrations come.

writing; not ready for TESS

I got some actual writing time in today! I worked on places in the Birky (UCSD) paper (on M-dwarf spectral models) where Birky had left me notes marked "HOGG". That's a great tool: She leaves "HOGG" notes; I search for them in my text editor, and I make the relevant changes or add the relevant text.

Late in the day I had a great conversation with Ben Pope (NYU) about things we can do right now or very soon with TESS artificial data or the first data release of full-frame images. We talked about dimensionality reduction methods, like the robust
PCA methods from Candès and related methods that use convex optimization. We also talked about independent components analysis. In general, when the first data arrive, there will be lots of low-hanging fruit. We also discussed what could be done in advance, with the available artificial data.

finishing a paper; latents

I dusted off the draft of my paper with Eilers (MPIA) and Rix (MPIA) about spectrophotometric measurements of red-giant distances or parallaxes using Gaia SDSS APOGEE, 2MASS, and WISE. It is nearly done! But we put it on ice while Eilers finished other things. I worked through more than half of the text, making notes on what small things remain to do.

The biggest to-do item? We have a linear model (for the log distance or log parallax or absolute magnitude). That's sweet, because it is simple, and it is interpretable, at least partially. Now we have to make that true by interpreting. Interpreting a linear model is harder than fitting a linear model!

I also had conversations with Storey-Fisher (NYU) about models for the correlation function and Price-Whelan (Princeton) about Milky Way non-equilibrium dynamical models. On the former, we discussed the difference between the correlation function and any particular estimate of the correlation function. It's a bit complex, because I'm not sure there is even agreement in the community about what would be considered the true latent correlation function in the low-ish redshift Universe.

stream-as-torus; TESS FFIs

I met up early with Price-Whelan (Princeton) to work on the chemical-tangents method papers. This work devolved into rearranging and organizing into categories the to-do list, using GitHub's project tools. That was useful! But it felt a bit like we didn't get anything done. I know that isn't true!

A bit later in the morning we called Jo Bovy (Toronto) to get some advice for Lauren Anderson (Flatiron) on fitting streams in the Milky Way halo. I had been summarizing one of Bovy's papers as saying that streams are close to orbits (that is, you can fit a stream as an orbit) but Bovy corrected us: His paper shows that streams are close to tori. That is, you can expect all the stars in the stream to have similar actions or invariants, but they will not line up as a line on the torus the same way that a single segment of a single orbit would. Duh! That makes good sense and suggests a beautifully simple method for modeling streams with tilted torus sections. I think I almost know how we might do that.

I also checked in with the group working on NASA TESS full-frame images (FFIs), led by Ben Montet (Chicago), who have been hacking at Flatiron all week. They intend to reformat the full-frame images into manageable (and more useful) data objects, extract aperture photometry flexibly, and perform best-in-class de-trending using other stars or other pixels, in the spirit of many things we have done over the years with Kepler data. They really look like a team that might take over the world! For context: The TESS Mission plans to release the raw FFIs with no proprietary period, and they plan to leave it to the community to build open-source (or not!) data-analysis tools around them. Go team!

GD-1 and chemical tangents

Tuesdays and Thursdays are lower on the research this semester! But I did get in two excellent discussions. The first was with Bonaca (Harvard) who has made an absolutely great visualization that compares the Gaia data on GD-1 and her model for GD-1. I think this figure might get featured in a lot of talks! We are still checking things, but it looks great. We discussed what would be the final scope of her paper, because—as with all projects—there is a huge possible scope but we need to finish a paper soon! I'm happy with the scope and it seems achievable and sensible. The big issue is that the constraints we have on the perturber than interacted with GD-1 come from a model that has toy aspects to it, while the full generative stream model is expensive enough that we don't want to go there for inference just yet. Soon, but not for this paper.

Over a late lunch I discussed many things with Price-Whelan (Princeton), both about GD-1 and about our chemical tangents project. On the latter, we discussed (for approximately the millionth time) how to describe the project most compactly. This project is strange enough for the typical astronomer, that we have to think carefully about how we present it. There are a lot of things that sound right but are wrong. And I am a huge believer in repeatedly re-describing projects. I think every time you go through it, you learn something new, and improve your presentation. This is a huge benefit of fully Open Science.

In that spirit: We are trying to find the surfaces in phase space along which the distribution of stars in abundance space is constant. Not the abundance is constant, but the distribution in abundances. Those surfaces contain the orbits! In some sense it comes down to the point that the joint distribution in actions and abundances is not separable, so the abundances can inform you about the actions! But that description is too terse. And Rix likes to say: Stars don't change their abundances as they orbit! So if you have drawn orbits through phase space that would require abundance changes, either your population isn't mixed or else you are wrong about those orbits.

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.

large-scale structure

Tuesdays are low-research days! But I did have a good conversation with Storey-Fisher (NYU) about our correlation-function estimator, and how to precisely test it. It has so many applications! We also discussed how our three projects fit together: Correlation-function estimation, adversarial mock catalogs, and searching for anomalies in the large-scale structure. The middle project—adversarial mocks—is about making mocks that have systematics that would defeat current systematics correction, and also making methods that would defeat even those mocks.

out sick

Mondays don't seem to agree with me!

there's no such thing as a Jeans model!

The Jeans Equations are remarkable: They relate moments and integrals of distribution functions to the underlying gravitational potential (or really force law), for phase-mixed populations. They are true for any distribution function! But they are equations, and they are not models. As my loyal reader knows, for me a model is a likelihood function!

When people do what is called Jeans modeling, they turn the equations into some procedure for estimating the gravitational potential (or force law or mass density). And although the Equations are independent of distribution function, the performance of this heuristic procedure—that goes from velocity moments to gravitational model parameters or densities—has statistical properties that do depend strongly on the distribution function. That is, you can't make a probabilistic statement (like a measurement and an uncertainty) of anything (like a density at the Milky Way disk midplane) without assuming things about the distribution function.

And because the Jeans Equations are independent of the distribution function, it is tempting to claim or believe that the results of the inference are also independent of the DF, which they aren't. There is no procedure you can write down that isn't. I spent time this weekend writing words about this, for reasons I can't currently understand.

Gotham AstroFest, day 2

As my loyal reader will recall, there are AstroFest events this September at Columbia (last week), Flatiron (today), and NYU (in two weeks). Todays meeting was long but excellent. I learned many things and was pleased to see all the new faces (so many new faces)! Here are a few personal highlights:

Shy Genel (Flatiron) showed that the details of star formation and feedback affecting a simulated galaxy disk or stars is very sensitive to the initial conditions or perturbations to the conditions made mid-simulation. That caused me to wonder if it is going to be very hard to infer things about galaxies from their observed properties! But Foreman-Mackey (Flatiron) pointed out that the sensitivity might be high but also highly structured, so not necessarily a problem. Good point; but it might take a lot of simulations to find out! Whatever the case, this is an excellent line of research.

Francisco Villaescusa-Navarro (Flatiron) described a project to see if, in the non-linear regime of large-scale structure evolution, the one, two, and higher-point functions, all combined, contain as much information as the one- and two-point functions in the linear regime. That is: What is the information content in the observables? This is, in some sense, the key question of cosmology at the present day! And relates to things I have been thinking about (but doing nothing about) for years.

Suvodip Mukherjee (Flatiron) delivered a beautifully simple (and yet novel) idea: He is looking at all the cosmological observables with gravitational-wave sources that we have with galaxies and the CMB. That's clever! It includes the GW LSW effect, and GW lensing. He pointed out that there might be new cosmological constraints from cross-correlating GW event properties with CMB properties, like the CMB lensing map. Clever! And possibly big, in the mid-term to long-term future.

Doyeon Avery Kim (Columbia) is building spectral-spatial models of the all-sky fields or maps that act as CMB foregrounds. She is doing this by interpolating in spatial and spectral directions the (necessarily incomplete, different sky coverage, different angular resolutions) information from many large-angular-scale surveys. This is also very much related to my (vapor-ware) latent-variable model approach here, and is looking like it is delivering exciting results.

chatting

I spoke briefly with Chris Ick (NYU) about quasi-periodic oscillations in Solar flares, Megan Bedell (Flatiron) about telluric lines in stars observed with HARPS, and Adrian Price-Whelan (Princeton) about finding overdensities in the halo in Gaia DR2 data. With Ick we discussed whether to use the Bayesian evidence or a parameter estimate to compare nested models. My loyal reader knows which side I was on! With Bedell we discussed how we might verify that our telluric model is good, using line covariances. With Price-Whelan we discussed how to estimate local overdensity in both position and proper motion that would be maximally sensitive to streams and the like.

dust mapping; information theory and orbits

In Stars Meeting today, visitors Greg Green (KIPAC) and Richard Teague (Michigan) both talked about mapping dust. Teague is working at protoplanetary-disk scale (using velocity maps to find planets), while Green is working at Milky Way scale (making 3-d extinction maps). Teague is working with Foreman-Mackey (Flatiron) to get better velocity maps out of ALMA data and they are getting good success with one of my favorite tricks: Fit the peak with a quadratic. We have shown, in astrometric contexts, that this saturates information-theoretic bounds. They have gorgeous maps!

Green is trying to apply more useful spatial priors to the dust maps he has made of the Milky Way, which are (currently) independently sampled in pixels. He is resampling the pixels, using neighbor information to regularize or as a prior. His method is slow, but a lot faster than using a fully general Gaussian Process prior. And it appears to be a good approximation thereto. Certainly the maps look better!

I presented my project to figure out orbits from chemistry. There was good discussion. Spergel (Flatiron) opined that I would do no better than Jeans modeling if I did the Jeans modeling conditioned on chemistry. I am sure that's wrong! But I have to demonstrate it with a good information-theoretic argument.

new correlation-function estimator

My research tidbit for the day was a long conversation with Kate Storey-Fisher (NYU), in which we discussed our new estimator for the correlation function that can estimate vector (or tensor or higher order) quantities. That is, it doesn't have to estimate the correlation function in bins, it can estimate any aribtrary parameterized representation sensibly. This includes, say, a parameterization that is derivatives with respect to cosmological parameters. That would estimate the cosmological parameters directly from the positions of galaxies! It also includes, say, a fourier representation. That would estimate the correlation function and the power spectrum simultaneously! It also includes, say, dependencies of the correlation function on redshift or position, which would test cosmological growth of structure and cosmological homogeneity. Etc! I'm stoked.

In the course of the discussion we came up with a strong test of the estimator: An affine-invariance test: If we make an affine transformation of the model regressors, do we get the same results at the correlation-function level? That's a great test, and something we can do easily and now. If we don't pass, our estimator is just plain wrong!

out sick

[No research today.]

AstroFest

For many years, Columbia Astronomy has had a tradition of having everyone in the Department give a short talk in a monster, full-day event called AstroFest. This year, we extended it to three Fridays, and covering all parts of NYC Astronomy. The first of these days was today, at Columbia, and it was great! I learned many things. Here is a smattering:

There is interesting laboratory astrophysics going on at Columbia, including experiments to measure deuterium molecular formation and dissociation rates (reported by Bowen) and experiments to measure aspects of Alfven wave propagation that might be relevant to Solar Coronal heating (reported by Bose).

Spinning black holes in a magnetic field charge up, and this might lead to pulsar-like activity in the late stages of a BH-NS inspiral (reported by Levin). After that I asked if any of the electromagnetic effects might affect the gravitational-wave signal itself, and the answer is unlikely, or only at a very low level.

You can't tell the shape of a transiting object from the shape of the transit (reported by Sandford). There are strict degeneracies! That led the audience to ask about regularization. You can break these degeneracies with regularization, but the answers will depend on the form of that regularization. I was wondering if star spots or limb darkening could break the degeneracies interestingly?

If you slowed down the rotation of the Earth, it would get colder, and more uniform in temperature between equator and pole (reported by Jansen)! That was a great use of Earth climate models to inform the study of exoplanets. And it maybe violates my simplest intuitions. New cure for global warming: Slow down Earth rotation!

And I was only there for the morning.

talking

My only real research today was conversations with Bonaca (Harvard) about her stream–dark-matter substructure collision problem, explaining features in the GD-1 stream. We discussed ways to analyze how important the stream thickness is, without actually building a realistic model of the stream thickness. That is, our simplest simulations treat the stream as arbitrarily thin, but the best impact models may not be clearly in the thin-stream limit.

comoving stars and chaos, tellurics and radial velocities

I'm back in the city and back for the Stars Meeting at Flatiron. It did not disappoint! We went around the room and did long, post-summer introductions. In that process, many good ideas came up! I learned that John Brewer (Yale) has a great result on the metallicity-dependence of the occurrence of various different kinds of planetary systems (currently under review). I learned that Spergel (Flatiron) is pursuing halo binaries at wide separations to look at halo dynamics. And I learned that Kathryn Johnston (Columbia) is thinking about how chaos might affect not just streams but also wide binaries or unbound comoving pairs. Maybe the comoving pairs will highlight regular (non-chaotic) orbits! That would be a super-cool constraint on Milky Way dynamics.

Late in the day I sat down with Bedell (Flatiron) who showed me the current state of our wobble project to model stars and the atmosphere in extreme-precision radial-velocity projects. It looks great! The data are very well described by the model, our statistical regularizations seem to be working, and there is every evidence that we are getting great telluric spectra. Now, are we doing well on the radial-velocity determination? Damn I hope so!

luminous red giants in APOGEE

Eilers (MPIA) and I went on the APOGEE science telecon to describe our results. I talked about how we calibrated a (purely linear) spectro-photometric distance estimate for luminous red giants that manages to correct for dust and luminosity, and Eilers talked about how we used those tracers to measure the circular velocity of the Milky Way disk (that is, the potential). We use the Jeans equation in cylindrical symmetry. We got great feedback from the APOGEE team, which we will use to improve our discussion in our papers.

how to describe my current project

My flight home got seriously delayed and I had an extra day in Aspen. I spent it talking about (and working on) my project to infer dynamical invariants in the well-mixed parts of the Milky Way from chemical (element-abundance) invariants. I had various epiphanies and useful discussions:

Rix (MPIA) and I worked on how you explain the project to the world. One explanation is this: In addition to dynamical invariants, there are chemical abundances, which depend on the dynamical invariants (and not on the conjugate angles). Therefore inference of the dynamical invariants must be better or improved if you model the abundance invariants as well or in tandem. Another explanation is this: Imagine you do a dynamical inference (like Jeans modeling) and you (effectively) determine orbit structure. If you are slightly off, the element abundances you have measured will reveal the issues, and can be used to adjust or update or improve the orbit-structure inference, because stars don't change their abundances as they orbit!

Price-Whelan (Princeton) and I worked on how to compare the project with Jeans modeling, Schwarzschild modeling, or fully marginalized forward modeling of the kinematics (which has almost never been done). I have a scaling argument that my new method must be better than any of these: Each of these methods gets some amount of information out of the positions and velocities of the stars. My chemical-tangents method gets more information from every new element abundance you measure (even if each new element is fully covariant physically with the ones you have measured before; it is the measurements that are near-independent). So in some limit (and I think that limit arrives very early), it will have more information than any of these methods. But of course I need to demonstrate this quantitatively in the very near future.

Another point of comparison is related to the conditional or generative or causal structure of the model: I am modeling the abundance distribution conditioned on the phase-space positions. This means that I don't need to know the selection function of the survey, which Jeans modeling does (to some extent) and the more serious methods do (to great precision). On the other hand, because I am conditioning on the positions and not generating them, I can't (gracefully) account for measurement uncertainties in position. (Of course that's true for Jeans too.)

Anyway, the reason I am writing all this is because: The best practice for writing (the paper) is writing (this blog and emails and etc).