validation

After lunch, Alice Shapley (UCLA) gave a great Astro Seminar about what we can learn about high-redshift galaxies with multi-band photometry and infrared spectroscopy and, soon (or we hope soon!), JWST. There are hopes of seeing a consistent story in the star-formation rates, the build-up of mass, and the metallicity evolution in the stars and the interstellar medium.

At the end of the day, Andy Casey (Monash), Soledad Villar (NYU), and I met to discuss Villar's generation of APOGEE spectra of stars with a GAN, and how we might validate that. We discussed various options, but we are more-or-less converging on the idea that the spectra have to tell consistent or sensible stories about temperature and logg. I have ways to operationalize that. But one of the funny things is that real spectra of stars don't tell consistent stories! Because the physical models aren't awesome. So we can only require that the generated spectra do no worse than the real spectra.

EPRV at Yale

I spent an absolutely great and energizing day at Yale today, with the groups of Debra Fischer (Yale) and Jessie Cisewski-Kehe (Yale), who are working together to bring the best in hardware and the best in statistics to the hard problem of making (much) better than m/s-level radial-velocity measurements. We talked about many things, but highlights included:

How do you put uncertainty estimates on extracted spectral pixels? In the 2d-to-1d extraction step, the estimation of a single 1d spectral pixel is a modification of a least-square fit in the 2d image. How to put a good uncertainty on that, especially when the model isn't strictly linear least squares? We discussed Fisher-information estimates, which are best-case estimates, and also bootstrap or jackknife estimates, which are probably more conservative. The nice thing is that the EXPRES spectrograph (Debra Fischer's instrument) has many 2d pixels per 1d pixel, so these empirical methods like jackknife are possible.

What parts of the spectrum are most sensitive to activity? One approach is to find activity labels and perform a regression from spectral pixels to activity labels. Bo Ning (Yale) is taking this approach, with strong regularization to force most pixels to zero out in the regression. He finds plausible results, with the centers of certain lines contributing strongly to the regression. We discussed the kinds of tests one can do to validate the results. Ning also has evidence that the ability to find good activity indicators might be a strong function of spectral resolution, which is good for projects like EXPRES and ESPRESSO, which have very high resolution.

How can we measure radial velocities in the presence of stellar variability? We now think that stellar variability is the tall pole in EPRV. If it is, we have some deep and fundamental questions to ask here, since the whole edifice of relative RV measurement relies on the source being constant in time! We discussed different approaches to his ill-posed problem, including using only spectral information about RV that is somehow orthogonal to the spectral variability, or placing strong priors on the RV signal to separate it from the variability signal, or performing some kind of causal-inference-like regression. There is room for good theory here. Parker Holzer (Yale) is working on some theory along the orthogonality lines.

not much

Today was a low-research day! But I did have a brief conversation with Anu Raghunathan (NYU) about making her box-least-squares code more pythonic and more modular. And I did work a bit on the abstract and typographic macros in my M-type dwarf paper with Jessica Birky (UCSD).

a book about writing

My only research today was finding and starting this interesting book about writing.

let's just see the orbits directly!

My main research today was a long call with Suroor Gandhi (NYU) about papers that determine the dark-matter density in the local part of the Milky Way disk by modeling the stars as an equilibrium population. The idea is that if the population is in equilibrium, it has some properties (like obeying the Jeans equation) that permit it to be used to do inference of the potential. I don't love these papers, both because of the assumptions they make (reaching equilibrium takes a very long time) and because of the ways that they boil down the data to some summary statistics before doing inference. Can't we generate the data and write down a proper likelihood? But more importantly, can't we do inference on non-equilibrium problems? I think we can! That's why Gandhi and I are looking at The Snail (the phase spiral). I think it reveals the orbit structure of the disk pretty-much directly, and we ought to be able to beat the equilibrium models both in precision (measuring orbits is better than measuring velocity moments) and in parsimony (we don't have to make assumptions that are as strong).

how to validate a generative model?

Soledad Villar (NYU) has created a deep-ish network that can generate fake APOGEE spectra. They look convincing! Now her question to me today was: How do we validate a generative model? How do we know that these generated spectra are reasonable or sensible? In astrophysics we have no ground truth. All we can think of so far is looking at whether it is possible to do parameter estimation using standard stellar spectroscopy pipelines on these stars, and whether different parts of the spectra deliver similar stellar parameters (or as similar as do different parts of the spectra of real stars, which is not always that similar!). We can also compare to The Cannon, which is also a generative model (though not a deep one!).

time-domain speckle models

I spent time on the long weekend and today working through the front parts of a new paper by Matthias Samland (MPIA) who is applying ideas we used for our pixel-level model for Kepler data to high-contrast (coronographic) imaging. Most high-performance data pipelines for coronograph imaging model the residual speckles in the data with a data-driven model. However, most of those models are spatial models: They are models for the imaging or for small imaging patches. They don't really capture the continuous time dependence of the speckles. In Samland's work, he is building temporal models, which don't capture the spatial continuity but do capture the time structure. The best possible methods I can imagine would capture some of both. Or really the right amount of both! But Samland's method is good for working at very small “inner working angle” where you don't have much training data for a spatial model because there just isn't that much space very near the null point.

spectroscopy, Earth-finding

At mid-day I spun out an extended fantasy with Andy Casey (Monash) about a general and generalizable spectroscopic software toolkit that could do data analysis, spectral extraction, parameter estimation, and radial-velocity measurement in arbitrary two-dimensional spectrograph imaging. One of the related ideas is to build low-dimensional descriptions of the calibration of the spectrograph to pool calibration data and reduce pressure on calibration observations. Another idea is to avoid going to one-d spectra, except when necessary (almost never necessary). Another is never to deconvolve to high resolution (spectro-perfectionism is a deconvolve–reconvolve method, to which I object). Etc. It would be a lot of work, but it could revolutionize the business.

Late in the day I had a conversation with Megan Bedell (Flatiron) about possible high-level goals for the Terra Hunting Experiment, which is finding Earth analogs. Some of the goals might be about discovery rate (or future-discounted discovery rate) and some might be about statistics (what is the abundance of Earth analogs?). Different high-level objectives lead to different operational decisions. Interesting. And hard.

binary stars and lots more

Today was a very very special Stars meeting, at least from my perspective! I won't do it justice. Carles Badenes (Pitt) led us off with a discussion of how much needs to be done to get a complete picture of binary stars and their evolution. It's a lot! And a lot of the ideas here are very causal. For example: If you find that the binary fraction varies with metallicity, what does it really vary with? Since, after all, stellar age varies with metallicity, as do all the specific abundance ratios. And also star-formation environment! It will take lots of data and theory combined to answer these questions.

Andreas Flörs (ESO) spoke about the problem of fitting models to the nebular phase of late-time supernovae, where you want to see the different elements in emission and figure out what's being produced and decaying. The problem is: There are many un-modeled ions and the fits to the data are technically bad! How to fix this. We discussed Gaussian-process fixes, both stationary and non-stationary. And also model elaboration. And the connection between these two!

Helmer Koppelman (Kapteyn) showed some amazing structure in the overlap of ESA Gaia data and various spectroscopic surveys (including LAMOST and APOGEE and others). He was showing visualizations in the z-max vs azimuthal-action plane. We discussed any ways it could be selection effects. It could be; it is always dangerous to plot the data in derived (rather than more closely observational) properties.

Tyson Littenberg (NASA Marshall) told us about white-dwarf–white-dwarf (see what I did with dashes there?) binaries in ESA LISA. He has performed an information-theoretic analysis for a realistic Milky Way simulation. He showed that many binaries will be very well localized; many thousands will be clearly detected; and some will get full 6-d kinematics because the chirp mass will be visible. Of course there are simplifying assumptions about the binary environments and accelerations, but there is no doubt that it will be incredible. Late in the day we discussed how you might model all the sea of sources that aren't individually detectable. But that said, everything to many tens of kpc in the MW will be visible, so incompleteness isn't a problem until you get seriously extragalactic. Amazing!

binaries

Great Astro Seminar today by Carles Badenes (Pitt), who has been studying binary stars, in the regime that you only have a few radial-velocity measurements. In this regime, you can tell that something is a binary, but you can't tell what its period or velocity amplitude is with any precision (and often almost no precision). He showed results relevant to progenitors of supernovae and other stellar explosions, and also exoplanet populations. Afterwards, Andy Casey (Monash) and I continued the discussion over drinks.

topological gravity; time domain

Much excellent science today. I am creating a Monday-morning check-in and parallel working time session for the undergraduates I work with. We spoke about box-least-squares for exoplanet transit finding, about FM-radio demodulators and what they have to do with timing approaches to timing-based planet finding, scientific visualization and its value in communication, and software development for science.

At lunch, the Brown-Bag talk (my favorite hour of the week) was by two CCPP PhD students. Cedric Yu (NYU) spoke about the topological form of general relativity. As my loyal reader could possibly know, I love the reformulation of GR in which you take the square-root of the metric (the tetrad, in the business). Yu showed that if you augment this with some spin fields, you can reformulate GR entirely in terms of topological invariants! That's amazing and beautiful. It relates to some cool things relating geometry and topology in old-school math. Oliver Janssen (NYU) spoke about the wave function of the Universe, and what it might mean for the initial conditions. There is a sign ambiguity, apparently, in the argument of an exponential in the action! That's a big deal. But the ideas are interesting because they force thinking about how quantum mechanics relates to the entire Universe (and hence gravity).

In addition to all this, today was the first-ever meeting of the NYU Time Domain Astrophysics group meeting, which brings together a set of people at NYU working in the time domain. It is super diverse, because we have people working on exoplanets, asteroseismology, stellar explosions, stellar mergers, black-hole binaries, tidal disruption events, and more. We are hoping to use our collective wisdom and power to help each other and also influence the time-domain observing projects in which many of us are involved.

the Snail

As my loyal reader knows, I like to call the phase spiral in the vertical structure of the disk (what's sometimes called the Antoja spiral) by the name The Snail. Today I discussed with Suroor Gandhi (NYU) how we might use the Snail to measure the disk midplane, the local standard of rest (vertically), the mass density of the disk, and the run of this density with Galactocentric radius. We have a 9-parameter model to fit, in each angular-momentum slice. More as this develops!

Sagittarius dark matter?

It's a bad week, research-wise. But I did chat with Bonaca (Harvard) this morning, and she showed that it is at least possible (not confirmed yet, but possible) that the dark substructure we infer from the GD-1 stream has kinematics consistent with it having fallen into the Milky Way along with the Sagittarius dwarf galaxy. This, if true, could lead to all sorts of new inferences and measurements.

Reminder: The idea is that there is a gap and spur in the stream, which we think was caused by a gravitational interaction with an unseen, compact mass. We took radial-velocity data which pin down the kinematics of that mass, and put joint constraints on mass, velocity, and timing. Although these constraints span a large space, it would still be very remarkable, statistically, if the constraints overlap the Sagittarius galaxy stream.

Philosophically, this connects to interesting ideas in inference: We can assume that the dark mass has nothing to do with Sag. This is conservative, and we get conservative constraints on its properties. Or we can assume that it is associated with Sag. This is not conservative, but if we make the assumption, it will improve enormously what we can measure or predict. It really gets at the conditionality or subjectivity of inference.

the photon sphere; 6-d math

The day started with the Event Horizon Telescope press release conference, which I watched at Flatiron (but could have watched at NYU or Columbia; a huge fraction of the community was watching!). It really is a beautiful result, and the data analysis looks (on cursory inspection of the papers) to be excellent and conservative. It is just incredible that we can observe a photon sphere, if that really is what it is! It seemed like such a thing of legend and story.

Interesting to think about language: Is this the first observation of a black hole? Or image of one? I'd say not, because any image of a quasar is just as much an image of the radiation around a black hole as this is. I think maybe it is the first image of the parts where strong gravity is acting (photons are orbiting!). But these are not objections in any way to the importance of the result! Just musing on the language. In what sense is this the first time we have taken an image of a black hole? And is it that? And etc.

In the afternoon, Kate Storey-Fisher and I went to the board and got confused about 6-dimensional integrals. We need them to understand correlation-function estimators. The “RR” term in the correlation function estimators is a 6-d integral over an outer product of space with space!

CMB

My only research time today was a nice astro seminar by Chris Sheehy (BNL), who convinced us that detecting primordial gravitational radiation in the b-mode polarization of the CMB at large scales will be hard but possible. It depends on some inflation physics, of course! He also showed some novel uses of what you might call “compressive sensing” to CMB foreground analyses, scooping some of my thoughts on the subject!

student projects; 2-pt function estimators

Most of my research time over the weekend and today was taken up reading proposals for a funding review. That doesn't count as research, by my Rules. I don't love that part of my job. But I did get in some time with students, reading thesis chapters by Malz (NYU), planning two papers with Storey-Fisher (NYU), and discussing graduate school options with Birky (UCSB). I love these parts of my job!

In the conversation with Storey-Fisher, we set the minimal (though still very large) scope for a paper that competes or tests large-scale structure correlation-function estimators in realistic and toy data. Our issues are: We have identified biases in the standard estimators, and we (additionally) don't love the tests or arguments that say that Landy–Szalay is optimal. So we want to test them again, and also add some new estimators, from the math literature on point processes.

the information theory of light curves

In Astronomical Data Group Meeting at Flatiron today, Rodrigo Luger (Flatiron) spoke about what he calls the “null space” for reconstruction of stellar surface features (or exoplanet surface features) from light curves. If you just have a rotating ball, glowing but with a surface pattern of emissivity, and you just get to see an integrated light curve, you can only reconstruct certain parts of any representation of its surface. For example, all the odd-ell modes (after ell of 1) contribute exactly zero signal! And there are other degeneracies, depending on orientation. These degeneracies are exact!

What Luger showed today is that some of these degeneracies are broken just by limb darkening! And others are broken if you have transiting planets. And if you are reconstructing a planet, others are broken by the terminator of any reflected light. All of these results and considerations will feed into an information theory of stellar and exoplanet light curves.

the statistics of box least squares

Last semester, I started a project with Anu Raghunathan (NYU) on the question of how much more sensitive we could be to planets in resonances than we are in more blind searches. My loyal reader knows that I'm interested in this. I think it has a simple answer, but even if it does, some playing in this statistical sandbox is fun. Today Raghunathan and I realized that we can generate a whole set of great results around box least squares, which is the dumb (but very effective, and very easy-to-analyze; I'm a fan) method that is used to generate candidate exoplanets in many transit surveys and searches. My vague idea is to use this as a place to understand multiple hypothesis testing (the physicists' “look-elsewhere effect”) and derive analytic false-positive rates for simple noise distributions, with searches of different kinds in data of different kinds.

six-volume, Fools, TOIs

I spent my science time today commenting on the first draft of a nice paper on phase-space volume by Matt Buckley (Rutgers). He shows that it is possible, in some cases, to measure the phase-space volume (six-volume) of structures in the ESA Gaia data. He wants to use Liouville's Theorem (that 6-volume is conserved) to measure the former bound masses of structures in the Milky Way halo that are now disrupted.

At Stars & Exoplanets Meeting at Flatiron, we discussed the Luger et al and Burns et al April-Fools papers. They both represent very impressive results, and are also a bit silly. On the Burns paper, we learned how to continue a spherical spectral representation down to zero radius without introducing a singularity. Reminded me of undergraduate quantum mechanics!

In addition, Bedell (Flatiron) spoke a bit about cool things that happened at #TessNinja2 last week in Chicago. Among other things, she showed a system that Foreman-Mackey (Flatiron) and collaborators set up to automatically fit the light curves of every announced TESS Object of Interest. It's hilarious: It produces a complete executable (and modifiable) Jupyter notebook for every TOI.

gravitational redshifts; point processes

I went down to Princeton to give a seminar to the particle physicists about dark matter, and in particular what we know or could know from dynamical and kinematic measurements of stars. Before my talk, I had a great conversation with Oren Slone (Princeton) and Matt Moschella (Princeton) about gravitational redshifts. They have been thinking about where gravitational redshifts might be both measurable and physically interesting. Ideas include: Surfaces of stars, stars as a function of location in our Galaxy, and different parts of external galaxies. The magnitudes are tiny! So although the gravitational redshift is an incredibly direct tool of some gravitational dynamics, it is very hard to measure.

After my talk at Princeton, I got in a short but fun conversation with Jim Peebles (Princeton) on point processes and estimators of two-point functions. Peebles, after all, wrote down the first estimators of the clustering of large-scale structure. He admitted that the history is unprincipled: They more-or-less made things up! I presented the things that I have been discussing with Kate Storey-Fisher (NYU) and Alex Barnett (Flatiron) and he was interested. And intrigued. Can we make better estimators?

where is the dark mass? April Fools

The day began with a call with Ana Bonaca (Harvard), in which she showed me that she can take her models of the GD-1 stream perturbation and predict the present-day location of the substructure (or dark mass) that created the perturbation. Because the model space is broad, the “error box” is large, but the fact that we have such a prediction is fun, and interesting. All this progress flows from the fact that we now have some radial-velocity data on the stream and the spur (which is the feature we think was raised by a dark-matter interaction).

On the arXiv today were the annual set of April Fools papers. My loyal reader knows that I love papers in this category when they are silly or funny but in fact contain an interesting or important calculation or inference. There were two in this category today with Flatiron origins. One was Luger et al, inferring the mean cloud cover on Earth from systematic effects in the NASA TESS imaging! Another was Burns et al, showing that instead of “cubing the sphere” (what climate modelers do to avoid spherical coordinate singularities in discretization) you can “sphere the cube” (embed a cubical simulation volume in a natively spherical-representation simulation). This latter project was ridiculous, but it showed very dramatically that they have a representation for simulating spherical domains with no singularity anywhere (and especially not at the center of the sphere, and at no angular position on the surface).