representation of flexible functions

Emily Griffith (Colorado) and I met today to look at replacing a spline interpolation function deep inside some of our code with a Fourier series. The idea is that we need a flexible function of one variable, and we were using a spline of a set of control points, but (for many reasons) we wanted to change to a sum of sines and cosines. The code work was a mess! The small change hits a lot of places inside our model, which is our K-process data-driven nucleosynthetic model. This same problem appears in the new version of wobble by Matt Daunt (NYU). I love flexible functions, but it's hard to implement them in a properly abstracted way. That is, it is hard to write a model so that you can just swap in a Fourier series or a Gaussian process where you used to have an interpolation of control points.

precision spectroscopy

One research highlight from the day was a conversation with Madeleine MacKenzie (ANU) about many things, including measuring magnesium isotopes in high-quality (high resolution and high SNR) stellar spectra. This comes just after a conversation (yesterday) with Matt Daunt (NYU) saying that he wants to do something with the extremely high-quality stellar spectra produced by the jax-wobble pipeline we are building. So I think there is a project to do. If we measure Mg isotopes, even for a few stars, we might be able to fit them into the 2d model of disk abundances that Emily Griffith (Colorado) and I are building. The model is so simple that we would only need a few stars to learn something interesting—including learn that the isotope ratio variations (seen by MacKenzie) represent some new kind of variability. Do they?

truly zero-metallicity stars

All week I have been discussing with Hans-Walter Rix (MPIA) the possibility that we could find the elusive, truly zero metallicity stars in the Milky Way halo. This from an email I wrote today, reacting to the observational point that no-one has ever seen such a star:

How could there be absolutely ZERO zero-metallicity stars in the Milky Way? Here's everything I got:

1. Maybe there are literally no low-mass stars ever made at zero metallicity. Absolutely none, at high precision. This is possible, given how little we know about star formation and the IMF.
2. Maybe stellar evolution is so weird at zero metallicity that low-mass stars go dark by 13 Gyr. I very much doubt that this is a possibility. But maybe low-mass stars at primordial abundances never burn and just slowly collapse into white-dwarf-like condensed objects on a very long cooling timescale. They would be super cold by now, like 100 K maybe??
3. Maybe low-mass stars form slower than high-mass stars in star-forming regions at zero metallicity. This permits a few of the high-mass stars to quickly evolve and explode, polluting the outsides of the just-forming low-mass stars. These low-mass stars would then have low but non-zero surface metallicities, and be very alpha-enhanced. This is possible, although would it really leave NO zero-metallicity low-mass stars behind?
4. Maybe low-mass stars somehow self-pollute at formation (or later in their lives). Maybe the nuclear fusion kicks in slightly before gravitational steady-state or radiative zones are set up, and the first bit of nuclear burning gets mixed in to the stellar envelopes? These stars would appear to have non-zero (but weird, carbon-enhanced maybe?) abundances. Or maybe this happens later in life because of some weird internal mixing. I have literally no idea whether any of this is possible.

co-writing

My only real work time today came at the end of the day, working with Emily Griffith (Colorado) on our paper about element abundance ratios in the SDSS-V APOGEE data. We find (like others) that the abundances can be explained pretty precisely with only two processes. My position (contrary to others) is that this is not because there are two dominant kinds of supernovae! It is because the disk mixes gas quickly in the azimuthal direction, such that a star's properties are mainly set by the (cosmic) time at which it was born, and the radius at which it was born. If I'm right, then you can't really use disk stars to understand process yields, since they are always an ugly mixture of processes. If I am wrong, there's lots more to do!

Are there young, alpha-rich stars?

I asked this question in Data Group meeting: With Emily Jo Griffith (Colorado) and I have a data-driven nucleosynthetic story for essentially every red-giant-branch star in the SDSS-IV APOGEE survey. Since the parameters of this model relate to the build-up of elements over time, they might be used to indicate age. We matched to the NASA Kepler asteroseismic sample and indeed, our nucleosynthetic parameters do a very good job of predicting ages.

On the RGB, age is mass, and the asteroseismology gives you masses, not ages. There are some funny outliers: Stars with large masses, which means young ages, but with abundances that strongly indicate old ages. Are they young or old? I am betting that they are old, but they’ve undergone mass transfer, accretion, or mergers. If I’m right, what should we look for? The Data Group (plus visitors) suggest looking for binarity, for vertical action (indicating age), for ultraviolet excess (indicating white dwarf companion), for abundance anomalies, and Gaia RUWE. Will do! My money is that all these stars are actually old.

scope of a paper

Emily J Griffith (Colorado) and I have been working on a two-process (or really few-process) model for the creation of the elements, fit to the abundances measured in the APOGEE survey. Our big conversation this week has been about the scope for our first paper: We have so many results and ideas we don’t know how to cut them into papers. Today we made a tentative scope for paper one: we’ll explain the model, deliver a huge catalog of abundance information, and demonstrate the usefulness for practitioners of Galactic archaeology. Then, later, we can actually do that archaeology!

degeneracies and optimization

With Emily Griffith (Colorado) I have been working on a purely data-driven nucleosynthetic model, trained on the abundances measured in stars by the APOGEE surveys. This model looks a lot like a non-negative matrix factorization, so it is a kind of model I've worked with many times in my life. We've figured out an optimization scheme and made it (exceedingly) fast with jax. Nonetheless, we have been having troubles with the optimization, getting stuck in bad local minima or even pathological locations in parameter space.

Today I discussed this model with Soledad Villar (JHU) who warned me that the model has potential pathologies, and strong degeneracies. I thought I was breaking these degeneracies with regularizations, but in fact the degeneracies are bigger than I thought. Villar's advice (which aligns with the machine learning zeitgeist) was to leave the degeneracies free and then rotate or transform the model to where I want it to be at the end. She also had useful advice about optimizing non-convex functions.

bi-linear-ish models

Before my day got ruined by a deadly SDSS-V Advisory Council meeting, I worked with Emily Griffith (Colorado) on a data-driven 2-process model for nucleosynthesis. This model is amplitudes (2 per star) times process yield vectors (2 per element). In this sense it is like a matrix factorization. But it involves a log-sum-exp (rather than just a matrix multiply), so it is mildly nonlinear. It can still be optimized the same way and it is well behaved. In some sense, I realized, it is very like The Cannon in form. But different! We failed to fully implement before I turned into a (very unhappy) technocrat.

SDSS-V Science Festival, day 2

On day two of the Collaboration meeting, I talked to Emily Griffith (Colorado) about data-driven models of nucleosynthetic processes. We were inspired by this paper, on which Griffith is an author. The paper builds an empirical two-process enrichment model based on the observed morphology of the [Fe/Mg] vs [Mg/H] plane. We discussed how to make this model into a full (but constrained) latent-variable model. I am interested in moving it towards causal inference, but we could also look at third processes, anomalous stars, anomalous elements, calibration issues, and so on. We wrote down math and started to write code.

aluminium abundances

A very good conversation broke out in our weekly Gaia DR3 & SDSS-V prep meeting today, about Aluminum abundnaces in stellar photospheres, which are the key tool in a new paper about the Milky Way being drafted by Vasily Belokurov (Cambridge). Keith Hawkins (Texas) is in town, and he also happens to be the discoverer of very interesting relationships between Fe, Al, Mg in low-metallicity stars. The ratio [Al/Fe] increases with [Fe/H] at low metallicities and decreases at high metallicities. That has something to do with the different timescales for different kinds of supernovae and different rates of star formation. This all might explain why Christina Eilers (MIT) and I are finding weird issues when we try to fit [Al/Fe] as a function of stellar evolutionary state and dynamical actions in the Galaxy.

black holes and nucleosynthesis

Today Selma de Mink (Harvard) gave a great and energizing Astrophysics Seminar at NYU. She talked about many things related to the extremely massive-star progenitors of the estremely massive black holes being observed in merger by LIGO. One assumption of her talk, which is retrospectively obvious but was great, is that the vast majority of LIGO events should be first-generation mergers. A second merger is very unlikely, dynamically. But that wasn't her point: Her point was that the masses that LIGO sees will constrain how very massive stars evolve. In particular, she showed that there is a strong prediction of a mass gap: There can't be black holes formed by stellar evolution in the mass range 45 to 150 solar masses. The physics is all about pair-instability supernovae from very low-metallicity stars. But the details of this black-hole mass gap depend on some nuclear reaction rates, so she concludes that LIGO will make nucleosynthetic measurements! The LIGO data probably already do. It's a new world!

alphas, robots, u-band

In an absolutely excellent Stars and Exoplanets Meeting, Rodrigo Luger (Flatiron) had everyone in the room (and that's more than 30 people) say what they plan to get done this summer!

Following that, Melissa Ness (Columbia) talked about the different alpha elements and alpha enhancement: Are all alpha elements enhanced the same way? Apparently models of type-Ia supernovae say that different alpha elements should form in different parts of the supernova, so it is worth looking to see if there are abundance differences in different alphas. The generic expectation is that there should be a trend with Z. She has some promising results from APOGEE spectra.

Mike Blanton (NYU) talked about how we figure out how to perform a set of multi-epoch, multi-fiber spectroscopic surveys in SDSS-V. He has a product called Robostrategy which tries to figure out whether a set of targets (with various requirements on signal-to-noise and repeat visits and cadence and so on) is possible to observe with the two observatories we have, in a realistic set of exposures. That's a really non-trivial problem! And yet it appears that Blanton may have working code. I'm impressed, because integer programming is hard.

And Shuang Liang (Stony Brook) showed us that it is possible to calibrate u-band observations using the main-sequence turn-off, as long as you account for the differences between the disk and the halo. He has developed empirical approaches, and he has good evidence that his calibration based on the MSTO is better than other more traditional methods!

phylogeny and nucleosynthesis

In Astronomical Data Group Meeting, Megan Bedell (Flatiron) talked about possible uses of phylogenetic methods for looking at the chemical evolution of stars in the Milky Way. That's an idea that has been tried a few times, but she has a new twist: There are methods that take explicit account of time, and there are now many stars for which we have precise ages. I'm not sure, in the end, that methods from biology will translate directly to astrophysics, but I bet the sandbox is worth digging in a little bit. This connects to my thoughts and hopes of building a data-driven model of nucleosynthesis.

Before that, in conversations (also) with Bedell, I down-selected my ideas for the NASA Exoplanets Research Program call. The stage-1 proposals are due next week, so this is about as late as I can leave it. My plan is to propose something about stellar spectral variability and the new NASA investments in extreme precision radial-velocity hardware. Watch my GitHub repos for details.

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.

Ringberg, day 3

Today Megan Bedell (Flatiron) and I called Jan Rybizki (MPIA) to discuss his nucleosynthesis (or chemical-evolution) models for the abundances Bedell sees in her Solar twin stars. His fits are not great—the yield tables from nuclear astrophysics don't do a good job explaining the Sun yet—but he can build a model that is best-fit under his assumptions. The realization we had today is that Bedell's abundances are referenced to the Solar abundances in the real world; and so if we are using Rybizki's model, we should reference her abundances to the Solar abundances in Rybizki's world! That should make everything work better and permit us to come to conclusions.

All this assumes that Rybizki's model is better at getting relative element abundances than absolute abundances. That remains to be seen! However, this also connects to the constant refrain on my blog that we need to do inference in the context of models we know to be wrong! That can't be helped; so what is the epistemological status of conclusions based on wrong models? Scientific inferences are only correct in the context of specific and questionable assumptions. But we still learn a lot and know a lot.

Gaia halo stars; neutron lifetime

In the morning, Lauren Anderson (Flatiron) and I discussed Gaia DR2 projects. First we talked about things we could do with David Blei (Columbia) and his group, who have variational methods for extremely large inferences of the types we would like to do. We drew some graphical models (and posted them on twitter). Then we looked at halo red giants selected by parallax and color. Sagittarius shows up beautifully, and now it is time to start to look at other features. The data are incredibly rich.

Alberto Sirlin (NYU) gave the brown-bag talk, on the neutron lifetime. He showed that the neutron lifetime and a certain coupling are related, and showed that measurements of each, and their combination, are consistent, for at least some measurements. There are interesting puzzles though: Some kinds of lifetime measurements disagree with other kinds, and there was a step change in the coupling measurements in 2002-ish. So there are hints of new physics, but also a consistent no-new-physics story. He also showed that the simplest new-physics scenarios are not sensible. The neutron lifetime is important for many things, but especially big-bang nucleosynthesis.

jackknife, radial migration, and chaos

Yesterday, in conversation with Andrew Mann (Columbia), Jessica Birky (UCSD) and I decided that she should do a full set of jackknife tests on her Cannon model of APOGEE M-dwarf stars. She did that overnight (I love working with such great people!) and the results indeed show that we don't have much good metallicity information about the M-dwarf stars in the training set we have. This inspired Mann to look for more training-set objects; he found a few dozen more, with a bit more metallicity span. Excellent.

In the afternoon, Kathryn Johnston (Columbia) organized a meeting of the Local Local-Group Group. As it were. There were many interesting things discussed. Megan Bedell (Flatiron) showed her Solar-twin abundances and this got a lot of interesting discussion going about their use to constrain Galactic chemical evolution and radial migration in the Milky Way disk. In particular, they could be very constraining if stellar birth composition is a nearly-unique function of time and Galactocentric radius. There were also questions about whether she can constrain nucleosynthetic yields, which I think she can!

Also in that session Tomer Yavetz spoke about chaos and chaotic orbits, and the properties of stellar streams thereon. He had a nice explanation for why chaos shows up so quickly and clearly in stellar streams: The relevant timescale is not the Lyapunov time, but the time it takes for orbits to wander around their local neighborhood in frequency space, which can be a much shorter time (short reason: because that frequency neighborhood can be small). I hope this is correct, because it has been a puzzle!

writing on dimensionality

Because of work Bedell did (on a Sunday!) in support of the Milky Way Mapper meeting, I got renewed excitement about our element-abundance-space dimensionality and diversity work: She was able to show that we can see aspects of the low dimensionality of the space in the spectra themselves, mirroring work done by Price-Jones (Toronto) in APOGEE, but with more specificity about the abundance origins of the dimensionality. That got me writing text in a document. As my loyal reader knows, I am a strong believer in writing text during (not after) the data-analysis phases. I'm also interested in looking at information-theoretic or prediction or measurement approaches to dimensionality.

Gaia and exoplanets

At this morning's Gaia DR2 prep workshop (parallel-working meeting), we gathered a group of people to discuss ideas for using Gaia DR2 data in the service of exoplanet science. We were focusing on easy ideas that could be executed quickly after the data release. These ideas fell into some broad categories. One is to use the astrometry and photometry to get stellar radii and thereby get better estimates of planet radii for the Kepler planets. Another is to use Gaia-based stellar age estimates to compare planetary systems around stars of different ages. Or compare ages for planetary systems of different architectures (as they say). One of my favorite age estimates is the (square of the) vertical action in the Milky-Way disk! Along the same lines: Test theories for pumping or damping of eccentricities with stellar ages. Because of recent work around Flatiron, there was substantial talk of whether Gaia could detect signatures of stars that have recently accreted their planets. There might be different signatures on different time-scales.

Late in the day, I worked some more on my #hackAAS project to look at the dimensionality of stars in element-abundance space. I think (but am not sure) that the best way to think about this problem for the purposes of chemical-tagging applications is in terms of how well we can predict unmeasured abundances. Because this gets at the value or trade-offs between measuring more elements or measuring the elements you already have but better. I need to write first and data-analyze second, but the data are so fun to play with!

batman and technetium

Today was a low-research day (letters of recommendation), but Elisabeth Andersson (NYU) and I got an optimization working, comparing a batman periodic transit model to a Kepler light curve. I left her with the problem of characterizing the six planets in the Trappist 1 system.

At lunch, Foreman-Mackey (Flatiron) proposed a model for stellar spectra that is intermediate in sophistication and computational complexity between The Cannon and the Eilers (MPIA) GPLVM. He also has a fast implementation in TensorFlow. Most of the TensorFlow speed-up comes from its clever use of GPUs. Late in the day, Bedell proposed that we look for short-lived radioactive isotopes in her Solar twins. That’s a great idea!