likelihood ratios not posteriors, please

There is an informal meeting at MPIA every Wednesday regarding binary stars, with a bit of a focus on massive binaries. Today there was a very nice presentation by Jakob Stegmann (MPA) about some anomalies among the (only six) black-hole–neutron-star binaries discovered by NSF LIGO. He showed the example of GW 200105, which shows a large eccentricity (0.15-ish). This eccentricity is very hard to explain, given how the inspirals evolve as they radiate. But the analysis of the eccentricity (from perhaps this paper) is Bayesian, so it isn't clear how much the eccentricity result is forced by the data and how much is forced by the prior over nuisance parameters. That's one of the main points of my forthcoming paper on measurement. I think maybe I should just re-analyze this one with a profile likelihood. I hope the data and code are public!

robust dimensionality reductions

Dimensionality reduction (the basic being PCA) is very sensitive to outliers: A single bad pixel can dominate most objectives and thus create a spurious dimension. One of the best and most classic solutions to this is the robust PCA method, which is presented in a (very long) paper with impressive math and beautiful results. Yesterday Hans-Walter Rix (MPIA) and I coded it up and applied it to ESA Gaia RVS spectra, with extensive (and impressive) help from Claude. It looks very promising, especially in capturing oddities in hot stars. Today I worked out that there should be something similar that takes into account data weights (inverses of squared uncertainties), and I wrote down the algorithm (on paper). We'll see.

stellar twins vs synthetic stellar twins

In the Milky Way meeting at MPIA today, a bit of a discussion broke out about using stellar twins, inspired by work by Yuan-Sen Ting (OSU). The idea is: If you have two stars with very similar overall metallicity, and very similar temperature and surface gravity, then it should be possible to measure accurate element abundnace anomalies between the two stars, even in the absence of an extremely accurate spectral synthesis code.

My view, which does not contradict this point, is that an even better way to use this stellar-twin idea is to synthesize a twin for every star, using stars that are similar in (either) parameters or else spectral space. After all, an interpolation to your target star should more accurately represent it than even the most similar individual comparison star. That idea, fundamentally, is the main idea behind The Cannon.

how did the Solar System form?

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

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

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

what is measured with stellar kinematics?

In work on Galaxy dynamics, from stellar kinematics, we measure relative velocities and relative positions, of nearby stars relative to the Sun (or really the Solar System barycenter). These relative positions and velocities are coordinate free, in the sense that they don't imply a rest frame for anything (and indeed, the SS barycenter is not anywhere near the rest-frame position or rest-frame velocity of the Milky Way or Local Group or anything else).

In addition to this, any measurements we make are insensitive to any overall or external acceleration: If the Milky way is in free-fall, accelerating towards some external “great attractor” or anything else, none of these observables are affected in any way by that acceleration. So what is it that stellar kinematics can really be used to measure? I think somehow the answer has to be Galilean covariant (covariant to boosts and translations), but even better it should be generally covariant (in the Newtonian sense, which is well defined, apparently).

I did some research on this subject, and the literature is all about Newton–Cartan theory, but this theory is a Newtonian limit of general relativity. That isn't quite what we care about in stellar kinematics, since in stellar kinematics, we don't get to see any orbits as a function of time (we don't observe geodesics or geodesic deviation). What, exactly do we observe? I think what we observe is something about gradients of accelerations, but I don't know yet. Great project for this summer.

scattering in the Universe

Distant objects in the Universe look the same as nearby ones, in the sense that a redshift 8 quasar looks like a point source just the same as a nearby M dwarf star looks like a point source. This must, somehow, strongly constrain the scattering properties of the Universe. The Universe is very transparent, but there definitely is scattering and absorption (by dust, by gas, by rocks); why don't we see this as some kind of “blurring” of distant sources? I discussed this today in the cafeteria at Flatiron with Charlie Epstein (Flatiron) and Marsha Berger (NYU).

My question was: What can we learn about scattering in the Universe from this fact that distant point sources look the same as nearby ones. They didn't have a simple answer. Epstein, however, said that, in the linear continuum limit, all that matters is epsilon and mu, so maybe we should just think about epsilon and mu fields that depend on position and frequency. Interesting thought. He also pointed out that pulsing sources should be dispersed (and they are!), and that dispersion should go up with distance (and it does!).

possible Trojan planet?

In group meeting last week, Stefan Rankovic (NYU undergrad) presented results on a very low-amplitude possible transit in the lightcurve of a candidate long-period eclipsing binary system found in the NASA Kepler data. The weird thing is that (even though the period is very long) the transit of the possible planet looks just like the transit of the secondary star in the eclipsing binary. Like just like it, only lower in amplitude (smaller in radius).

If the transit looks identical, only lower in amplitude, it suggests that it is taking an extremely similar chord across the primary star, at the same speed, with no difference in inclination. How could that be? Well if they are moving at the same speed on the same path, maybe we have a 1:1 resonance, like a Trojan? If so, there are so many cool things about this system. It was an exciting group meeting, to be sure.

submitted!

OMG I actually just submitted an actual paper, with me as first author. I submitted to the AAS Journals, with a preference for The Astronomical Journal. I don't write all that many first-author papers, so I am stoked about this. If you want to read it: It should come out on arXiv within days, or if you want to type pdflatex a few times, it is available at this GitHub repo. It is about how to combine many shifted images into one combined, mean image.

IAIFI Symposium, day two

Today was day two of a meeting on generative AI in physics, hosted by MIT. My favorite talks today were by Song Han (MIT) and Thea Aarestad (ETH), both of whom are working on making ML systems run ultra-fast on extremely limited hardware. Themes were: Work at low precision. Even 4-bit number representations! Radical. And bandwidth is way more expensive than compute: Never move data, latents, or weights to new hardware; work as locally as you can. They both showed amazing performance on terrible, tiny hardware. In addition, Han makes really cute 3d-printed devices! A conversation at the end that didn't quite happen is about how Aarestad's work might benefit from equivariant methods: Her application area is triggers in the CMS device at the LHC; her symmetry group is the Lorentz group (and permutations and etc). The day started with me on a panel in which my co-panelists said absolutely unhhinged things about the future of physics and artificial intelligence. I learned that many people think we are only years away from having independently operating, fully functional aritificial physicists that are more capable than we are.

IAIFI Symposium, day one

Today was the first day of a two-day symposium on the impact of Generative AI in physics. It is hosted by IAIFI and A3D3, two interdisciplinary and inter-institutional entities working on things related to machine learning. I really enjoyed the content today. One example was Anna Scaife (Manchester) telling us that all the different methods they have used for uncertainty quantification in astronomy-meets-ML contexts give different and inconsistent answers. It is very hard to know your uncertainty when you are doing ML. Another example was Simon Batzner (DeepMind) explaining that equivariant methods were absolutely required for the materials-design projects at DeepMind, and that introducing the equivariance absolutely did not bork optimization (as many believe it will). Those materials-design projects have been ridiculously successful. He said the amusing thing “Machine learning is IID, science is OOD”. I couldn't agree more. In a panel at the end of the day I learned that learned ML controllers now beat hand-built controllers in some robotics applications. That's interesting and surprising.

The Cannon and El Cañon

At the end of the day I got a bit of quality time in with Danny Horta (Flatiron) and Adrian Price-Whelan (Flatiron), who have just (actually just before I met with them) created a new implementation of The Cannon (the data-driven model of stellar photospheres originally created by Melissa Ness and me back in 2014/2015). Why!? Not because the world needs another implementation. We are building a new implementation because we plan to extend out to El Cañon, which will extend the probabilistic model into the label domain: It will properly generate or treat noisy and missing labels. That will permit us to learn latent labels, and de-noise noisy labels.

black holes as the dark matter

Today Cameron Norton (NYU) gave a great brown-bag talk on the possibility that the dark matter might be asteroid-mass-scale black holes. This is allowed by all constraints at present: If the masses are much smaller, the black holes evaporate or emit observably. If the black holes are much smaller, they would create observable microlensing or dynamical signatures.

She and Kleban (NYU) are working on methods for creating such black holes primordially, by modifying hte potential at inflation, creating opportunities for bubble nucleations in inflation that would subsequently collapse into small black holes after the Universe exits inflation. It's speculative obviously, but not ruled out at present!

An argument broke out during and after the talk whether you would be injured if you were intersected by a 10²⁰ g black hole! My position is that you would be totally fine! Everyone else in the room disagreed with me, for many different reasons. Time to get calculating.

Another great idea: Could we find stars that have captured low-mass black holes by looking for the radial-velocity signal? I got really interested in this one at the end.

APOGEE spectra as a training set

I spent a lot of the day building a training set for a machine-learning problem set. I am building the training set out of the SDSS-V APOGEE spectra, which are like one-dimensional images for training CNNs and other kinds of deep learning tasks. I wanted relatively raw data, so I spent a lot of time going deep in the SDSS-V data model and data directories, which are beautiful. I learned a lot, and I created a public data set. I chose stars in a temperature and log-gravity range in which I think the APOGEE pipelines work well and the learning problem should work. I didn't clean the data, because I am hoping that contemporary deep learning methods should be able to find and deal with outliers and data issues. If you want to look at my training set (or do my problem set), start here.

getting the absolutely rawest APOGEE data

I spent time today (at the bar!) understanding the data model and directory structure for the raw, uncalibrated APOGEE data. The idea is that I want to do a real-data example for my paper with Casey (Monash) on combining spectra, and I want to get back to the raw inputs. I also might use these spectra for a problem set in my machine-learning class. The code I wrote is all urllib and request and re, because I think it is necessary to read directories to understand the data dependencies in the survey. Is that bad?

Putting aside my concerns: The coolest thing about this project is that the SDSS family of projects (currently SDSS-V) puts absolutely every bit of its data on the web, in raw and reduced form, for re-analysis at any level or stage. That's truly, really, open science. If you don't believe me, check out this this code that spelunks the raw data. It's all just URL requests with no authentication!

combining spectral exposures

I wrote words! I got back to actually doing research this week, in part inspired by a conversation with my very good friend Greg McDonald (Rum & Code). I worked on the words in the paper I am finishing with Andy Casey (Monash) about how to combine individual-visit exposures into a mean spectrum. The biggest writing job I did today was the part of the paper called “implementation notes”, which talks about how to actually implement the math on a finite computer.