extracting spectra using models or filters

I had an interesting conversation with Matt Nixon (Cambridge) today, about new ways one might extract spectra of stars if the true goal is exoplanet atmosphere transmission spectra. Right now most methods bin down the data until there is enough signal-to-noise in every bin/super-pixel to extract a difference spectrum in every pixel. But there are other ways to bin down, which could be guided by the theoretical spectral models. In the most extreme case, you would do the atmospheric retrieval (as they call it in the business) in the un-extracted 2D image data from the spectrograph! We discussed what pieces of technology would be needed to make this happen. I love this idea, because it is at the intersection of sophisticated hardware (these spectrographs are amazing) and sophisticated theory (the exoplanet atmospheres codes are non-trivial).


the baryon-induced displacement field

Today Kate Storey-Fisher (NYU) showed me very nice visualizations of two matched simulations, one dark matter only, and one dark matter plus baryons. The simulations are matched in the sense that they have identical initial conditions, the only difference is that the latter simulation has baryon physics, such as cooling, star formation (approximately), AGN feedback (approximately), and so on. The simulations are from the IllustrisTNG project.

The thing that is interesting to us is whether we can model the differences between the simulations, and in particular whether building such a model will lead to insights about the fundamental physical mechanisms that lead to the differences. Large-scale gravity, after all, doesn't care about the small-scale composition or state of the matter; it only cares about the mass, so why are these simulations different at all? Of course there are lots of things about baryon physics that move matter, so it isn't a paradox, it's just interestingly non-trivial.

Now the question is: If we throw some gauge-invariant machine learning at this problem, will it lead to new insights about physical cosmology? That would be a real win.


SDSS-V MWM target selection

Today Jennifer Johnson (OSU) crashed the weekly Manhattan-area SDSS-V discussion meeting to give us the current state of Milky Way Mapper (a component of SDSS-V) target selection. It was a great discussion, because there are many, many target categories, and many of them are interesting to Manhattan-area locals. For me the most impressive thing about the meeting was that Johnson could answer almost any question from anyone on any of the literally dozens of target categories! It was a tour de force as they say. And we learned a lot. One of my goals with this meeting (which was started and is operated by Katie Breivik, Flatiron) is to increase excitement in Manhattan for SDSS-V and Johnson did that admirably.


review of methods for EPRV

Lily Zhao (Yale) walked Megan Bedell (Flatiron) and me through her summary or review of all the methods that have been submitted to her stellar activity challenge for extreme precision radial velocity spectroscopy. She has made the (very good) decision to organize the methods by the assumptions they make rather than the tools they use. For instance, several use principal components analysis, and several others use Gaussian processes. But if they use them in different places, they are effectively making different assumptions. But of course it isn't easy to take someone else's method and decide what assumptions it is making! So this review of all methods—which started out as just a small, necessary part of her paper about the challenge—is in the end one of the big intellectual achievements of this project. I'm excited about it. I'm rarely this excited about a paper that will have dozens and dozens of authors (although I guess I would make exceptions for this paper and this paper)!


k near n?

Teresa Huang (JHU) has a nice paper (with Villar and me) that shows the risk and regularization of linear regression involving PCA. We discussed it more today, in particular whether we can say more about the regime in which the PCA dimensionality reduction (to k dimensions) doesn't do much (because k is close to the number of data points n). We think we can, because the Marchenko-Pastur distribution of eigenvalues is so skew: Cutting off even one small eigenvalue (k=n-1) can be useful!


issues with SDSS-IV APOGEE data

I'm proud of my new undergraduate researcher Katherine Alsfelder (NYU). She has been working with me to understand the differences between the North (Apache Point Observatory) and South (Las Campanas Observatory) spectrographs used in the APOGEE-2 survey in SDSS-IV. We chose one fiber in the North spectrograph to compare with one fiber in the South spectrograph (just to get started). She noticed some discrepancies in the data model: Some of the data have inconsistent telescope IDs in different files. We sent an example we couldn't figure out to Mike Blanton (NYU) and he pointed out that a star at a Dec of -70 deg can't be observed with the Apache Point Observatory 2.5m! Haha well I guess that one was easy. But anyway, I'm happy because it shows the value of being careful in the reading and vetting of data, especially housekeeping data. And we developed a work-around.


how to simulate a spectrum

I had a great conversation today with Matt Daunt (NYU), building on discussion yesterday with also Megan Bedell (Flatiron), about how to simulate data from an extreme-precision radial-velocity spectrograph. We decided to simulate the star, the atmosphere, and the (gasp!) gas cell all at very high resolution, then combine them physically, then reduce resolution to the spectrograph resolution (which is very high nonetheless) and then sample and noisify the resulting data. The idea is: Make the structure of the code like the structure of our physical beliefs, or causal beliefs. We decided to fork this data simulation into its own project.


SDSS-V meeting

Katie Breivik (Flatiron) has started a meeting in New York for those interested in SDSS-V data and science. This has been fun; I have learned about a lot of different projects that I didn't know about. In today's meeting, Adrian Price-Whelan (Flatiron) showed some plots of the distribution of different abundances in the Milky Way disk, showing that we can probably see the Galaxy mid-plane way better in the abundances than in the kinematics. And kinematic evolution aligns the abundances with the kinematics! Nice result there. We vowed to have an expert come and walk us through SDSS-V target selection soon, since we were all soft on what, exactly, we would target!


more sailing

I spent the weekend in an undisclosed location working on my ram-pressure model for a sailboat. I realized that there are multiple models, even if you decide that it will be ram pressure! I coded up multiple models, and also worked on writing text. I made figures like this one!


talking about equivariant functions

I gave one of the internal/informal CCA seminars today. I spoke about our recent work on equivariant functions. I gave a pretty non-mathematical description of it, concentrating on things like Einstein summation notation and the symmetries of physical law, and the like. Afterwards, Ken Van Tilburg (NYU) commented that our result is so very simple that it must be known. I agree! But we couldn't find it in the literature anywhere clearly.


coarse-graining a point cloud with a kd-tree?

As my loyal reader knows, I am interested in fast-multipole method and whether it could be used to improve or speed machine-learning methods on graphs or spatial point clouds. Over the last months, I have learned about lots of limitations of FMMs, some of which we discuss here. I'm still interested! But when I last spoke with Leslie Greengard (Flatiron) he indicated that he felt like if you want to take FMMs scale up to very clustered data in high dimensions, maybe you have to think of truly adaptive trees (not the fixed tree of an FMM), like perhaps kd-trees. Today Soledad villar (JHU) and I discussed this idea. The question is: What could be proved about such an approach, or are there such approaches where you could get things like accuracy guarantees? The FMM has the beautiful property that you can compute the precision of your approximation, and dial up the order to get better precision.


abundance calibration and abundance gradients

Today Christina Eilers (MIT) updated Hans-Walter Rix (MPIA) and me on our project to self-calibrate the element-abundance measurements in APOGEE. We are looking at self-consistency of the abundance distribution as a function of actions; in a well-mixed Galaxy this could be used to calibrate the biases of the abundance measurements with surface gravity (a known effect in the data) and spectral resolution (a possible effect). Eilers has beautiful results: The abundances get better and the abundance gradients in the Galaxy (with radius or azimuthal action, and with vertical height or vertical action) become more clear and more sensible. So we have a paper to write!


machine-learning group meeting

Today Soledad Villar (JHU), Kate Storey-Fisher (NYU), Weichi Yao (NYU), and I crashed the machine-learning group meeting hosted by Shirley Ho (Flatiron) and Gaby Contardo (Flatiron). Villar presented our new paper on gauge-invariant functions and we started the conversation about what to do with it. We vowed to come back to the meeting to discuss that: What are the best applications of machine learning in cosmology and astrophysics right now?


a model for sailing (yes, sailing)

I've had a lifetime of conversations with Hans-Walter Rix (MPIA) about the point that you could in principle sail with a sailboat with flat sails: Nothing about the curvature of the sails is integral or required by sailing. The curvature helps, but isn't necessary. I have had another lifetime of conversations with Matt Kleban (NYU) about the point that sailing depends on the relative velocity between the air and the water, and this leads to some hilarious physics problems involving sailing on rivers in zero wind (it's possible because a flowing river is moving relative to the dead air).

These worlds collided this weekend because—inspired by a twitter conversation—I finally built a proper ram-pressure model of a flat-sail, flat-keel sailboat and got it all working. It's sweet! It sails beautifully. Much more to say, but question is: Is there a paper to write?


counting repeat spectra in APOGEE

I worked today with Katherine Alsfelder (NYU) to develop statistics on APOGEE spectra: There are two spectrographs (one in the North and one in the South) and there are 300 fibers per spectrograph. How many stars have been observed in each of the 600 different options, and how many of the 600-choose-2 options have seen the same star? This all in preparation for empirical cross-calibration of the spectrographs. There is a lot of data! But 600-choose-2 is a huge number.


information theory at Cambridge

Today I gave a colloquium at the University of Cambridge. My slides are here. I spoke about how to make precise measurements, how to design surveys, and how to exploit structure in noise. It's a rich set of things, and most of the writing about information theory in astronomy is only in the cosmology domain. Time to change that, maybe? It is also the case that the best book about information and inference ever written was written in Cambridge! So I was bringing coals to Newcastle, ish!


machine learning at #AAS238

Today I spoke at the “meeting-in-meeting” on machine learning at the summer AAS meeting. My slides are here. I started out a bit negative but I ended up saying very positive things about what machine learning can do for astrophysics. I got as much feedback on the twitters afterwards (maybe more) than I did in real time. Several of the other speakers in my session mentioned or discussed contrastive learning, which looks like it might be an interesting unsupervised technique.


making slides for AAS and Cambridge

I'm giving two talks this week, one at #AAS238 and one at the University of Cambridge. Because I am a masochist (?) I put in titles and abstracts for both talks that are totally unlike those for any talks I have given previously. So I have to make slides entirely from scratch! I spent every bit of time today not in meetings working on slides. I'm not at all ready!


vectors, bras, and kets

One of my PhD advisors—my official advisor—was Roger Blandford (now at Stanford). Blandford, being old-school, responded to a tweet thread I started by sending me email. I am trying to move over to always describing tensors and rotation operators and Lorentz transformations and the like in terms of unit vectors, and I realized that the most enlightened community along these lines are the quantum mechanics. Probably because they work in infinite-dimensional spaces often! Anyway, there are deep connections between vectors in a space and functions in a Hilbert space. I'm still learning; I think I will never fully get it.


objective functions and Nyquist sampling

Adrian Price-Whelan and I discussed today some oddities that Matt Daunt (NYU) is finding while trying to measure radial velocities in extremely noisy, fast APOGEE sub-exposures. He finds that the objective function we are using is not obviously smooth on 10-ish km/s velocity scales. Why not? We don't know. But what we do know is that a spectrograph with resolution 22,500 cannot put sharp structures into a likelihood function on scales smaller than about 13 km/s.

There's a nice paradox here, in fact: The spectrograph can't see features on scales smaller than 13 km/s, and yet we can reliably measure radial velocities much better than this! How? The informal answer is that the radial-velocity precision is 13 km/s divided by a certain, particular signal-to-noise. The formal answer involves information theory—the Fisher information, to be precise.


Dr Lily Zhao

I had the great honor to be on the PhD committee of Lily Zhao (Yale), who defended her dissertation today. It was great and remarkable. She has worked on hardware, calibration, software, stellar astrophysics, and planets. Her seminar was wide-ranging, and the number and scope of the questions she fielded was legion. She has already had a big impact on extreme precision radial-velocity projects, and she is poised to have even more impact in the future. One of the underlying ideas of her work is that EPRV projects are integrated hardware–software systems. This idea should inform everything we do, going forward. I asked a million technical questions, but I also asked questions about the search for life, and the astronomical community's management and interoperation of its large supply of diverse spectrographs. In typical Zhao fashion, she had interesting things to say about all these things.


orthogonalization in SR, continued

Soledad Villar (JHU) and I discussed more the problem of orthogonalization of vectors—or finding orthonormal basis vectors that span a subspace—in special (and general) relativity. She proposed a set of hacks that correct the generalization of Gram–Schmidt orthogonalization that I proposed a week or so ago. It's complicated, because although the straightforward generalization of GS works with probability one, there are cases you can construct that bork completely. The problem is that the method involves division by an inner product, and if the vector becomes light-like, that inner product vanishes.