extreme infrared excesses

Gaby Contardo (SISSA) showed up in Heidelberg today to make progress on our project on infrared excesses in normal, non-young FGK stars. Because we are using NASA WISE data (along with ESA Gaia and NASA 2MASS), we are only sensitive to bright, hot infrared excesses, much hotter and brighter than typical debris disks around old stars. We have some candidates, which range in temperature from 300 to 1500 K and are reprocessing maybe one percent or a fraction of a percent of the stellar light. (Warning: I haven't calculated this; this is just a guesstimate based on looking at plots.) What are those things? Today we figured out that they can't be warm substellar companions, so they have to be dust (I guess??).

infrared excesses for planet-hosting stars

Gaby Contardo (Flatiron) and I went to the Gaia EDR3 Archive to make use of its matched catalogs, matching up Gaia, 2MASS, and WISE. We are looking at very short-period planet hosts, which might show interesting photometric deviations. We took one host star, and then found many other stars with similar photometry in the visible. Do they agree in the infrared? It looks like maybe there is a tiny discrepancy? But the power will come from doing many, not just one.

we have new spectrophotometric distances

After a couple of days of hacking and data munging—and looking into the internals of Jax—Adrian Price-Whelan and I produced stellar distance estimates today for a few thousand APOGEE spectra. Our method is based on this paper on linear models for distance estimation with some modifications inspired by this paper on regression. It was gratifying! Now we have hyper-parameters to set and valication to do.

re-doing spectroscopic distances in EDR3 with high-alpha too

Christina Eilers (MIT) and I discussed our ESA Gaia EDR3 projects today. Our top priority is to re-do our machine-learning (linear regression, really) spectrophotometric distance estimates for very luminous red-giant stars, and then re-map the Milky Way disk in abundances and kinematics. We think that even a small improvement in the parallaxes (as we expect to get on Thursday) might make a big difference to our inferred spectroscopic distances. We discussed the point that in our DR2 work we only used stars on the “low-alpha sequence”; we want to generalize if we are going to make complete abundance maps. But also the stars with different abundance trends might want very different distance estimation parameters. That suggests doing the EDR3 regression in a more “abundance-aware” way.

visualizing substructure in large data

Today Doug Finkbeiner (Harvard), Josh Speagle (Harvard), and Ana Bonaca (Harvard) came to visit me in my undisclosed location in Heidelberg. We discussed many different things, including Finkbeiner's recent work on finding outliers and calibration issues in the LAMOST spectral data using a data-driven model, and Speagle's catalog of millions of stellar properties and distances in PanSTARRS+Gaia+2MASS+WISE.

Bonaca and I took that latter catalog and looked at new ways to visualize it. We both have the intuition that good visualization could and will pay off in these large surveys. Both in terms of finding structures and features, and giving us intuition about how to build automated systems that will then look for structures and features. And besides, excellent visualizations are productive in other senses too, like for use in talks and presentations. I spent much of my day coloring stars by location in phase space or the local density in phase space, or both. And playing with the color maps!

There's a big visualization literature for these kinds of problems. Next step is to try to dig into that.

ready to submit!

I worked on the weekend to finish my paper with Eilers (MPIA) and Rix (MPIA). It is ready to submit! And yet I can't push my changes properly to GitHub because they are (in a very rare moment) down! I made some compromises in finishing up this paper; I can only justify them by promising myself I will address the final issues while the referee considers the manuscript.

finishing papers; galaxy morphology regressions

The morning started with a conversation between Eilers (MPIA) and I in which we decided that we will finish our connected papers (first draft anyway) by Friday. I think she will make it! But will I make it? I am going to be strong. We also went through some ideas about testing the assumptions that underly our Jeans model for the Milky Way disk, and what to write about the outcomes of those tests.

Mid-day I had good conversations with Storey-Fisher (NYU) about building pseudo-simulations that make point sets with low-amplitude non-trivial power spectra. We spent an unfortunate amount of time figuring out how the numpy fft module organizes and stores fourier transform data. It isn't trivial!

In the afternoon, Elisa Chisari (Oxford) gave a nice (and pleasantly technical) talk about weak lensing, which evolved into a longer discussion about how we might get more information out of galaxy imaging surveys. I pitched my ideas of thinking about how we might train regression models that can predict dark-matter structure from galaxy morphologies or even better large-scale-structure morphologies. And Chisari has (indirect) evidence that such approaches might be very powerful, because (with simulations) she showed (in the context of intrinsic-alignment contamination of weak-lensing data) that even simple measures of galaxy morphology are expected to be very sensitive to the local gravitational tidal field.

One thing that came up in this discussion is my suspicion that ellipticity is a very blunt tool. I have counter-examples that show that ellipticity is not necessarily the galaxy property most sensitive to the weak-lensing field (in an information-theoretic sense). But we formulated a challenge: Make an adversarial morphology distribution for galaxies such that none of the weak-lensing information in the data is in the galaxy ellipticities. That would be hilarious (or instructive, or both).

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.

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.

bad development cycle is bad

My day started with a conversation with Christina Eilers (MPIA) about the Milky Way rotation curve. We found some strange kinematics points that might be messing with us, and realized that they are almost all stars at or past the Bulge, and therefore not affecting our results, which are only for Galactocentric radii greater than 5 kpc, to avoid the craziness of the bar (which violates our dynamical assumptions). Her figures are ready, so I encouraged her to write figure captions and assemble the paper.

I spent my research time getting MCMC running on my Chemical Tangents project. I have a marginalized likelihood, so all I had to do is put on priors and insert into emcee. Oh how I would have benefitted from a testing environment! When I packaged it all up for emcee I messed up the units of almost all the inputs, so I got garbage in every MCMC run. And the runs took a long time, so diagnosis was painful. Unit testing. And for units! Live and fail to learn, that's what I say.

Once everything appeared to be working, I set up some (nasty) multi-processing, set my laptop to stay awake all night, and blew processes. I should have converged samplings by morning.

The Cannon again, chemical tori

Within one frantic half-hour, Eilers (MPIA) and I completely implemented a new version of The Cannon and ran it on her sample of luminous red giants. We did this so that we can compare the internals of her linear model for parallax estimation to the internal derivatives or label dependencies for The Cannon. This will let us take a step towards interpreting the internals of the spectrophotometric-parallax model. We scanned the comparison but it doesn't look quite as easy to interpret as I had hoped.

As soon as this was done, I said some words in MPIA Milky Way group meeting about my ideas for Chemical Tangents: That is, the idea that orbits must lie in the level surfaces (hyper-surfaces in 6-d phase space) of the chemical abundance distribution. The method puts an enormous number of constraints on the orbit space, so it has the potential to be extremely constraining. Rix (MPIA) is suspicious that it all sounds too good to be true: The method requires no knowledge of the selection function (to zeroth order) and no second-order statistics. It is entirely first-order in the data. Damn I hope I'm not wrong here.

In the morning, Rene Andrae (MPIA) showed me his enormous cross-match of spectroscopic surveys that he is putting together in part to understand the stellar parameter pipelines of Gaia (to which he is a contributor). He has the input data for a combinatoric diversity of projects we could do with The Cannon or stellar-parameter self-calibration.

projects examined

Rix (MPIA) started the day concerned with substantial issues with the linear parallax model that Eilers (MPIA) and I have built; we spent much of the day following them up. Our precision gets worse with distance—an effect we have noticed all summer but haven't been able to explain—and now we have to explain it! We compared stars in clusters and looked at parallax offsets as a function of various things; we don't yet have an explanation. But we did do some straightforward error propagation and guess what: Our precision really can't be much better than the 9-ish percent that we are seeing. The whole exercise left me more confident in the quality of the model in the end: The model really seems to have learned how to cope with dust, age, and intrinsic luminosity effects, even though we didn't tell it how.

In a call with Bonaca (Harvard) we looked at oddities in her model of the morphology of the GD-1 stream gaps. We had some provable scalings that should be there but the code wasn't reproducing them. We worked out today that the stream perturbation isn't quite in the regime we thought it was. In more detail: An encounter of a massive perturber with a stream is impulsive if GM/(b v^2) is much less than 1, where G is Newton's constant, M is the perturber's mass, b is the impact parameter, and v is the relative velocity of the encounter (or maybe some component thereof). That is, you have to have this dimensionless number much less than unity if you want the impulse approximation to hold. Duh! But now we understand the simulations she is making.

The day ended with Birky (UCSD) and I calling Andrew Mann (UNC) and Adam Burgasser (UCSD) to discuss Birky's results modeling M-type dwarf spectra in APOGEE. She has beautiful results, and can show both that her spectral models are accurate (in the space of the spectral data) and that her inferences about latents (temperature and metallicity) are reasonable when compared with proxies and tests of various kinds. So it is time to finish writing it up! We made plans for that. One amusing thing about her project is that it creates a beautiful translation between temperature, metallicity, and spectral type. And it isn't trivial!

RR Lyrae like red giants

At the suggestion of Rix (MPIA), Eilers (MPIA), Rix, and I applied Eilers's and my linear model for parallax prediction to the RR Lyrae sample from PanSTARRS and Gaia DR2 today. It worked beautifully, delivering an error-convolved scatter of less than 7 percent, and an error-deconvolved intrinsic scatter of something more like 5 percent in distance. That's exciting! Our features are magnitudes, period, and light-curve shape parameters. Eilers was able to do this all in under an hour, because it was a plug-in replacement for the model we built for upper-red-giant-branch stars. This is another confirmation that on sufficiently small parts of the color–magnitude diagram, linear models can do a great job of predicting stellar properties, especially absolute magnitude or distance. Deep learning be damned!

Aside from this, most of my research time today (and this weekend) was spent writing. Trying to submit the red-giant paper before I depart Germany.

optimization is the worst

After the incredibly valuable Milky Way Group Meeting discussion of the spectrophotometric parallaxes, Eilers (MPIA) and I simplified our model, re-factored the code, and re-ran. And, despite the fact that the new model is provably better than the old model, everything failed. The reason is: Our objective isn't convex. Not only that, but there is an enormously high-dimensional degenerate bad optimum that is hard to avoid. That sent us back to the books: Optimization is hard!

The trick we settled on (and you are allowed to do many, many tricks here) is to take the very highest signal-to-noise stars (in terms of Gaia parallax) to optimize an initialization and then do our final optimization with all stars, but starting off from that initialization. That is, we burn in to the optimum using the best stars first. It's a hack but it worked, and now the better model is performing the way it should be. That's good! Because it is discouraging when you refactor your code and everything goes worse.

A MPIA Galaxy Coffee, Wolfgang Brandner (MPIA) described the new GRAVITY results on the perihelion passage of S2 at the Galactic Center. The perihelion passage shows gravitational and transverse-Doppler redshifts and puts an amazingly strong constraint on the geometry and kinematics of the Galactic Center.

spectrophotometric parallax; optimization fail

Today was spectrophotometric-parallax day. I did writing in the paper, I presented the method at MPIA Milky Way Group Meeting, and Eilers (MPIA) and I refactored slightly the model. In the presentation I gave, we got lots of feedback about how to present the method, which I tried to record carefully in the to-do list at the top of our LaTeX document. We also realized that without much change, we could move the model from a model for magnitude to a direct model for the parallax, bypassing any physical idea of how the star indicates its parallax (which is through its brightness and its log-g, to leading order). So our model is now truly data-driven. We also realized that we could make changes to how we represent the spectral pixels that might make the parameters more well-behaved.

All these things are great things! But when we made the relevant code changes, everything borked. The reason appears simple: It is because the model has a bad pathology: While it has a very good, sensible, non-trivial optimum, it has an enormous family of degenerate trivial optima in which the exponential underflows, the predicted parallaxes are all zero, and the derivatives all vanish. And at 7400 free parameters, this degenerate set of minima has a huge space (huge entropy) to find and eat our optimizer. So by the end of the day, Eilers and I realized we have to get much more clever about initializing the optimizer.

Question of the day: Does the method need a name, like The Cygnet? Or is it okay to just call it “linear spectrophotometric parallax”?

writing

I spent the day writing in the spectroscopic-parallax project. I wrote six or seven paragraphs, and that's about it! (Actually, that's a great day: My goal is two paragraphs per day.)

But in addition to the writing, I did have an interesting conversation with Tom Herbst (MPIA), Thomas Bertram (MPIA), and Kalyan Radhakrishnan (MPIA) about adaptive optics. The idea is to think about using the science data (the imaging you care about) to update the adaptive mirrors. What new things might be unlocked by that, especially if used in concert with the wavefront sensors? This reminds me of old conversations I have had with Matthew Kenworthy (Leiden). I also asked what kinds of science you might do with the wavefront sensors. Just as the imaging detector gives wavefront information, the wavefront sensors give imaging information!

I also was present for presentations by Eilers (MPIA) and Birky (UCSD) on their stellar projects in the MPIA Stars Group Meeting.

all talk

Today was an all-talk day! But I did get in a bit of morning time writing in the spectroscopic-parallax method paper. I have to figure out whether the model is convex. I am not sure that it is, but I can't see why not. In the talking part of my day, I spoke with Bedell (Flatiron) about continuum-normalization of stars. I think I have improvements to the sigma-clipping hack we are currently doing, but I feel like I am reinventing the wheel! I spoke with Bonaca (Harvard) about our plans to drop dark-matter-halo-perturbed streams into toy Galaxy potentials. She had a very small-scope recommendation, which I accepted. And I spoke with Rene Andrae (MPIA) about computationally permitted options for the Gaia CU8 pipelines. They have extremely restricted memory and time requirements for their pipeline, so they can't do all the things they would like to do. He showed me some nice results with random-basis methods, which have good properties both statistically and computationally.

hike-writing and hike-coding

I was off the grid for a few days, but I took opportunities when others were hiking to sit at the Hütte and do some writing in the spectroscopic-parallax (or spectroscopic estimates of luminosity and distance) project. I have structured the paper in our new style, which is to lay out all assumptions clearly at the beginning and then find the method that flows from those assumptions. If no method flows, new or different or additional assumptions are needed. This makes the subjectivity clear, but also protects us from the complaint that there are implicit assumptions. A referee can object to the assumptions but (we hope) not the method given the assumptions.

I also worked out with Adrian Price-Whelan (Princeton) the details of the simplest possible inference of dynamics from element abundances. The idea is to find the dynamical model that makes the abundances a function (only) of the dynamical actions (or other invariants). For the demonstration project, we are just going to do vertical dynamics, and just with very simple moments of the abundance distribution. I built and tested a leap-frog integrator to integrate the vertical orbits.

Ringberg, day 2

While I was on vacation, Jessica Birky (UCSD) used Gaia DR2 to identify many M-type dwarfs among the APOGEE spectroscopy, and type them using our data-driven models. The effective temperatures and metallicities that she finds vary beautifully along and across (respectively) the main sequence. It looks great. There are also many stars way above the main sequence, and we think these may be very young stars that are falling onto the main sequence. If that's true, it looks like we will have age indicators too. But we might postpone that to a second paper.

Megan Bedell (Flatiron) and I discussed the regularization scheme in her wobble code to measure precise radial velocities of stars, and also deliver extremely precise telluric and micro-telluric models. We decided to revisit all of the regularization and try to set it sensibly. The problem we are facing is that there are more regularization parameters and choices than we can comfortably cross-validate. So we have to do something more greedy for now. We discussed and Bedell started to implement. We also discussed the new scope for our note on information-theory bounds on radial-velocity precision; my job is to write that up tonight or tomorrow.

Christina Eilers (MPIA) and I made many improvements to her code to map the Milky-Way disk with red-giant stars, including changing slightly the absolute-magnitude model, estimating uncertainties on kinematic quantities through proper (nonlinear) error-propagation, switching to cylindrical coordinates, and working out (with the enormous help of Hans-Walter Rix and Ortwin Gerhard) a Jeans approach to getting the rotation curve in the face of asymmetric drift. At the end of the day I became convinced that the simplicity of our data-driven model for stellar luminosities will permit us to infer a dust map from our results; as my loyal reader knows, this is why I love linear models! I hope I'm right.

linear models for the win

Christina Eilers (MPIA) and I have been debating what photometry and colors to put into our linear model for distance estimation or distance-modulus estimation. And then we realized: It is a general linear model! So we should just put in all photometry and the code will decide what colors to create and use. We did, and the model improved for the stars behind the most dust. Just a reminder: We don't explicitly extinction-correct anything! We ask the model to figure out extinction on its own, by training on a sample that has stars at different extinctions.

In the afternoon I had a conversation with Maryam Modjaz (NYU) and Marc Williamson (NYU) about applying PCA and other simple machine-learning techniques to their library of supernova spectra across type and phase. They have some nice results, that show that the first few PCA components do a good job of separating types, and they can show that the separation quality is a function of time (relative to maximum light, or the explosion). We discussed using something like a purely linear support vector machine to do classification that would be highly interptetable. As my loyal reader knows, I am happy to sacrifice some performance for interpretability.