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.

writing and integrating

I spent the day hiding from all responsibilities in order to write. I wrote in my spectrophotometric-distances paper, and I wrote in my new chemical-tangents paper. I am trying to get the first of these done and submitted before I leave Heidelberg this month.

I also did a little bit of coding in the chemical-tangents project. I wrote up a general integrator that can take a general vertical density profile in the Milky Way and integrate one-dimensional orbits. It produces position, velocity, and phase for general orbits in the general one-d gravitational problem. Next up: Using this to characterize the GALAH data.

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.

spiral arms? and model-grid troubleshooting

The excitement of the day is that we looked at velocity-tensor maps (maps of the means of average velocity-velocity products) across the disk with Eilers (MPIA): We see lots of structure, including possible evidence of spiral arms or bar resonances on the off-diagonal tensor components. Reminder: If the Galaxy is axisymmetric, there will only be diagonal tensor components in the R, phi, z coordinate system. If we find off-diagonal components: Non-axisymmetry. Could be interesting. Rix (MPIA) encouraged us to stay on target for a Jeans model and leave these hints of complex disk morphology for later investigations.

In addition to this, I had a great chat with Maria Bergemann (MPIA) and Mikhail Kovalev (MPIA) about fitting spectra with spectral models, given that the models are amazingly expensive to compute. They do a (random) grid and then interpolate using The Payne. They are getting some results they aren't happy with, so I walked through basic tests that can be done in these situations.

Basic sanity checks—when you are fitting data using an interpolation of a grid or random assemblage of model predictions—are the following: Find the closest model point in the grid, and then the K next closest, where K is larger than the dimensionality of the model parameter space. Is the best-fit model in the convex hull of the K? Are the K in one group or multiple groups? Do the K look like they hit the edge of the grid? And what are the chi-squared values? And is the interpolated best point also in the convex hull? All these pieces of information go into an analysis of whether you have enough model evaluations and how to interpolate them.

evidence for dark-matter in (exceedingly large) colliders

Today Ana Bonaca (Harvard) showed beautifully that the features seen in the GD-1 stellar stream are very well described by an encounter in the past (collision, if you will) with a dark-matter substructure. Her argument is fundamentally qualitative, but so many aspects of the data are matched by the toy model she has made that it is hard to see how to get around the conclusion. This could be huge! We discussed the scope of the paper she could write (or really the content of the abstract).

don't cut Gaia on parallax signal-to-noise!

We spent the day discussing Milky-Way halo and disk structures with Amina Helmi (Kapteyn). It was fun! Along the way, Adrian Price-Whelan (Princeton) and I spent time looking at large halo structures that have been found in the literature. We could find some extremely odd structures when we match the cuts used in the papers we were looking at. And then we found the following:

Say you are cutting at parallax signal-to-noise of 5 (parallax over parallax error greater than 5). And then you look at the configuration-space shape of the stellar distribution you find? Well guess what? Since parallax errors are a strong function of sky position, the shape of your object will be very strange at large distance. For instance, the parallax errors only go below 0.05 mas in some parts of the sky. So your stellar distribution will only extend out past 4 kpc in some specific directions (and not all directions).

All this relates to various things I have said repeatedly in this forum: Build your science on measured quantities, not estimated uncertainties on those quantities! Your uncertainties are not really your data, and it is almost impossible to know your uncertainties on your uncertainties. Furthermore, the people who want to cut on parallax signal-to-noise are also using inverse-parallax as distance, and that's dangerous too. Finally, if you cut on parallax signal-to-noise, you will bias any means or averages or regressions you do using those parallaxes.

My advice: Find ways to work that don't require these cuts. These issues are a big danger for people using actions to study the stellar distribution: Actions require distances, distances are generally inverse-parallax, and then low signal-to-noise parallaxes must get cut. These arguments apply there too. We have to forward-model the data if we want to understand spatial structures, I am afraid.

tidal distortions and disruption

At lunch we had a discussion (inspired by Bertrand Goldman, MPIA) about the expected shapes of open clusters. I think they should be elongated along their orbits. There was some back and forth but this made me more confident: Once the clusters start to disperse, they should distort through orbital phase-frequency differences. I proposed a simple test of this. But I'm more interested in the point that this should help us find new kinds of (maybe older) clusters!

In the afternoon, Amina Helmi (Kapteyn) showed up and Bonaca (Harvard), Price-Whelan (Princeton), and I discussed many things with her. We discussed the question of when and how stellar streams in the Milky Way halo constrain purely local properties of the Galaxy. Does this result (from Bonaca) depend on the potential being time-dependent? I think it does. Helmi didn't disagree but is optimistic that we can handle the time dependence.

We also discussed the lack of tidal tails around globular clusters: Is it surprising that only Palomar 5 has these tails? Price-Whelan has looked at a few of the most likely clusters in Gaia, and nada. This led to (or was part of) a longer discussion of the statistics of streams: How many will there be and how many do we expect?

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 5

Bedell (Flatiron) and I worked out a greedy method to optimize the regularization parameters for wobble, at least roughly. The method is necessary, because there are 72 orders and we have come to the conclusion that for every order, for every different kind of star, we are going to need a unique set of regularization parameters.

Birky (UCSD) showed that M-dwarf stars with different kinds of pathologies (fast rotation, pre-main-sequence, flaring, or binary) have larger chi-squared values against our Cannon model. We are going to leave it at that, but because we have these dependencies, we are going to be able to make data-driven spectral indicators of all these things.

Rix (MPIA) and I discussed the results that Eilers (MPIA) produced this week. We realized that we don't have to get the full density model for the tracers right; we can just show our results in the context of various sensible assumptions about those tracers. That's a simplification, and sensible, given what we have.

Ringberg, day 4

Today was almost all Milky-Way rotation-curve work, all day. Eilers (MPIA) and I worked through a checklist of things we need to figure out, and some of them made the project clearer, and some much less clear. In order to model the rotation curve with a set of tracers that are phase-mixed but not on circular orbits, we need a model for the asymmetric drift. This model is fundamentally a Jeans model, for which we need to know various second moments of the velocity field, and some derivatives of density and velocity dispersion with respect to radius. The second moments are (relatively) easy to measure, but without a selection function it is hard to get the derivatives of the density field!

For now, we decided to get our density models from the literature, if we can. That doesn't look super-hopeful. But I'm still hoping!

Other work included conversations with Bedell (Flatiron) about how the regularization we are using in wobble to control spectral model complexity doesn't seem to want to be the same in different parts of the stellar spectrum (which are differently complex!); with Lauer (NOAO) about using PCA to build data-driven models of nuisances; and with Anderson (Flatiron) about using RR Lyrae stars from PanSTARRS to characterize (and also find new) halo substructures.

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.

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.