Because of various bits of bad luck, it was a low-research day today. The one real research thing I got into today was exploring all the nearly-geometric approaches to improving Gaia parallaxes. The idea is: If you are a hard-core astrometrist, you only believe geometric distances. And Gaia measures those! But how can you improve upon Gaia without bringing in additional assumptions about stars, stellar photospheres, stellar evolution, and so on? The answer is that you can't, trivially. However, you can think about approaches that use very minimal additional information, and nothing so dirty and gastrophysical as a stellar model:
You can use joint information of all the stars to improve every individual star! This is what we did in Anderson et al. We assumed that all stars come from a stationary distribution in color and magnitude, but we used a very flexible model for that and trained it entirely on purely geometric information. So it was like an amplification of the geometric information latent in the larger data set, applied to each individual star.
What Dustin Lang (Toronto), Megan Bedell (Flatiron), and I are thinking about is whether we can use stars that appear to move together to make new information. That is, if two stars are co-moving and near each other in an angular sense, they are very likely to be close in radial distance. So we can combine parallax information, and improve both stars. That is a purely geometric method, although it does make (fairly weak) assumptions about the existence of binary stars.
On another thread, Boris Leistedt (NYU) and I are thinking about how to use proper motion to constrain distances. This definitely makes strong assumptions about the Galaxy, but they are very reasonable and testable, and they exist only in the kinematic domain (not the gastrophysical). So that's promising. But it's early days.
To do better than Gaia, you have to make additional assumptions. Duh! But what are the most anodyne and conservative assumptions that we can make that still have the effect of betterizing parallax or distance inferences?