EPRV at Yale

I spent an absolutely great and energizing day at Yale today, with the groups of Debra Fischer (Yale) and Jessie Cisewski-Kehe (Yale), who are working together to bring the best in hardware and the best in statistics to the hard problem of making (much) better than m/s-level radial-velocity measurements. We talked about many things, but highlights included:

How do you put uncertainty estimates on extracted spectral pixels? In the 2d-to-1d extraction step, the estimation of a single 1d spectral pixel is a modification of a least-square fit in the 2d image. How to put a good uncertainty on that, especially when the model isn't strictly linear least squares? We discussed Fisher-information estimates, which are best-case estimates, and also bootstrap or jackknife estimates, which are probably more conservative. The nice thing is that the EXPRES spectrograph (Debra Fischer's instrument) has many 2d pixels per 1d pixel, so these empirical methods like jackknife are possible.

What parts of the spectrum are most sensitive to activity? One approach is to find activity labels and perform a regression from spectral pixels to activity labels. Bo Ning (Yale) is taking this approach, with strong regularization to force most pixels to zero out in the regression. He finds plausible results, with the centers of certain lines contributing strongly to the regression. We discussed the kinds of tests one can do to validate the results. Ning also has evidence that the ability to find good activity indicators might be a strong function of spectral resolution, which is good for projects like EXPRES and ESPRESSO, which have very high resolution.

How can we measure radial velocities in the presence of stellar variability? We now think that stellar variability is the tall pole in EPRV. If it is, we have some deep and fundamental questions to ask here, since the whole edifice of relative RV measurement relies on the source being constant in time! We discussed different approaches to his ill-posed problem, including using only spectral information about RV that is somehow orthogonal to the spectral variability, or placing strong priors on the RV signal to separate it from the variability signal, or performing some kind of causal-inference-like regression. There is room for good theory here. Parker Holzer (Yale) is working on some theory along the orthogonality lines.