The conversation on Friday with Cisewski and Bedell got me thinking all weekend. It appears that the problem of precise RV difference measurement becomes ill-posed once we permit the stellar spectrum to vary with time. I felt like I nearly had a breakthrough on this today. Let me start by backing up.
It is impossible to obtain exceedingly precise absolute radial velocities (RVs) of stars, because to get an absolute RV, you need a spectral model that puts the centroids of the absorption lines in precisely the correct locations. Right now physical models of convecting photospheres have imperfections that lead to small systematic differences in line shapes, depths, and locations between the models of stars and the observations of stars. Opinions vary, but most astronomers would agree that this limits absolute RV accuracy at the 0.3-ish km/s level (not m/s level, km/s level).
How is it, then, that we measure at the m/s level with extreme-precision RV (EPRV) projects? The answer is that as long as the stellar spectrum doesn't change with time, we can measure relative velocity changes to arbitrary accuracy! That has been an incredibly productive realization, leading as it did to the discovery, confirmation, or characterization of many hundreds of planets around other stars!
The issue is: Stellar spectra do change with time! There is activity, and also turbulent convection, and also rotation. This puts a long-term wrench in the long-term EPRV plans. It might even partially explain why current EPRV projects never beat m/s accuracy, even when the data (on the face of it) seem good enough to do better. Now the question is: Do the time variations of stellar spectra put an absolute floor on relative-RV measurement? That is, do they limit ultimate precision?
I think the answer is no. But the Right Thing To Do (tm) might be hard. It will involve making some new assumptions. No longer will we assume that the stellar spectrum is constant with time. But we will have to assume that spectral variations are somehow uncorrelated (in the long run) with exoplanet phase. We might also have to assume that the exoplanet-induced RV variations are dynamically predictable. Time to work out exactly what we need to assume and how.