Simultaneously infer telluric correction

Simultaneously infer telluric correction

The problem: The near-infrared wavelength range is peppered with telluric absorption lines that vary depending on many atmospheric and observation properties. Removal of the telluric lines is usually performed by observing relatively featureless spectra (A stars), and deriving a telluric correction spectrum, which is then divided out of the target star. This process is imperfect and generally leaves artifacts, especially if the wavelength solution is mismatched between the target and telluric standard. Another strategy for removing the telluric lines is to model directly the telluric spectrum with Earth atmospheric models. Kevin Gullikson (@kgullikson88) has done this with his TelFit package, and solutions exist for ESO and elsewhere.

The problem is that TelFit struggles when the continuum is not smooth, as in a relatively featureless spectrum (like an A star). As a result, the telluric models derived for M-dwarfs are biased, and telluric correction is poor. Besides, the uncertainty in the telluric correction is never taken into account, and therefore stellar properties could be biased. The Right Thing To Do is simultaneously model the telluric absorption lines and stellar spectrum.

Suggested solution:
Incorporate the TelFit atmospheric model directly into the Starfish Model, treating the atmospheric model parameters as nuisance parameters.

Practical Consideration and Costs:
Let's just clear the air that this idea is very low priority. There are many costs to get this to work. First, the upfront cost involves splitting out the relevant part of TelFit and incorporating it into the Starfish Model. Once in the Starfish Model, the telluric model had better be fast, otherwise it's going to slow down our likelihood calculation unacceptably. And for all that work, 1) only a small portion of the spectrum has been affected so its impact on derived stellar parameters will probably be low, and 2) we still might not get a good telluric fit anyways. Plus to really get this right, the user has to go through some outside research to acquire the Earth's upper atmosphere profile for the date, time, and location of the observation. In principle this profile could also be inferred, but that's overkill.

The issue names the Starfish Model and the external TelFit package, but no repository files or tests. Start by locating the Starfish Model and reviewing how TelFit could be incorporated into it as nuisance parameters. Done would require a fast simultaneous stellar and telluric fit that propagates telluric-correction uncertainty.