Simultaneously infer telluric correction

[gully]

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.

[kgullikson88]

I'll chime in on this one with some suggestions and concerns:

• Don't use the telfit.TelluricFitter class; use telfit.Modeler directly instead because that only makes a telluric model.

• There are a couple options for speed that I can think of:

  1. If you use the modeler directly with everything default, it will take ~1 second to make the model which is probably much too long for an MCMC calculation. You could speed it up by at most an order of magnitude by generating your own binary linefile that only includes the wavelength range you are interested in (the default goes from 300nm to 5um). You could even do something clever like having a separate very small linefile for each echelle order.

  2. Treat the telluric model in the same way as you treat the stellar models; e.g. generate a large grid once, and pre-convolve to the instrumental resolution. This would probably make things much faster in the likelihood evaluation, but the grid needs to be huge. Even if you ignore the effect of the atmosphere profile, it needs to encompass:

     • Temperature at the observatory
     • Pressure at the observatory (though this rarely changes by much)
     • Humidity at the observatory
     • Each of 11 other molecules at the observatory location (though you could probably get by with just co2, co, n2o, no, ch4)
     • Telescope zenith angle / airmass

     You would in fact need to make such a grid for every observatory, or add grid axes for observatory altitude and latitude. As you can imagine, this grid will be gigantic.

  3. You might be able to be clever by making a course grid and using linear approximations in between grid points. See the Beer's law section in the Advanced notebook of my recent tutorial. For instance, you could approximate unsaturated lines at a 45 degree zenith angle pretty well by just adjusting a 40 degree model; it will do poorly for saturated lines though, so watch out!