ericagol
commented
7 years ago There are limb-darkening coefficients computed at specific wavelengths by, e.g., the Phoenix model. How reliable these are, I'm not sure, especially since there is a lot of complicated physics going on at the surfaces of stars - the hydrodynamic models computed by Ashland and collaborators seem to give the most reliable broad-band limb-darkening curves - https://arxiv.org/abs/1403.3487 https://doi.org/10.1051/0004-6361/201117868 - and I suspect these are the best at individual wavelengths - Zazralt Magic shared these with me, if you would like to use them, or you can check out https://doi.org/10.1093/mnras/stv1857. One thing I know is that the limb-darkening can change dramatically within absorption lines since the opacity changes dramatically within a line. This can even lead to limb-brightening within lines (which is fairly common: https://doi.org/10.1051/0004-6361/201526386), and should definitely be accounted for when doing high resolution transit transmission spectroscopy, and can lead to significant errors (http://dx.doi.org/10.1051/0004-6361/201219888). I think the hope is that the molecular features are not present in the stellar photosphere, but this isn't guaranteed for atomic features, such as sodium and potassium, nor is it guaranteed for very cool stellar photospheres (at what temperature can a star, or star spot, support steam in its atmosphere?). Another issue is that star spots (even unocculted spots) can affect the inferred transmission spectrum, if unaccounted for; star spots that are distributed in longitude may not manifest strongly in stellar variability, but may skew the spectrum (. And, transit-transmission spectroscopy probes high in the atmosphere, which may have a different composition, and can be affected by clouds, especially since models predict clouds tend to form at the terminator. These are all of the reasons I prefer second-eclipse spectrometry and direct imaging over transit-transmission spectroscopy. @jlustigy (PS - I just came across this paper, which looks interesting: https://arxiv.org/abs/1704.08232)
rodluger
There doesn't seem to be a standard way to easily treat wavelength-dependent limb darkening. The Claret models provide tabulated coefficients for the intensity variation over the surface of the star in a variety of photometric filters, but what we need are the coefficients at specific wavelengths -- or, better yet, the coefficients for the effective temperature variation over the stellar surface. That's how I'm currently treating limb darkening -- by assuming that the star is a perfect blackbody, but with an effective temperature that decreases towards the limb.
Unfortunately, there's nothing in the literature that provides coefficients or models for how the effective temperature changes over the stellar surface. It's not strictly true that the wavelength dependence of limb darkening follows a blackbody, so perhaps it's not the best way to treat this?
I was thinking that we could have the users provide the limb darkening coefficients in some filter, then we run a curve-fitting routine to find the temperature coefficients that would match the corresponding intensity variation after convolving with the filter response. Is it worth doing this?
What do people do when modeling limb darkening in transit transmission spectroscopy? Do they assume it's the same coefficients at all wavelengths? That's crazy!