Efficient, uninformative sampling of limb-darkening coefficients for a three-parameter law
Abstract
Stellar limb darkening impacts a wide range of astronomical measurements. The accuracy to which it is modelled limits the accuracy in any covariant parameters of interest, such as the radius of a transiting planet. With the ever growing availability of precise observations and the importance of robust estimates of astrophysical parameters, an emerging trend has been to freely fit the limb-darkening coefficients (LDCs) describing a limb-darkening law of choice, in order to propagate our ignorance of the true intensity profile. In practice, this approach has been limited to two-parameter limb-darkening laws, such as the quadratic law, due to the relative ease of sampling the physically allowed range of LDCs. Here, we provide a highly efficient method for sampling LDCs describing a more accurate three-parameter non-linear law. We first derive analytic criteria which can quickly test if a set of LDCs are physical, although naive sampling with these criteria leads to an acceptance rate less than 1 per cent. We then show that the loci of allowed LDCs can be transformed into a cone-like volume, from which we are able to draw uniform samples. We show that samples drawn uniformly from the conal region are physically valid in 97.3 per cent of realizations and encompass 94.4 per cent of the volume of allowed parameter space. We provide python and fortran code (ldc3) to sample from this region (and perform the reverse calculation) at https://github.com/davidkipping/LDC3, which also includes a subroutine to efficiently test whether a sample is physically valid or not.
- Publication:
-
Monthly Notices of the Royal Astronomical Society
- Pub Date:
- January 2016
- DOI:
- 10.1093/mnras/stv2379
- arXiv:
- arXiv:1509.03483
- Bibcode:
- 2016MNRAS.455.1680K
- Keywords:
-
- Astrophysics - Solar and Stellar Astrophysics;
- Astrophysics - Earth and Planetary Astrophysics;
- Astrophysics - Instrumentation and Methods for Astrophysics
- E-Print:
- 12 pages, 8 figures. Accepted to MNRAS. Code and LaTeX source at https://github.com/davidkipping/LDC3