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[1812.01606] qpower2 – a fast and accurate algorithm for the computation of exoplanet transit light curves with the power-2 limb-darkening law


(Submitted on 4 Dec 2018)

Abstract: The power-2 law, $I_λ(μ)=1- c (1 – μ^α)$, accurately
represents the limb-darkening profile for cool stars. It has been implemented
in a few transit models to-date using numerical integration but there is as-yet
no implementation of the power-2 law in analytic form that is generally
available. An algorithm to implement the power-2 law is derived using a
combination of an approximation to the required integral and a Taylor expansion
of the power-2 law. The accuracy of stellar and planetary radii derived by
fitting transit light curves with this approximation is tested using light
curves computed by numerical integration of limb-darkening profiles from 3D
stellar model atmospheres. Our algorithm (qpower2) is accurate to about 100 ppm
for broad-band optical light curves of systems with a star-planet radius ratio
p = 0.1. The implementation requires less than 40 lines of python code so can
run extremely fast on graphical processing units (GPUs; $sim$ 1 million models
per second for the analysis of 1000 data points). Least-squares fits to
simulated light curves show that the star and planet radius are recovered to
better than 1% for p < 0.2. The qpower2 algorithm can be used to efficiently
and accurately analyse large numbers of high-precision transit light curves
using Monte Carlo methods.

Comments:8 pages. The qpower2 algorithm is available as a part of the pycheops package at this https URL
Subjects:Earth and Planetary Astrophysics (astro-ph.EP); Instrumentation and Methods for Astrophysics (astro-ph.IM); Solar and Stellar Astrophysics (astro-ph.SR)
Cite as:arXiv:1812.01606 [astro-ph.EP]
 (or
arXiv:1812.01606v1 [astro-ph.EP]
for this version)

Submission history

From: Pierre Maxted [view email]

[v1]
Tue, 4 Dec 2018 09:08:14 UTC (79 KB)



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