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

Abstract

The power-2 law, $I_{\lambda }(\mu )=1-c(1-{\mu }^{\alpha })$, 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.

8 pages. The qpower2 algorithm is available as a part of the pycheops package at https://pypi.python.org/pypi/pycheops

References in corpus (17)

• emcee: The MCMC Hammer
• Analytic Lightcurves for Planetary Transit Searches
• The K2 Mission: Characterization and Early results
• The PLATO 2.0 Mission
• batman: BAsic Transit Model cAlculatioN in Python
• Efficient, uninformative sampling of limb darkening coefficients for two-parameter laws
• HST/STIS Optical Transit Transmission Spectra of the hot-Jupiter HD209458b
• ELLC - a fast, flexible light curve model for detached eclipsing binary stars and transiting exoplanets
• The Stagger-grid: A grid of 3D stellar atmosphere models - IV. Limb darkening coefficients
• Properties of analytic transit light curve models
• On stellar limb darkening and exoplanetary transits
• Limb-darkening and exoplanets II: Choosing the Best Law for Optimal Retrieval of Transit Parameters
• Detection of Potential Transit Signals in 17 Quarters of Kepler Data: Results of the Final Kepler Mission Transiting Planet Search (DR25)
• An Independent Analysis of Kepler-4b through Kepler-8b
• High-precision stellar limb-darkening in exoplanetary transits
• Comparison of the power-2 limb-darkening law from the Stagger-grid to Kepler light curves of transiting exoplanets
• Limb Darkening and Planetary Transits: Testing Center-to-limb Intensity Variations and Limb-Darkening Directly from Model Stellar Atmospheres

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