TY - JOUR

T1 - Limb darkening and exoplanets - II. Choosing the best law for optimal retrieval of transit parameters

AU - Espinoza, Néstor

AU - Jordán, Andrés

N1 - Publisher Copyright:
© 2016 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society.

PY - 2016/2/10

Y1 - 2016/2/10

N2 - Very precise measurements of exoplanet transit light curves both from ground-and space-based observatories make it now possible to fit the limb-darkening coefficients in the transit-fitting procedure rather than fix them to theoretical values. This strategy has been shown to give better results, as fixing the coefficients to theoretical values can give rise to important systematic errors which directly impact the physical properties of the system derived from such light curves such as the planetary radius. However, studies of the effect of limb-darkening assumptions on the retrieved parameters have mostly focused on the widely used quadratic limb-darkening law, leaving out other proposed laws that are either simpler or better descriptions of model intensity profiles. In this work, we show that laws such as the logarithmic, square-root and three-parameter law do a better job that the quadratic and linear laws when deriving parameters from transit light curves, both in terms of bias and precision, for a wide range of situations. We therefore recommend to study which law to use on a case-by-case basis. We provide code to guide the decision of when to use each of these laws and select the optimal one in a mean-square error sense, which we note has a dependence on both stellar and transit parameters. Finally, we demonstrate that the so-called exponential law is non-physical as it typically produces negative intensities close to the limb and should therefore not be used.

AB - Very precise measurements of exoplanet transit light curves both from ground-and space-based observatories make it now possible to fit the limb-darkening coefficients in the transit-fitting procedure rather than fix them to theoretical values. This strategy has been shown to give better results, as fixing the coefficients to theoretical values can give rise to important systematic errors which directly impact the physical properties of the system derived from such light curves such as the planetary radius. However, studies of the effect of limb-darkening assumptions on the retrieved parameters have mostly focused on the widely used quadratic limb-darkening law, leaving out other proposed laws that are either simpler or better descriptions of model intensity profiles. In this work, we show that laws such as the logarithmic, square-root and three-parameter law do a better job that the quadratic and linear laws when deriving parameters from transit light curves, both in terms of bias and precision, for a wide range of situations. We therefore recommend to study which law to use on a case-by-case basis. We provide code to guide the decision of when to use each of these laws and select the optimal one in a mean-square error sense, which we note has a dependence on both stellar and transit parameters. Finally, we demonstrate that the so-called exponential law is non-physical as it typically produces negative intensities close to the limb and should therefore not be used.

KW - Methods: data analysis

KW - Stars: atmospheres

KW - Stars: individual: exoplanets

KW - Techniques: photometric

UR - http://www.scopus.com/inward/record.url?scp=84963800645&partnerID=8YFLogxK

U2 - 10.1093/mnras/stw224

DO - 10.1093/mnras/stw224

M3 - Article

AN - SCOPUS:84963800645

SN - 0035-8711

VL - 457

SP - 3573

EP - 3581

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

IS - 4

ER -