Limb darkening laws for two exoplanet host stars derived from 3D stellar model atmospheres

Comparison with 1D models and HST light curve observations^⋆

¹ Astrophysics Group, School of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, UK
e-mail: hayek@astro.ex.ac.uk; sing@astro.ex.ac.uk; fpont@astro.ex.ac.uk
² Research School of Astronomy & Astrophysics, Cotter Road, Weston Creek 2611, Australia
e-mail: martin@mso.anu.edu.au
³ Max Planck Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany

Received: 10 August 2011
Accepted: 14 January 2012

Abstract

We compare limb darkening laws derived from 3D hydrodynamical model atmospheres and 1D hydrostatic MARCS models for the host stars of two well-studied transiting exoplanet systems, the late-type dwarfs HD 209458 and HD 189733. The surface brightness distribution of the stellar disks is calculated for a wide spectral range using 3D LTE spectrum formation and opacity sampling^⋆. We test our theoretical predictions using least-squares fits of model light curves to wavelength-integrated primary eclipses that were observed with the Hubble Space Telescope (HST).

The limb darkening law derived from the 3D model of HD 209458 in the spectral region between 2900 Å and 5700 Å produces significantly better fits to the HST data, removing systematic residuals that were previously observed for model light curves based on 1D limb darkening predictions. This difference arises mainly from the shallower mean temperature structure of the 3D model, which is a consequence of the explicit simulation of stellar surface granulation where 1D models need to rely on simplified recipes. In the case of HD 189733, the model atmospheres produce practically equivalent limb darkening curves between 2900 Å and 5700 Å, partly due to obstruction by spectral lines, and the data are not sufficient to distinguish between the light curves. We also analyze HST observations between 5350 Å and 10 500 Å for this star; the 3D model leads to a better fit compared to 1D limb darkening predictions.

The significant improvement of fit quality for the HD 209458 system demonstrates the higher degree of realism of 3D hydrodynamical models and the importance of surface granulation for the formation of the atmospheric radiation field of late-type stars. This result agrees well with recent investigations of limb darkening in the solar continuum and other observational tests of the 3D models. The case of HD 189733 is no contradiction as the model light curves are less sensitive to the temperature stratification of the stellar atmosphere and the observed data in the 2900–5700 Å region are not sufficient to distinguish more clearly between the 3D and 1D limb darkening predictions.