THE REFLECTION EFFECT IN INTERACTING BINARIES OR IN PLANET-STAR SYSTEMS

Abstract

There are many similarities between interacting binary stars and stars with a close-in giant extrasolar planet. The reflection effect is a well-known example. Although the generally accepted treatment of this effect in interacting binaries is successful in fitting light curves of eclipsing binaries, it is not very suitable for studying cold objects irradiated by hot objects or extrasolar planets. The aim of this paper is to develop a model of the reflection effect which could be easily incorporated into the present codes for modeling of interacting binaries so that these can be used to study the aforementioned objects. Our model of the reflection effect takes into account the reflection (scattering), heating, and heat redistribution over the surface of the irradiated object. The shape of the object is described by the non-spherical Roche potential expected for close objects. Limb and gravity darkening are included in the calculations of the light output from the system. The model also accounts for the orbital revolution and rotation of the exoplanet with appropriate Doppler shifts for the scattered and thermal radiation. Subsequently, light curves and/or spectra of several exoplanets have been modeled and the effects of the heat redistribution, limb darkening/brightening, (non-)gray albedo, and non-spherical shape have been studied. Recent observations of planet-to-star flux ratio of HD189733b, WASP12b, and WASP-19b at various phases were reproduced with very good accuracy. It was found that HD189733b has a low Bond albedo and intense heat redistribution, while WASP-19b has a low Bond albedo and low heat redistribution. The exact Roche geometries and temperature distributions over the surface of all 78 transiting extrasolar planets have been determined. Departures from the spherical shape may vary considerably but departures of about 1% in the radius are common within the sample. In some cases, these departures can reach 8%, 12%, or 14%, for WASP-33b, WASP-19b, and WASP-12b, respectively. The mean temperatures of these planets also vary considerably from 300 K to 2600 K. The extreme cases are WASP-18b, WASP-12b, and WASP-33b, with mean temperatures of 2330 K, 2430 K, and 2600 K, respectively.