Polarimetry of transiting planets: Differences between plane-parallel and spherical host star atmosphere models

Context. To properly interpret photometric and polarimetric observations of exoplanetary transits, accurate calculations of center-to-limb variations of intensity and linear polarization of the host star are needed. These variations, in turn, depend on the choice of geometry of stellar atmosphere. Aims. We want to understand the dependence of the flux and the polarization curves during a transit on the choice of the applied approximation for the stellar atmosphere: spherical and plane-parallel. We examine whether simpler plane-parallel models of stellar atmospheres are good enough to interpret the flux and the polarization light curves during planetary transits, or whether more complicated spherical models should be used. Methods. Linear polarization during a transit appears because a planet eclipses a stellar disk and thus breaks left-right symmetry. We calculate the flux and the polarization variations during a transit with given center-to-limb variations of intensity and polarization. Results. We calculate the flux and the polarization variations during transit for a sample of 405 extrasolar systems. Most of them show higher transit polarization for the spherical stellar atmosphere. Our calculations reveal a group of exoplanetary systems that demonstrates lower maximum polarization during the transits with spherical model atmospheres of host stars with effective temperatures of Teff = 4400−5400 K and surface gravity of log g = 4.45−4.65 than that obtained with plane-parallel atmospheres. Moreover, we have found two trends of the transit polarization. The first trend is a decrease in the polarization calculated with spherical model atmosphere of host stars with effective temperatures Teff = 3500−5100 K, and the second shows an increase in the polarization for host stars with Teff = 5100−7000 K. These trends can be explained by the relative variation of temperature and pressure dependences in the plane-parallel and spherical model atmospheres. Conclusions. For most cases of known transiting systems the plane-parallel approximation of stellar model atmospheres may be safely used for calculation of the flux and the polarization curves because the difference between two models is tiny. However, there are some examples where the spherical model atmospheres are necessary to get proper results, such as the systems with grazing transits, with Earth-size planets, or for the hot host stars with effective temperatures higher than 6000 K.