Orbital parameters of extrasolar planets derived from polarimetry

Context. Polarimetry of extrasolar planets becomes a new tool for their investigation, which requires the development of diagnostic techniques and parameter case studies. Aims. Our goal is to develop a theoretical model which can be applied to interpret polarimetric observations of extrasolar planets. Here we present a theoretical parameter study that shows the influence of the various involved parameters on the polarization curves. Furthermore, we investigate the robustness of the fitting procedure. We focus on the diagnostics of orbital parameters and the estimation of the scattering radius of the planet. Methods. We employ the physics of Rayleigh scattering to obtain polarization curves of an unresolved extrasolar planet. Calculations are made for two cases: (i) assuming an angular distribution for the intensity of the scattered light as from a Lambert sphere and for polarization as from a Rayleigh-type scatterer; and (ii) assuming that both the intensity and polarization of the scattered light are distributed according to the Rayleigh law. We show that the difference between these two cases is negligible for the shapes of the polarization curves. In addition, we take the size of the host star into account, which is relevant for hot Jupiters orbiting giant stars. Results. We discuss the influence of the inclination of the planetary orbit, the position angle of the ascending node, and the eccentricity on the linearly polarized light curves both in Stokes Q/I and U/I. We also analyze errors that arise from the assumption of a point-like star in numerical modeling of polarization as compared to consistent calculations accounting for the finite size of the host star. We find that errors due to the point-like star approximation are reduced with the size of the orbit, but still amount to about 5% for known hot Jupiters. Recovering orbital parameters from simulated data is shown to be very robust even for very noisy data because the polarization curves react sensitively to changes in the shape and orientation of the orbit. Conclusions. The proposed model successfully diagnoses orbital parameters of extrasolar planets and can also be applied to predict polarization curves of known exoplanets. Polarization curves of extrasolar planets thus provide an ideal tool to determine parameters that are difficult to obtain with other methods, namely inclination and position angle of the ascending node of orbits as well as true masses of extrasolar planets.