2020MNRAS.493.1596S

Scattered starlight from an exoplanet, commonly called reflected light, can be used to characterize the planet including the determination of its albedo and inclination of orbit. The relatively low flux ratio between directly observed starlight and starlight scattered off hot Jupiters make these systems the prime candidates for detection of reflected light using high-resolution spectroscopy. The first detections have been claimed for 51 Peg b. In a first calculation, we derive the Doppler shift of reflected light measured by a remote observer for a planet modelled as a point-like particle in orbit around a star. We find that the Doppler shift of reflected light from planets have a different Doppler shift to that of light emitted directly from the planet with magnitude equivalent to the radial motion of the planet with respect to the star. This only occurs for non-circular orbits. Secondly, restricting our investigation to planets that are tidally locked and orbit in circular orbits we account for the finite size of the star and planet by integrating the contribution to a simulated spectral line across both their surfaces. Since exact analytical expressions cannot be easily derived as a function of all free parameters of the problem, we have developed a software tool called REFLECTED STARLIGHT (RESTART) that produces the resulting line profiles. By applying it to study cases found in the literature, we explicitly show that hot Jupiters such as WASP-19b and 51 Peg b should show substantial broadening and asymmetric distortions compared to the nominal stellar line.