A Dynamical Method for Measuring the Masses of Stars with Transiting Planets

Abstract

As a planet transits the face of a star, it accelerates along the line of sight. The changing delay in the propagation of photons produces an apparent deceleration of the planet across the sky throughout the transit. This persistent transverse deceleration breaks the time-reversal symmetry in the transit light curve of a spherical planet in a circular orbit around a perfectly symmetric star. For ``hot Jupiter'' systems, ingress advances at a higher rate than egress by a fraction of ~10-4-10-3. Forthcoming space telescopes such as Kepler or COROT will reach the sensitivity required to detect this asymmetry. The scaling of the fractional asymmetry with stellar mass M* and planetary orbital radius a, as M*/a2, is different from that of the orbital period, which scales as (M*/a3)-1/2. Therefore, this effect constitutes a new method for a purely dynamical determination of the mass of the star. Radial velocity data for the reflex motion of the star can then be used to determine the planet's mass. Although orbital eccentricity could introduce a larger asymmetry than the light-propagation delay, the eccentricity is expected to decay by tidal dissipation to negligible values for a close-in planet with no perturbing third body. Future detection of the eclipse of a planet's emission by its star could be used to measure the light-propagation delay across the orbital diameter, 46.7(a/7×1011 cm) s, and also determine the stellar mass from the orbital period.