Periodic Flux Variability of Stars due to the Reflex Doppler Effect Induced by Planetary Companions

Abstract

Upcoming space-based photometric satellites offer the possibility of detecting continuum flux variability at the micro-magnitude level. We show that the Doppler flux variability induced by the reflex motion of stars due to planetary companions has an amplitude of (3-alpha)K/c, where K is the reflex radial velocity amplitude and alpha is the logarithmic slope of source spectral flux in the observed frequency band. For many of the known close-in planetary systems with periods less than ~0.2 years, the periodic Doppler variability is of order a micromagnitude, and is significant relative to the variability caused by reflected light from the planetary companion. For companions with periods greater than ~0.2 years, the Doppler signal is larger than the reflected light signal. We show that the future photometric satellites should reach the sensitivity to detect this Doppler variability. In particular, the Kepler satellite should have the photon-noise sensitivity to detect at a signal-to-noise ratio > 5, all planets with minimum mass greater than 5 Jupiter masses, and periods less than 0.1 years around the 10,000 main-sequence stars with spectral types A through K and apparent magnitude V<12 in its field-of-view.