Periodic flux variability of stars due to the reflex Doppler effect induced by planetary companions

Upcoming space-based photometric satellites offer the possibility of detecting continuum flux variability at the micromagnitude (mumag) 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 approximate to (d ln F-v/d ln nu) is the logarithmic slope of the source spectral flux in the observed frequency band. For many of the known close-in planetary systems with periods P less than or similar to 0.2 yr, the periodic Doppler variability, O(mumag), is significant relative to the variability caused by reflected light from the planetary companion. For companions with P greater than or similar to 0.2, 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 greater than or similar to5 all planets with minimum mass M-p sin i greater than or similar to 5M(J) and P less than or similar to 0.1 around the similar to10(4) main-sequence stars with spectral types A-K and apparent magnitude V < 12 in its field of view.