Radial Velocity Detectability of Low‐Mass Extrasolar Planets in Close Orbits

Abstract

Detection of Jupiter-mass companions to nearby solar-type stars with precise radial velocity measurements is now routine, and Doppler surveys are moving toward lower velocity amplitudes. The detection of several Neptune-mass planets with orbital periods of less than a week has been reported. The drive toward the search for close-in, Earth-mass planets is on the agenda. Successful detection or meaningful upper limits will place important constraints on the process of planet formation. In this paper, we quantify the statistics of detection of low-mass planets in close orbits, showing how the detection threshold depends on the number and timing of the observations. In particular, we consider the case of a low-mass planet close to but not on the 2 : 1 mean motion resonance with a hot Jupiter. This scenario is a likely product of the core-accretion hypothesis for planet formation coupled with migration of Jupiters in the protoplanetary disk. It is also advantageous for detection because the orbital period is well constrained. We show that the minimum detectable mass is ≈4 M⊕ (N/20)-1/2(σ/m s-1)(P/days)1/3(M*/M☉)2/3 for N ≥ 20, where N is the number of observations, P is the orbital period, σ is the quadrature sum of Doppler velocity measurement errors and stellar jitter, and M* is the stellar mass. Detection of few Earth-mass rocky cores will require ~1 m s-1 velocity precision and, most important, a better understanding of stellar radial velocity jitter.