The range of masses and periods explored by radial velocity searches for planetary companions

Abstract

In this paper we develop an analytical expression relating the sensitivity to a periodic signal to the duration and accuracy of a given set of data. The effects of windowing are explored, and also the sensitivity to periods longer than the total length of observations. As specific examples, we outline the performance of our technique on large amplitude and large eccentricity radial velocity signals recently discussed in the literature and we delineate the region explored by the measurements of 14 single stars made over a twelve year period by Walker et al. (1995). Had any of these stars shown motion like that caused by the exo-planets recently detected, it would have been easily detected. Finally, we suggest an observing strategy for future large radial velocity surveys which, if implemented, will allow coverage of the largest range of parameter space with the smallest amount of observing time per star. We suggest that about 10-15 measurements be made of each star in the first two years of the survey, then 2--3 measurements per year thereafter, provided no (or slow) variation is observed. More frequent observations would of course be indicated if such variations were present.