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

Radial velocity measurements have proven a powerful tool for finding planets in short-period orbits around other stars. 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 and the sensitivity to periods longer than the total length of observations are explored. We show that current observations are not yet long or accurate enough to make unambiguous detection of planets with the same mass and period as Jupiter. However, if measurements are continued at the current levels of accuracy (5 m s(-1)) for a decade, then planets of Jovian mass and brown dwarfs will either be detected or ruled out for orbits with periods less than similar to 15 yr. 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 12 yr period by Walker et al. Had any of these stars shown motion like that caused by the exoplanets recently detected, it would have been easily detected. The data set interesting limits on the presence of brown dwarfs at orbital radii of 5-10 AU. The most significant features in the Walker et al. data are apparent long-term velocity trends in 36 UMa and beta Vir, consistent with super planets of mass of 2 M-J in a 10 yr period, or 20-30 M-J in a 50 yr period. If the data are free of long-term systematic errors, the probability of just one of the 14 stars showing this signal by chance is about 15%. Finally, we suggest an observing strategy for future large radial velocity surveys that, 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 2 yr of the survey, then 2-3 measurements yr(-1) thereafter, provided no (or slow) variation is observed. More frequent observations would of course be indicated if such variations were present.