The frequency of low-mass exoplanets. II. The "Period Valley"

Radial-velocity planet search campaigns are now beginning to detect low-mass "Super-Earth" planets, with minimum masses M sin i 10 M ⊕. Using two independently developed methods, we have derived detection limits from nearly four years of the highest-precision data on 24 bright, stable stars from the Anglo-Australian Planet Search. Both methods are more conservative than a human analyzing an individual observed data set, as is demonstrated by the fact that both techniques would detect the radial-velocity signals announced as exoplanets for the 61 Vir system in 50% of trials. There are modest differences between the methods which can be recognized as arising from particular criteria that they adopt. What both processes deliver is a quantitative selection process such that one can use them to draw quantitative conclusions about planetary frequency and orbital parameter distribution from a given data set. Averaging over all 24 stars, in the period range P< 300 days and the eccentricity range 0.0 < e < 0.6, we could detect 99% of planets with velocity amplitudes K 7.1 m s–1. For the best stars in the sample, we are able to detect or exclude planets with K 3 m s–1, corresponding to minimum masses of 8 M ⊕ (P = 5 days) or 17 M ⊕ (P = 50 days). Our results indicate that the observed "period valley," a lack of giant planets (M > 100 M ⊕) with periods between 10 and 100 days, is indeed real. However, for planets in the mass range 10-100 M ⊕, our results suggest that the deficit of such planets may be a result of selection effects. [please see online version for correct notation]