The Lick Planet Search: Detectability and Mass Thresholds

We present an analysis of 11 yr of precision radial velocity measurements of 76 nearby solar-type stars from the Lick radial velocity survey. For each star, we report on variability, periodicity, and long-term velocity trends. Our sample of stars contains eight known companions with mass less than 8 (M p sin i) Jupiter masses six of which were discovered at Lick. For the remaining stars, we place upper limits (M J ), on the companion mass as a function of orbital period. For most stars, we can exclude companions with velocity amplitude m s~1 at the 99% level, or for orbital radii K Z 20 M p sin i Z 0.7M J (a/AU)1@2 a [ 5 AU. We examine the implications of our results for the observed distribution of mass and orbital radius of companions. We show that the combination of intrinsic stellar variability and measurement errors most likely explains why all conÐrmed companions so far have m s~1. The Ðnite duration of the K Z 40 observations limits detection of Jupiter-mass companions to AU. Thus it remains possible that the a [ 3 majority of solar-type stars harbor Jupiter-mass companions much like our own, and if so these companions should be detectable in a few years. It is striking that more massive companions with are rare at orbital radii 4È6 AU; we could have detected such objects in D90% of stars, M p sin i [ 3M J yet found none. The observed companions show a ““ piling-up ÏÏ toward small orbital radii, and there is a paucity of conÐrmed and candidate companions with orbital radii between D0.2 and D1 AU. The small number of conÐrmed companions means that we are not able to rule out selection e†ects as the cause of these features. We show that the traditional method for detecting periodicities, the Lomb-Scargle periodogram, fails to account for statistical Ñuctuations in the mean of a sampled sinusoid, making it nonrobust when the number of observations is small, the sampling is uneven, or for periods comparable to or greater than the duration of the observations. We adopt a ““ Ñoating-mean ÏÏ periodogram, in which the zero point of the sinusoid is allowed to vary during the Ðt. We discuss in detail the normalization of the periodogram and the probability distribution of periodogram powers. We stress that the three di†erent prescriptions in the literature for normalizing the periodogram are statistically equivalent and that it is not possible to write a simple analytic form for the false alarm probability, making Monte Carlo methods essential. Subject headings : binaries : spectroscopic È methods : statistical È planetary systems