Constraints on Extrasolar Planet Populations from VLT NACO/SDI and MMT SDI and Direct Adaptive Optics Imaging Surveys: Giant Planets are Rare at Large Separations

Abstract

We examine the implications for the distribution of extrasolar planets based on the null results from two of the largest direct imaging surveys published to date. Combining the measured contrast curves from Masciadri et al.  (2005) and Biller et al.  (2007), we consider what distributions of planet masses and semi-major axes can be ruled out by these data, based on Monte Carlo simulations of planet populations. We can set the following upper limit with 95% confidence: the fraction of stars with planets with semi-major axis between 20 and 100 AU, and mass above 4 M_Jup, is 20% or less. Also, with a distribution of planet mass of $\frac{{\rm d}N}{{\rm d}M} \propto M^{-1.16}$ in the range of 0.5–13 M_Jup, we can rule out a power-law distribution for semi-major axis ($\frac{{\rm d}N}{{\rm d}a} \propto a^{\alpha}$) with index 0 and upper cut-off of 18 AU, and index –0.5 with an upper cut-off of 48 AU. For the distribution suggested by Cumming et al.  (2008), a power-law of index –0.61, we can place an upper limit of 75 AU on the semi-major axis distribution.