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

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 23 of the stars observed with the VLT NACO adaptive optics system by Masciadri et al. (2005), and 47 of the stars observed with the VLT NACO SDI and MMT SDI devices by Biller et al. (2007) (for a total of 59 unique stars: the median star for our survey is a 30 Myr K2 star at 25 pc), we consider what distributions of planet masses and semimajor 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 15 and 100 AU, and mass above 4 MJup, is 20% or less. Also at the 95% confidence level, with a distribution of planet mass of dN dM ∝ M in the range of 0.5-13 MJup, we can rule out a power-law distribution for semi-major axis ( da ∝ a) with index 0 and upper cut-off of 16 AU, and index -0.5 with an upper cut-off of 42 AU. For the distribution suggested by Cumming et al. (2007), a power-law of index -0.61, we can place an upper limit of 70 AU on the semi-major axis distribution, again at the 95% confidence level. In other words, given these assumptions for the semi-major axis distribution, and using the models of Burrows et al. (2003), giant planets are rare past 70 AU. At the 68% confidence level, these upper limits