2008ApJ...674..466N

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 22 of the stars observed with the VLT NACO adaptive optics system by Masciadri and coworkers and 48 of the stars observed with the VLT NACO SDI and MMT SDI devices by Biller and coworkers (for a total of 60 unique stars), 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 semimajor axis between 20 and 100 AU, and mass above 4 M_Jup, is 20% or less. Also, with a distribution of planet mass of dN/dM∝M^–1.16 in the range of 0.5-13 M_Jup, we can rule out a power-law distribution for semimajor axis (dN/da∝a^α) with index 0 and upper cutoff of 18 AU, and index -0.5 with an upper cutoff of 48 AU. For the distribution suggested by Cumming et al., a power-law of index -0.61, we can place an upper limit of 75 AU on the semimajor axis distribution. In general, we find that even null results from direct imaging surveys are very powerful in constraining the distributions of giant planets (0.5-13 M_Jup) at large separations, but more work needs to be done to close the gap between planets that can be detected by direct imaging, and those to which the radial velocity method is sensitive.