Maximum-likelihood method for estimating the mass and period distributions of extrasolar planets

Abstract

We investigate the distribution of mass M and orbital period P of extrasolar planets, taking account of selection effects caused by the limited velocity precision and duration of existing surveys. We fit the data on 72 planets to a power-law distribution of the form dn = C M-α P-β (dM/M)(dP/P), and find α = 0.11 ± 0.10, β = -0.27 ± 0.06 for M ≲ 10 MJ, where MJ is the mass of Jupiter. The correlation coefficient between these two exponents is -0.31, indicating that uncertainties in the two distributions are coupled. We estimate that 4 per cent of solar-type stars have companions in the range 1 MJ < M < 10 MJ, 2 d < P < 10 yr.