Maximum likelihood method for estimating the mass and period distributions of extra-solar planets
Abstract
We investigate the distribution of mass M and orbital period P of extra-solar planets, taking account of selection effects due to the limited velocity precision and duration of existing surveys. We fit the data on 63 planets to a power-law distribution of the form dn=CM-alphaP-beta(dM/M)(dP/P), and find alpha=0.12+-0.10, beta=-0.26+-0.06 for M<10MJ, where MJ is the Jupiter mass. The correlation coefficient between these two exponents is -0.32, indicating that uncertainties in the two distributions are coupled. We estimate that 3% of solar-type stars have companions in the range 1MJ<M<10MJ, 2d<P<10yr.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.