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

Serge Tabachnik·Scott Tremaine
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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^{-alpha}P^{-beta}(dM/M)(dP/P), and find alpha=0.12+-0.10, beta=-0.26+-0.06 for M<10M_J, where M_J 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 1M_J<M<10M_J, 2d<P<10yr.

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Serge Tabachnik, Scott Tremaine. 2001-10-22. Maximum likelihood method for estimating the mass and period distributions of extra-solar planets. https://doi.org/10.1046/j.1365-8711.2002.05610.x

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