Derivation of the Mass Distribution of Extrasolar Planets with MAXLIMA - a Maximum Likelihood Algorithm

Abstract

We construct a maximum-likelihood algorithm - MAXLIMA, to derive the mass distribution of the extrasolar planets when only the minimum masses are observed. The algorithm derives the distribution by solving a numerically stable set of equations, and does not need any iteration or smoothing. Based on 50 minimum masses, MAXLIMA yields a distribution which is approximately flat in log M, and might rise slightly towards lower masses. The frequency drops off very sharply when going to masses higher than 10 Jupiter masses, although we suspect there is still a higher mass tail that extends up to probably 20 Jupiter masses. We estimate that 5% of the G stars in the solar neighborhood have planets in the range of 1-10 Jupiter masses with periods shorter than 1500 days. For comparison we present the mass distribution of stellar companions in the range of 100--1000 Jupiter masses, which is also approximately flat in log M. The two populations are separated by the "brown-dwarf desert", a fact that strongly supports the idea that these are two distinct populations. Accepting this definite separation, we point out the conundrum concerning the similarities between the period, eccentricity and even mass distribution of the two populations.

arXiv comment19 pages, 3 figures, submitted to The Astrophysical Journal

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