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

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 that is approximately flat in log M. The frequency drops off very sharply as masses go higher than 10 M_J, although we suspect there is still a higher mass tail that extends up to probably 20 M_J. We estimate that 5% of the G stars in the solar neighborhood have planets in the range 1-10 M_J with periods shorter than 1500 days. For comparison we present the mass distribution of stellar companions in the range 100-1000 M_J, 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.