Tuesday, March 3, 2015

The Mass Distribution Function of Planets

The Mass Distribution Function of Planets


Malhotra et al


The distribution of orbital period ratios of adjacent planets in extra-solar planetary systems discovered by the {\it Kepler} space telescope exhibits a peak near ∼1.5--2, a long tail of larger period ratios, and a steep drop-off in the number of systems with period ratios below ∼1.5. We find from this data that the dimensionless orbital separations have an approximately log-normal distribution. The paucity of small orbital separations implies that the population of planets does not increase monotonically as planet mass decreases. Using Hill's criterion for the dynamical stability of two planets, we find an upper bound on planet masses such that the most common planet mass does not exceed 10−3.2m∗, or about two-thirds Jupiter mass for solar mass stars. We generalized Hill's criterion in a statistical way to estimate the planet mass distribution function from the distribution of orbital separations. We suggest that the planet mass function is peaked in logarithm of mass, and we estimate that the most probable value of logm/M⊕ is ∼(0.64−0.72).

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