The Mass Distribution Function of Planets
Abstract
The distribution of orbital period ratios of adjacent planets in extrasolar planetary systems discovered by the Kepler space telescope exhibits a peak near ∼1.52, a long tail of larger period ratios, and a steep dropoff in the number of systems with period ratios below ∼1.5. We find from these data that the dimensionless orbital separations have an approximately lognormal distribution. 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}^{3.2}{m}_{*}, or about twothirds of Jupiter’s mass for solarmass stars. Assuming that the mass ratio and the dynamical separation (orbital spacings in units of mutual Hill radius) of adjacent planets are independent random variates, and adopting empirical distributions for these, we use Hill’s criterion in a statistical way to estimate the planet mass distribution function from the observed distribution of orbital separations. We find that the planet mass function is peaked in logarithm of mass, with a peak value and standard deviation of {log}m/{M}_{\oplus } of ∼ (0.61.0) and ∼ (1.11.2), respectively.
 Publication:

The Astrophysical Journal
 Pub Date:
 July 2015
 DOI:
 10.1088/0004637X/808/1/71
 arXiv:
 arXiv:1502.05011
 Bibcode:
 2015ApJ...808...71M
 Keywords:

 celestial mechanics;
 planetary systems;
 planets and satellites: dynamical evolution and stability;
 planets and satellites: formation;
 planets and satellites: general;
 Astrophysics  Earth and Planetary Astrophysics
 EPrint:
 Updated analysis with debiased period ratio data and updated discussion