THE MASS DISTRIBUTION FUNCTION of PLANETS

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Abstract

The distribution of orbital period ratios of adjacent planets in extrasolar planetary systems discovered by the Kepler space telescope exhibits a peak near ∼1.5-2, 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 these data that the dimensionless orbital separations have an approximately log-normal 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 , or about two-thirds of Jupiter's mass for solar-mass 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 of and , respectively.

Original languageEnglish (US)
Article number71
JournalAstrophysical Journal
Volume808
Issue number1
DOIs
StatePublished - Jul 20 2015

Keywords

  • celestial mechanics
  • planetary systems
  • planets and satellites: dynamical evolution and stability
  • planets and satellites: formation
  • planets and satellites: general

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

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