The orbital eccentricity distribution of planets orbiting M dwarfs
Sheila Sagear, Sarah Ballard
Abstract
We investigate the underlying distribution of orbital eccentricities for planets around early-to-mid M dwarf host stars. We employ a sample of 163 planets around early- to mid-M dwarfs across 101 systems detected by NASA’s Kepler Mission. We constrain the orbital eccentricity for each planet by leveraging the Kepler lightcurve together with a stellar density prior, constructed using metallicity from spectroscopy, K s magnitude from 2MASS, and stellar parallax from Gaia. Within a Bayesian hierarchical framework, we extract the underlying eccentricity distribution, assuming alternately Rayleigh, half-Gaussian, and Beta functions for both single- and multi-transit systems. We described the eccentricity distribution for apparently single-transiting planetary systems with a Rayleigh distribution with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>σ</mml:mi> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>0.19</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.03</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.04</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> , and for multitransit systems with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>σ</mml:mi> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>0.03</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.01</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.02</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> . The data suggest the possibility of distinct dynamically warmer and cooler subpopulations within the single-transit distribution: The single-transit data prefer a mixture model composed of two distinct Rayleigh distributions with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>σ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>0.02</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.00</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.11</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>σ</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>0.24</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.03</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.20</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> over a single Rayleigh distribution, with 7:1 odds. We contextualize our findings within a planet formation framework, by comparing them to analogous results in the literature for planets orbiting FGK stars. By combining our derived eccentricity distribution with other M dwarf demographic constraints, we estimate the underlying eccentricity distribution for the population of early- to mid-M dwarf planets in the local neighborhood.