Synthesizing Exoplanet Demographics From Radial Velocity and Microlensing Surveys. I. Methodology

Abstract

Motivated by the order-of-magnitude difference in the frequency of giant planets orbiting M dwarfs inferred by microlensing and radial velocity (RV) surveys, we present a method for comparing the statistical constraints on exoplanet demographics inferred from these methods. We first derive the mapping from the observable parameters of a microlensing-detected planet to those of an analogous planet orbiting an RV-monitored star. Using this mapping, we predict the distribution of RV observables for the planet population inferred from microlensing surveys, taking care to adopt reasonable priors for, and properly marginalize over, the unknown physical parameters of microlensing-detected systems. Finally, we use simple estimates of the detection limits for a fiducial RV survey to predict the number and properties of analogs of the microlensing planet population such an RV survey should detect. We find that RV and microlensing surveys have some overlap, specifically for super-Jupiter mass planets (m p 1 M Jup ) with periods between ∼ 3 − 10 years. However, the steeply falling planetary mass function inferred from microlensing implies that, in this region of overlap, RV surveys should infer a much smaller frequency than the overall giant planet frequency (m p 0.1 M Jup ) inferred by microlensing. Our analysis demonstrates that it is possible to statistically compare and synthesize data sets from multiple exoplanet detection techniques in order to infer exoplanet demographics over wider regions of parameter space than are accessible to individual methods. In a companion paper, we apply our methodology to several representative microlensing and RV surveys to derive the frequency of planets around M dwarfs with orbits of 30 years.

Ogle-2012-BLG-0724lb: A Saturn-Mass Planet Around an M Dwarf

“…Clanton & Gaudi (2014) found that the planet abundances estimated by microlensing are consistent with those found by radial velocity. Recently, Shvartzvald et al (2015) estimated planet abundance and mass function based on nine events and found that 55% of stars host a planet beyond the snow line and Neptune-mass planets are ∼10 times more common than Jupiter-mass planets.…”

OGLE-2016-BLG-1190Lb: The First Spitzer Bulge Planet Lies Near the Planet/Brown-dwarf Boundary

“…However, if the method for measuring complete Kepler orbits can be extended from binaries to planets (as we begin to do here), then it will permit much stricter comparison between RV and microlensing samples, which has so far been possible only statistically, (e.g., Gould et al 2010;Clanton & Gaudi 2014a, 2014b. In particular, we provide here the first evidence for a non-circular orbit of a microlensing planet.…”

Predictions of the WFIRST Microlensing Survey. I. Bound Planet Detection Rates

“…In addition to uncertainties in the planet mass function, there is even greater uncertainty in the form of the planet occurrence as a function of semimajor axis near to WFIRST's peak sensitivity. Clanton & Gaudi (2014a) have shown that that there is at present very little overlap in the sensitivity regions of current microlensing and radial velocity (RV) surveys, but radial velocity surveys tend to show an increase in planet occurrence with log semimajor axis or log period (e.g., Cumming et al 2008;Bonfils et al 2013) that appears to be consistent with microlensing occurrence rates when extrapolated (see, e.g., Gould et al 2010;Suzuki et al 2016). Results from Kepler show a similar rising trend for large planets, but a shallow decline in occurrence beyond P ∼10 d for planets smaller than Neptune (e.g.…”