The effects of viewing angle on the mass distribution of exoplanets

TL;DR

This paper introduces a mathematical method to statistically correct for unknown inclination angles in radial-velocity exoplanet data, revealing the true mass distribution and challenging previous assumptions about low-mass decline.

Contribution

It develops a novel statistical approach to recover the true exoplanet mass distribution from observed data, accounting for unknown viewing angles.

Findings

The recovered mass distribution fits observed data well at both mass ends.

The low-mass decline may be explained by the true distribution, not sample incompleteness.

The exoplanet mass distribution likely changes form at low masses, deviating from a single power law.

Abstract

We present a mathematical method to statistically decouple the effects of unknown inclination angles on the mass distribution of exoplanets that have been discovered using radial-velocity techniques. The method is based on the distribution of the product of two random variables. Thus, if one assumes a true mass distribution, the method makes it possible to recover the observed distribution. We compare our prediction with available radial-velocity data. Assuming the true mass function is described by a power-law, the minimum mass function that we recover proves a good fit to the observed distribution at both mass ends. In particular, it provides an alternative explanation for the observed low-mass decline, usually explained as sample incompleteness. In addition, the peak observed near the the low-mass end arises naturally in the predicted distribution as a consequence of imposing a low-mass cutoff in the true-distribution. If the low-mass bins below 0.02 M_J are complete, then the mass distribution in this regime is heavily affected by the small fraction of lowly inclined interlopers that are actually more massive companions. Finally, we also present evidence that the exoplanet mass distribution changes form towards low-mass, implying that a single power law may not adequately describe the sample population.