A numerical inversion of m sin i exoplanet distribution: the sub-Saturn desert is more depleted than observed and hint of a Uranus mass gap

Abstract

ABSTRACT The detection of an exoplanet orbiting another star with the radial velocity (RV) method allows to determine only a minimum mass of the planet, msin i, m being the true mass and i the angle of inclination of the planet orbital polar axis with the line of sight. Given an observed discretized distribution of m sin i apparent masses f0(msin i), we have designed a simple algorithm to find a unique true mass distribution f(m) that would reproduce exactly the observed distribution f0(m sin i). The method is based on a particular geometrical representation of exoplanets. It calls for the use of spheres and cylinders, and is somewhat similar (though different) to the Abel inversion, widely used in atmospheric physics. We have applied this algorithm to the latest sample of RV discovered planets containing 909 planets. We confirm the existence of a sub-Saturn desert (at least for periods < 100 d), most depleted in the mass Srange in the range 0.1–0.2 Mjup (∼32–64 M⊕), detected in the raw m sin i distribution, and amplified in the inverted f(m) true mass distribution by a factor ∼1.7. We argue that this result is robust, and would remain even if other biases of the RV surveys would be included. Differences with a recent model of population synthesis are discussed. Focusing on lighter planets, we found a likely statistically significant gap of planets in the observed m sin i distribution in the narrow range of 13.7–15.2 M⊕ containing Uranus.