A new numerical inversion scheme of m sin i exo-planet mass distribution: its double peak remains after inversion.

International audienceThe use of radial velocity (RV) measurements of stars has proven very successful at the indirect detection of planets orbiting other stars, since both the planet (unseen) and the star are orbiting around their common center of mass. Unfortunately the mass m of the exo-planet cannot be retrieved: only the product m sin i is derived from the amplitude of the RV wobble, where i is the inclination of the polar axis of the orbit on the line of sight (LOS) from the observer to the star.However, when a reasonable number of exo-planets are detected, giving an observed distribution of m sin i it is possible to retrieve the distribution function of planetary masses f(m) that will give the observed distribution fO(m sin i). One has to make the assumption that the orientations of orbital polar axis are isotropically distributed in space, and independent of the distribution f(m). We have developed a new representation of exo-planets in a 3D space, and established a formally exact solution to the inversion problem, based on spheres and cylinders. We have applied this method to the more than 700 known exo-planets masses. The observed distribution of m sin i shows two peaks, one around 0.025 Mjup (Jupiter mass) and one around 2 Mjup. After inversion, the true distribution of masses still present a double peak, showing that this double peak is not an artefact or shortcoming of the RV method. Our new inversion scheme will be presented and the double peak discussed. Coauthors from IKI acknowledge support from the Russian Government Grant #14.W03.31.0017

Distribution of RV- and transiting exoplanets by masses and orbital periods taking into account observational selection

International audienceMore than 95% of the known exoplanets were discovered by the transit-and radial velocity techniques. However, the observed distributions of planets by their masses and by their orbital periods are significantly distorted by numerous observational selections, different for these techniques and different surveys

Exoplanet mass distribution considering selection factors for transit technique

International audienceRetrieving the mass distribution of exoplanets was performed for photometric observed planets from space-and ground-based surveys. True statistical distribution requires debiasing (correction) of observation selection. Retrieved distribution of transit exoplanets by mass accounts the probability of mass determination and the probability of transit configuration. As a not normalized probability density function (PDF), the corrected (debiased) exoplanet mass distribution can be approximated by the power law: dN/dm ∝ m-2. Minima significances in the retrieved mass distribution have been verified by Kolmogorov-Smirnov test

Mass distribution of exoplanets considering some observation selection effects in the transit detection technique

International audienceWhile the radial velocity technique (RV) allows to determine only the product m·sin i of the mass m of one exoplanet by sin i (i, angle of inclination of orbital pole to the observer), when it is applied to a planet already detected while transiting its host star, the true mass m is determined, since angle i is near 90° and sin i ~ 1. Therefore, the mass distribution of transiting exoplanets discovered by photometric observations is of particular interest. However, there are some selection effects that distort the true (original) mass distribution into the observed mass distribution. We have studied the whole observed mass distribution of transiting exoplanets that were discovered from space-borne and ground-based surveys (NASA Exoplanet Archive 2019) and corrected them from some selection effects to retrieve a de-biased true mass distribution. For this, we take into account two factors: the probability of mass determination and the probability of transit configurations. The first factor is a bias introduced by a number of effects inherent to the RV method. The bias factor could be estimated by computing the fraction of transiting planets for which the mass was determined from the RV or TTV (Transit Timing Variations) methods. Photometric surveys for transit detection allow determining the planetary radii, and the bias factor was estimated for various bins of planetary sizes. The second factor is the transit probability, a geometrical factor which is precisely known for each detected transiting planet and therefore easy to account for. The mass distribution of exoplanets corrected for the first factor (de-biased) was analyzed, and it is found that this distribution can be well approximated by a power law: dN/dm ∝ m−2. When both factors of observation selection are taken into account, a flat statistically significant area (plateau) in the mass interval of 0.3–2 mJ appears on the mass distribution. The mass distributions derived from transiting planets is preliminary and can be updated after the RV follow-up of K2 planets will be more complete and the number of Kepler1 confirmed planets definitive. The significances of the local minima (plateau) in the retrieved mass distribution have been estimated by the Kolmogorov-Smirnov test.Our de-biased mass distribution was compared to the theoretical model of Mordasini (2018). The slopes are similar, but a plateau present in the model in the range 0.1–5 Jupiter mass is appearing in the data if one considers the probability of transit configuration and considers the lower sensitivity of transit method (with follow-up mass measurement by RV) to planets with long periods and large orbits. In fact, Mordasini (2018) included exoplanets on all orbits. The Gaia2 astrometric method should be able to clarify this discrepancy.Radial velocity surveys are more complete than transits for long period planets. And though the sin i effect is present, its amplitude is indeed not strongly relevant from a statistical point of view (and can actually be taken into account). However RV-database is formed by surveys with substantially different durations, sensitivities, and other sources of inhomogeneities. Some examples of regularization of RV data are shown by e.g. (Mordasini, 2018; Ananyeva et al., 2019; Tuomi et al., 2019), but it is hoped that more biases/inhomogeneities may be dealt with in the future