Estimating the masses of extra-solar planets

All extra-solar planet masses that have been derived spectroscopically are lower limits since the inclination of the orbit to our line-of-sight is unknown except for transiting systems. In theory, however, it is possible to determine the inclination angle, i, between the rotation axis of a star and an observer's line-of-sight from measurements of the projected equatorial velocity (v sin i), the stellar rotation period (Prot) and the stellar radius (R*). For stars which host planetary systems this allows the removal of the sin i dependency of extra-solar planet masses derived from spectroscopic observations under the assumption that the planetary orbits lie perpendicular to the stellar rotation axis. We have carried out an extensive literature search and present a catalogue of v sin i, Prot and R* estimates for stars hosting extra-solar planets. In addition, we have used Hipparcos parallaxes and the Barnes–Evans relationship to further supplement the R* estimates obtained from the literature. Using this catalogue, we have obtained sin i estimates using a Markov-chain Monte Carlo analysis. This technique allows proper 1σ two-tailed confidence limits to be placed on the derived sin i's along with the transit probability for each planet to be determined. While we find that a small proportion of systems yield sin i's significantly greater than 1, most likely due to poor Prot estimations, the large majority are acceptable. We are further encouraged by the cases where we have data on transiting systems, as the technique indicates inclinations of ∼90° and high transit probabilities. In total, we are able to estimate the true masses of 133 extra-solar planets. Of these 133 extra-solar planets, only six have revised masses that place them above the 13MJ deuterium burning limit; four of those six extra-solar planet candidates were already suspected to lie above the deuterium burning limit before correcting their masses for the sin i dependency. Our work reveals a population of high-mass extra-solar planets with low eccentricities, and we speculate that these extra-solar planets may represent the signature of different planetary formation mechanisms at work. Finally, we discuss future observations that should improve the robustness of this technique.