Selection functions in doppler planet searches

Abstract

We present a preliminary analysis of the sensitivity of Anglo-Australian Planet Search data to the orbital parameters of extrasolar planets. To do so, we have developed new tools for the automatic analysis of large-scale simulations of Doppler velocity planet search data. One of these tools is the 2-Dimensional Keplerian Lomb-Scargle periodogram, that enables the straightforward detection of exoplanets with high eccentricities (something the standard Lomb-Scargle periodogram routinely fails to do). We used this technique to re-determine the orbital parameters of HD20782b, with one of the highest known exoplanet eccentricities (e = 0.97 ± 0.01). We also derive a set of detection criteria that do not depend on the distribution functions of fitted Keplerian orbital parameters (which we show are non-Gaussian with pronounced, extended wings). Using these tools, we examine the selection functions in orbital period, eccentricity and planet mass of Anglo-Australian Planet Search data for three planets with large-scale Monte Carlo-like simulations. We find that the detectability of exoplanets declines at high eccentricities. However, we also find that exoplanet detectability is a strong function of epoch-to-epoch data quality, number of observations, and period sampling. This strongly suggests that simple parametrisations of the detectability of exoplanets based on “whole-of-survey” metrics may not be accurate. We have derived empirical relationships between the uncertainty estimates for orbital parameters that are derived from least-squares Keplerian fits to our simulations, and the true 99% limits for the errors in those parameters, which are larger than equivalent Gaussian limits by factors of 5-10. We quantify the rate at which false positives are made by our detection criteria, and find that they do not significantly affect our final conclusions. And finally, we find that there is a bias against measuring near-zero eccentricities, which becomes more significant in small, or low signal-to-noise-ratio, data sets