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. (abridged)