Semi-supervised standardized detection of extrasolar planets

Abstract

Context. The detection of small exoplanets with the radial velocity (RV) technique is limited by various poorly known noise sources of instrumental and stellar origin. As a consequence, current detection techniques often fail to provide reliable estimates of the significance levels of detection tests in terms of false-alarm rates or p-values. Aims. We designed an RV detection procedure that provides reliable p-value estimates while accounting for the various noise sources typically affecting RV data. The method is able to incorporate ancillary information about the noise (e.g., stellar activity indicators) and specific data- or context-driven data (e.g. instrumental measurements, magnetohydrodynamical simulations of stellar convection, and simulations of meridional flows or magnetic flux emergence). Methods. The detection part of the procedure uses a detection test that is applied to a standardized periodogram. Standardization allows an autocalibration of the noise sources with partially unknown statistics (algorithm 1). The estimation of the p-value of the test output is based on dedicated Monte Carlo simulations that allow handling unknown parameters (algorithm 2). The procedure is versatile in the sense that the specific pair (periodogram and test) is chosen by the user. Ancillary or context-driven data can be used if available. Results. We demonstrate by extensive numerical experiments on synthetic and real RV data from the Sun and αCenB that the proposed method reliably allows estimating the p-values. The method also provides a way to evaluate the dependence of the estimated p-values that are attributed to a reported detection on modeling errors. It is a critical point for RV planet detection at low signal-to-noise ratio to evaluate this dependence. The python algorithms developed in this work are available on GitHub. Conclusions. Accurate estimation of p-values when unknown parameters are involved in the detection process is an important but only recently addressed question in the field of RV detection. Although this work presents a method to do this, the statistical literature discussed in this paper may trigger the development of other strategies.