A Study of Periodograms Standardized Using Training Datasets and Application to Exoplanet Detection
Context. The abilities of radial velocity exoplanet surveys to detect the lowest-mass extra-solar planets are currently limited by a combination of instrument precision, lack of data, and “jitter”. Jitter is a general term for any unknown features in the noise, and reflects a lack of detailed knowledge of stellar physics (asteroseismology, starspots, magnetic cycles, granulation, and other stellar surface phenomena), as well as the possible underestimation of instrument noise. Aims. We study an extensive set of radial velocities for the star HD 10700 (τ Ceti) to determine the properties of the jitter arising from stellar surface inhomogeneities, activity, and telescope-instrument systems, and perform a comprehensive search for planetary signals in the radial velocities. Methods. We perform Bayesian comparisons of statistical models describing the radial velocity data to quantify the number of significant signals and the magnitude and properties of the excess noise in the data. We reach our goal by adding artificial signals to the “flat” radial velocity data of HD 10700 and by seeing which one of our statistical noise models receives the greatest posterior probabilities while still being able to extract the artificial signals correctly from the data. We utilise various noise components to assess properties of the noise in the data and analyse the HARPS, AAPS, and HIRES data for HD 10700 to quantify these properties and search for previously unknown low-amplitude Keplerian signals. Results. According to our analyses, moving average components with an exponential decay with a timescale from a few hours to few days, and Gaussian white noise explains the jitter the best for all three data sets. Fitting the corresponding noise parameters results in significant improvements of the statistical models and enables the detection of very weak signals with amplitudes below 1 ms−1 level in our numerical experiments. We detect significant periodicities that have no activity-induced counterparts in the combined radial velocities. Three of these signals can be seen in the HARPS data alone, and a further two can be inferred by utilising the AAPS and Keck data. These periodicities could be interpreted as corresponding to planets on dynamically stable close-circular orbits with periods of 13.9, 35.4, 94, 168, and 640 days and minimum masses of 2.0, 3.1, 3.6, 4.3, and 6.6 M⊕, respectively.