BGLS : a Bayesian formalism for the generalised Lomb-Scargle periodogram

The research leading to these results received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement number 313014 (ETAEARTH). We also acknowledge the support from Fundação para a Ciência e a Tecnologia (FCT, Portugal) through FEDER funds in program COMPETE, as well as through national funds, in the form of grants reference RECI/FIS-AST/0176/2012 (FCOMP-01-0124-FEDER-027493) and RECI/FIS-AST/0163/2012 (FCOMP-01-0124-FEDER-027492). We also acknowledge the support from the European Research Council/European Community under the FP7 through Starting Grant agreement number 239953 and the Marie Curie Intra-European Fellowship with reference FP7-PEOPLE-2011-IEF, number 300162 (for CC). N.C.S. was supported by FCT through the Investigador FCT contract reference IF/00169/2012 and POPH/FSE (EC) by FEDER funding through the program Programa Operacional de Factores de Competitividade - COMPETE. A.S. is supported by the European Union under a Marie Curie Intra-European Fellowship for Career Development with reference FP7-PEOPLE-2013-IEF, number 627202.Context. Frequency analyses are very important in astronomy today, not least in the ever-growing field of exoplanets, where short-period signals in stellar radial velocity data are investigated. Periodograms are the main (and powerful) tools for this purpose. However, recovering the correct frequencies and assessing the probability of each frequency is not straightforward. Aims: We provide a formalism that is easy to implement in a code, to describe a Bayesian periodogram that includes weights and a constant offset in the data. The relative probability between peaks can be easily calculated with this formalism. We discuss the differences and agreements between the various periodogram formalisms with simulated examples. Methods: We used the Bayesian probability theory to describe the probability that a full sine function (including weights derived from the errors on the data values and a constant offset) with a specific frequency is present in the data. Results: From the expression for our Baysian generalised Lomb-Scargle periodogram (BGLS), we can easily recover the expression for the non-Bayesian version. In the simulated examples we show that this new formalism recovers the underlying periods better than previous versions. A Python-based code is available for the community.Publisher PDFPeer reviewe