The generalised LombScargle periodogram. A new formalism for the floatingmean and Keplerian periodograms
Abstract
The LombScargle periodogram is a common tool in the frequency analysis of unequally spaced data equivalent to leastsquares fitting of sine waves. We give an analytic solution for the generalisation to a full sine wave fit, including an offset and weights (χ^{2} fitting). Compared to the LombScargle periodogram, the generalisation is superior as it provides more accurate frequencies, is less susceptible to aliasing, and gives a much better determination of the spectral intensity. Only a few modifications are required for the computation and the computational effort is similar. Our approach brings together several related methods that can be found in the literature, viz. the datecompensated discrete Fourier transform, the floatingmean periodogram, and the “spectral significance” estimator used in the SigSpec program, for which we point out some equivalences. Furthermore, we present an algorithm that implements this generalisation for the evaluation of the Keplerian periodogram that searches for the period of the bestfitting Keplerian orbit to radial velocity data. The systematic and nonrandom algorithm is capable of detecting eccentric orbits, which is demonstrated by two examples and can be a useful tool in searches for the orbital periods of exoplanets.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 March 2009
 DOI:
 10.1051/00046361:200811296
 arXiv:
 arXiv:0901.2573
 Bibcode:
 2009A&A...496..577Z
 Keywords:

 methods: data analysis;
 methods: analytical;
 methods: statistical;
 techniques: radial velocities;
 Astrophysics  Instrumentation and Methods for Astrophysics
 EPrint:
 8 pages, 6 figures, 1 table, accepted by A&