EDP Sciences
Free access
Volume 496, Number 2, March III 2009
Page(s) 577 - 584
Section Astronomical instrumentation
DOI http://dx.doi.org/10.1051/0004-6361:200811296
Published online 20 January 2009
A&A 496, 577-584 (2009)
DOI: 10.1051/0004-6361:200811296

The generalised Lomb-Scargle periodogram

A new formalism for the floating-mean and Keplerian periodograms
M. Zechmeister and M. Kürster

Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
    e-mail: zechmeister@mpia.de

Received 5 November 2008 / Accepted 19 December 2008

The Lomb-Scargle periodogram is a common tool in the frequency analysis of unequally spaced data equivalent to least-squares fitting of sine waves. We give an analytic solution for the generalisation to a full sine wave fit, including an offset and weights ($\chi^{2}$ fitting). Compared to the Lomb-Scargle 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 date-compensated discrete Fourier transform, the floating-mean 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 best-fitting Keplerian orbit to radial velocity data. The systematic and non-random 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.

Key words: methods: data analysis -- methods: analytical -- methods: statistical -- techniques: radial velocities

© ESO 2009