Inflection point in the power spectrum of stellar brightness variations

I. The model

¹ Max-Planck-Institut fur Sonnensystemforschung, Goettingen, Germany
e-mail: shapiroa@mps.mpg.de
² Georg-August Universität Göttingen, Institut für Astrophysik, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
³ School of Space Research, Kyung Hee University, Yongin, Gyeonggi 446-701, Korea

Received: 4 June 2019
Accepted: 16 October 2019

Abstract

Context. Considerable effort has gone into using light curves observed by such space telescopes as CoRoT, Kepler, and TESS for determining stellar rotation periods. While rotation periods of active stars can be reliably determined, the light curves of many older and less active stars, such as stars that are similar to the Sun, are quite irregular. This hampers the determination of their rotation periods.

Aims. We aim to examine the factors causing these irregularities in stellar brightness variations and to develop a method for determining rotation periods for low-activity stars with irregular light curves.

Methods. We extended the Spectral And Total Irradiance Reconstruction approach for modeling solar brightness variations to Sun-like stars. We calculated the power spectra of stellar brightness variations for various combinations of parameters that define the surface configuration and evolution of stellar magnetic features.

Results. The short lifetime of spots in comparison to the stellar rotation period, as well as the interplay between spot and facular contributions to brightness variations of stars with near solar activity, cause irregularities in their light curves. The power spectra of such stars often lack a peak associated with the rotation period. Nevertheless, the rotation period can still be determined by measuring the period where the concavity of the power spectrum plotted in the log–log scale changes its sign, that is, by identifying the position of the inflection point.

Conclusions. The inflection point of the (log–log) power spectrum is found to be a new diagnostic for stellar rotation periods which is shown to work even in cases where the power spectrum shows no peak at the rotation rate.