Inflection point in the power spectrum of stellar brightness variations

E M Amazo-Gómez,S K Solanki,T Reinhold,G Kopp,N A Krivova,A I Shapiro,A Reiners,M Oshagh

doi:10.1051/0004-6361/201936925

Abstract

Context. Young and active stars generally have regular, almost sinusoidal, patterns of variability attributed to their rotation, while the majority of older and less active stars, including the Sun, have more complex and non-regular light curves, which do not have clear rotational-modulation signals. Consequently, the rotation periods have been successfully determined only for a small fraction of the Sun-like stars (mainly the active ones) observed by transit-based planet-hunting missions, such as CoRoT, Kepler, and TESS. This suggests that only a small fraction of such systems have been properly identified as solar-like analogues. Aims. We aim to apply a new method of determining rotation periods of low-activity stars, such as the Sun. The method is based on calculating the gradient of the power spectrum (GPS) of stellar brightness variations and identifying a tell-tale inflection point in the spectrum. The rotation frequency is then proportional to the frequency of that inflection point. In this paper, we compare this GPS method to already-available photometric records of the Sun. Methods. We applied GPS, auto-correlation functions, Lomb-Scargle periodograms, and wavelet analyses to the total solar irradiance (TSI) time series obtained from the Total Irradiance Monitor on the Solar Radiation and Climate Experiment and the Variability of solar IRradiance and Gravity Oscillations experiment on the SOlar and Heliospheric Observatory missions. We analysed the performance of all methods at various levels of solar activity. Results. We show that the GPS method returns accurate values of solar rotation independently of the level of solar activity. In particular, it performs well during periods of high solar activity, when TSI variability displays an irregular pattern, and other methods fail. Furthermore, we show that the GPS and light curve skewness can give constraints on facular and spot contributions to brightness variability. Conclusions. Our results suggest that the GPS method can successfully determine the rotational periods of stars with both regular and non-regular light curves.

Highlights

A star’s rotation period defines the action of the stellar dynamo, transport of magnetic flux through the convective zone, and its emergence on the stellar surface
We applied gradient of the power spectrum (GPS), auto-correlation functions, Lomb-Scargle periodograms, and wavelet analyses to the total solar irradiance (TSI) time series obtained from the Total Irradiance Monitor on the Solar Radiation and Climate Experiment and the Variability of solar IRradiance and Gravity Oscillations experiment on the SOlar and Heliospheric Observatory missions
In Shapiro et al (2020), we proposed the GPS method aimed at the determination of periods in old inactive stars, like our Sun

Summary

Introduction

A star’s rotation period defines the action of the stellar dynamo, transport of magnetic flux through the convective zone, and its emergence on the stellar surface (see Charbonneau 2010 for a general review of dynamo theory, and Reiners et al 2014, Isık et al 2018 for the relation between the rotation period and activity). Knowledge of the stellar rotation period helps distinguish the radial velocity jitter of a star from the planetary signal (see, e.g. Dumusque et al 2011; Oshagh 2018). This is crucial for detection, as well as for confirming Earth-size planets in ongoing and upcoming surveys, such as the ESPRESSO (see Pepe et al 2010) and PLATO missions (see Roxburgh et al 2007; Rauer et al 2016, 2014)

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Conclusion