Correlation with stellar rotation period

In Top panel in Fig.1.20, we present RV-RMS and the peak-to-peak light curve variation for the subsample of 71 stars with measured rotation periods (coded with marker size).

The color bar represents the effective temperature. One can easily notice that stars with large RV-RMS and a large peak-to-peak photometric variability are mostly fast rotating stars (less than 13 days) and there is a hint of temperature dependency. Bottom panel in Fig.1.20shows the same 71 stars but color bar indicates the rotation period value, and circle size thev sin iobtained spectroscopically, which again confirms the previous result we found.

In Fig.1.21, we present a similar plot to Fig.1.20but this time for 29 stars where we could identify facular or spot dominated patterns using the method described in Sec.1.9.2.

We found 9 faculae dominated stars (which were also slow rotators as is expected for faculae dominated stars), and 20 spot-dominated stars. We show faculae and spot dominated stars in yellow and black, respectively. In this sample, 20 stars can be classified as fast rotators (rotation period<15 days), and large fraction of them (13 out 20) are spot dominated. This result is in strong agreement withMontet et al.(2017), where they reported 15 days as the threshold in rotation period for separating spot-faculae dominated regimes. Moreover, faculae-dominated stars tend to have low photometric peak-to-peak variability, due to the low contrast of facular region, and therefore are mostly below the 6.5 ppt limit. Thus, the 6.5 ppt limit can be also interpreted as the photometric variability transition between the spot-dominated and the faculae-dominated regime. However, the sample of 29 stars is too small to generalize.

We were able to estimate the rotation period of 71 stars, out of 171 stars in our sample, using the TESS light curve. Then we investigated the effect of this parameter on the correlation between RV-RMS and peak-to-peak of light curve variability. Our result demonstrated that slow rotating stars (which are the ones also we found to be faculae dominated) create lower RV jitter as well as lower peak-to-peak photometric variability, and on the other hand fast rotating star,Prot ≤5 day (which are the ones also we found to be spot dominated) generate much larger RV jitter and photometric variability.

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1.9 The correlation between photometric variability and radial velocity jitter

Figure 1.20: RV-RMS and peak-to-peak of light curve variation for the subsample of 71 stars. Top plot: Circle sizes represents the value of rotation period found by GPS method. Color bar indicates the stellar effective temperature. Bottom plot: Similar than top panel but, color bar indicates the rotation period value, and circle size thev sin iobtained spectroscopically

1 Introduction

Figure 1.21: RV-RMS and the peak-to-peak of light curve variation for the subsample of 20 stars with spot dominance and 9 stars with faculae dominance in their light curves.

Circle sizes represents thev sin ivalue determined spectroscopically. Black color indicates spot dominated and yellow indicates faculae dominated. The Blue vertical line shows the knee point peak-to-peak light curve variation at 6.5 ppt.

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1.9 The correlation between photometric variability and radial velocity jitter

Main publications for the GPS method Thesis:

The following chapters includes the three main manuscripts describing, proposing and testing the GPS method. Being this

the core of my Thesis disputation.

2 Inflection point in the power spectrum of stellar brightness variations: I. The model

This chapter is based on the article published at: Astronomy&Astrophysics, volume 633, article number A32, by A.I. Shapiro, E.M. Amazo-Gómez, N.A. Krivova&S.K. Solanki.

My participation in this work compromised the co-developing of the method, as well the testing of the preliminary models and wavelets in order to understand the signals obtained.

The printed version is reproduced here with permission from Astronomy&Astrophysics,c ESO.

Abstract chapter 2

Considerable efforts has been put into using light curves observed by space telescopes such as CoRoT,Keplerand 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 (e.g., stars similar to the Sun) are quite irregular, which hampers determination of their periods. We examine the factors causing the irregularities in stellar brightness variations and develop a method for determining rotation periods of low activity stars with irregular light curves. We extend the Spectral And Total Irradiance Reconstruction (SATIRE) approach for modelling solar brightness variations to Sun-like stars. We calculate the power spectra of stellar brightness variations for various combinations of parameters defining the surface configuration and evolution of stellar magnetic features. 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 associ-ated 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 sign, i.e., by identifying the position of the inflection point. The inflection point of the (log-log) power spectrum is found to be a new diagnostic for stellar rotation periods that is shown to work even in cases where the power spectrum shows no peak at the rotation rate.

keywords: Stars - rotation periodicity - Sun - activity - photometry.

2 Inflection point in the power spectrum of stellar brightness variations: I. The model