Variability of Sun-like stars: reproducing observed photometric trends

Abstract

Context. The Sun and stars with low magnetic activity levels become photometrically brighter when their activity increases. Magnetically more active stars display the opposite behavior and become fainter when their activity increases. Aims. We reproduce the observed photometric trends in stellar variations with a model that treats stars as hypothetical suns with coverage by magnetic features different from that of the Sun. Methods. The model attributes the variability of stellar spectra to the imbalance between the contributions from different components of the solar atmosphere, such as dark starspots and bright faculae. A stellar spectrum is calculated from spectra of the individual components by weighting them with corresponding disk-area coverages. The latter are obtained by extrapolating the solar dependences of spot and facular disk-area coverages on chromospheric activity to stars with different levels of mean chromospheric activity. Results. We find that the contribution by starspots to the variability increases faster with chromospheric activity than the facular contribution. This causes the transition from faculae-dominated variability and direct activity-brightness correlation to spot-dominated variability and inverse activity-brightness correlation with increasing chromospheric activity level. We show that the regime of the variability also depends on the angle between the stellar rotation axis and the line-of-sight and on the latitudinal distribution of active regions on the stellar surface. Our model can be used as a tool for extrapolating the observed photometric variability of the Sun to Sun-like stars at different activity levels, which makes a direct comparison between solar and stellar irradiance data possible.

A Decade of Hα Transits for HD 189733 b: Stellar Activity versus Absorption in the Extended Atmosphere

“…We believe facular coverage fractions of ∼10%, and possibly higher, are not unreasonable considering the stronger activity level of HD 189733 compared with the Sun. Solar facular coverage can reach ∼5% during solar active periods (Shapiro et al 2015) and plage coverage can reach ∼8% (Foukal 1998). On the other hand, Shapiro et al (2015) (see also Foukal 1998; Lockwood et al 2007) find that photometric variations for more active stars are spot-dominated and that the ratio of facular/plage coverage to spot coverage decreases with increasing activity level.…”

“…Solar facular coverage can reach ∼5% during solar active periods (Shapiro et al 2015) and plage coverage can reach ∼8% (Foukal 1998). On the other hand, Shapiro et al (2015) (see also Foukal 1998; Lockwood et al 2007) find that photometric variations for more active stars are spot-dominated and that the ratio of facular/plage coverage to spot coverage decreases with increasing activity level. Lanza et al (2011) find that RV modulations in HD 189733's spectrum are best modeled with values of Q = A f ac /A spot ∼0, i.e., they find no evidence of facular/plage effects on the measured RV values.…”

The Influence of Metallicity on Stellar Differential Rotation and Magnetic Activity

“…(Shapiro et al 2015). Together with the inclination of the rotation axis, metallicity is also known to have an effect on the visibility of activity-related phenomena like spots and faculae (Shapiro et al 2014). Unfortunately, this effect is poorly constrained because there are few metal-rich solar-analogs with measured activity cycles and inclinations.…”

The nature of solar brightness variations

“…This is a feasible task since a) reliable simulations of granulation patterns on main sequence stars are gradually becoming available 20,30 , b) new methods for extrapolating the magneticallydriven brightness variations from the Sun to Sun-like stars with various levels of magnetic activity observed at arbitrary angles between rotational axis and line-of-sight have been recently developed 6,28 .…”