A calibration of the Rossby number from asteroseismology

Abstract

Stellar activity and rotation are tightly related in a dynamo process. Our understanding of this mechanism is mainly limited by our capability of inferring the properties of stellar turbulent convection. In particular, the convective turnover time is a key ingredient through the estimation of the stellar Rossby number, which is the ratio of the rotation period and the convective turnover time. In this work, we propose a new calibration of the (B − V) color index dependence of the convective turnover time, hence, of the stellar Rossby number. Our new calibration is based on the stellar structure properties inferred through the detailed modeling of solar-like pulsators using asteroseismic observables. We show the impact of this calibration via a stellar activity-Rossby number diagram by applying it to a sample of about 40,000 stars observed with Kepler and for which the values for the photometric activity proxy S ph and surface rotation periods are available. Additionally, we provide a new calibration for the convective turnover time as function of the (G BP − G RP ) color index for allowing applicability in the ESA Gaia photometric passbands.

On the Evolution of Rotational Modulation Amplitude in Solar-mass Main-sequence Stars

“…Here, we investigate how the photometric modulation amplitude R per evolves as a function of P rot . As has been shown in previous works (Corsaro et al 2021;See et al 2021), the relation between R per and P rot for roughly solar-mass stars is concisely summarized in terms of the Rossby number Ro = P rot /τ c . We revisit such a relation for our sample stars and use it for the discussion of detectability in Section 4.…”

“…The formula by Noyes et al (1984) has widely been used, which is based on the theoretical evaluation of the local turnover timescale near the bottom of the convective envelope as described in Gilman (1980) and has been calibrated to minimize the scatter in the ¢ R log HK -Ro relation. Other scales have been proposed based on up-to-date stellar models and direct inference of the thickness of convective envelopes from asteroseismology (Landin et al 2010;See et al 2021;Lehtinen et al 2021;Corsaro et al 2021). These works generally yield τ c values that are larger by a factor of a few than those of Noyes et al (1984) for solar-mass , is the uniform distribution between a and b.…”

Further Evidence of Modified Spin-down in Sun-like Stars: Pileups in the Temperature–Period Distribution

“…Figure 21 shows a Gaussian KDE of the LAMOST-McQuillan T eff -P rot distribution for stars with g log > 4.1. The short-period pileup is Corsaro et al (2021), which is valid in the color range 0.55 < (G BP G RP ) < 0.97. The top rows show 2D histograms of the probability density for the entire sample (left), a subsample with low reddening (middle), and the same low reddening subsample with a −0.1 mag color shift applied to the data and cluster sequences.…”

“…We found that the long-period pileup is clearly visible in the (G BP −G RP )P rot plane once stars with high reddening (A V > 0.2) are excluded (Figures 19 and 20). In order to match a curve of constant Rossby number, given by Ro = Ro e = 0.496 on the Corsaro et al (2021) scale, we found that a ≈−0.1 mag shift to the Gaia colors of the data was required (or, equivalently, a +0.1 mag shift applied to the constant Rossby curve). While there is no justification for such a large shift, it may indicate the presence of a systematic offset in the τ cz relation.…”

“…We then compared the (G BP −G RP )P rot distribution with constant Rossby curves. For this exercise, we used the empirically calibrated τ cz relation of Corsaro et al (2021), who presented τ cz as a quadratic function of Gaia G BP −G RP color using the Kepler LEGACY asteroseismic sample as calibrators. We found that the long-period pileup is clearly visible in the (G BP −G RP )P rot plane once stars with high reddening (A V > 0.2) are excluded (Figures 19 and 20).…”