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Asteroseismic calibration of the Rossby number and its connection to the stellar dynamo and fundamental properties

Alfio Bonanno, Enrico Corsaro, Travis S. Metcalfe, Sylvain Breton, Orlagh L. Creevey, Christopher J. Lindsay

TL;DR

This work aims to provide a robust calibration of the convective turnover time $\tau_c$ to enable meaningful Rossby numbers $\mathrm{Ro} = P_{\rm rot}/\tau_c$ for Sun-like stars across evolutionary stages. It introduces a Gaia-enhanced, asteroseismic approach that combines $(G_{\rm BP}-G_{\rm RP})_0$, $\log g$, $[\mathrm{Fe/H}]$, and $T_{\rm eff}$ in a four-parameter log-linear relation for $\tau_c$, estimated via a Bayesian multi-linear framework. Among eight candidate models, the full model $\mathcal{M}_8$ provides the best predictive power across samples, with metallicity and effective temperature playing nontrivial, physically meaningful roles; separate calibrations for MS and RGB stars improve accuracy, though a single relation remains promising. The refined $\tau_c$ calibrations have direct implications for interpreting stellar dynamos, illustrating how deep-seated $\alpha$-effects near the convection-zone base and diffusion profiles can yield diverse magnetic cycles, and thereby enhancing our understanding of magnetic evolution in Sun-like stars.

Abstract

The stellar Rossby number, a dimensionless parameter quantifying the influence of Coriolis forces on convective motions, plays a pivotal role in understanding magnetic stellar evolution. In this work, we explore the connection between the Rossby number and potential dynamo mechanisms in Sun-like stars, as well as its dependence on fundamental stellar properties. We present a novel, detailed asteroseismic calibration of the convective turnover time, incorporating for the first time Gaia photometry alongside surface gravity, effective temperature, and stellar metallicity. Our analysis employs an expanded sample of more than 150 stars, including targets from the Kepler LEGACY and KOI surveys, as well as more evolved stars observed by TESS and K2. This sample spans evolutionary stages from the main sequence to the early red giant branch (RGB), enabling a comprehensive investigation of Rossby number trends across stellar evolution.

Asteroseismic calibration of the Rossby number and its connection to the stellar dynamo and fundamental properties

TL;DR

This work aims to provide a robust calibration of the convective turnover time to enable meaningful Rossby numbers for Sun-like stars across evolutionary stages. It introduces a Gaia-enhanced, asteroseismic approach that combines , , , and in a four-parameter log-linear relation for , estimated via a Bayesian multi-linear framework. Among eight candidate models, the full model provides the best predictive power across samples, with metallicity and effective temperature playing nontrivial, physically meaningful roles; separate calibrations for MS and RGB stars improve accuracy, though a single relation remains promising. The refined calibrations have direct implications for interpreting stellar dynamos, illustrating how deep-seated -effects near the convection-zone base and diffusion profiles can yield diverse magnetic cycles, and thereby enhancing our understanding of magnetic evolution in Sun-like stars.

Abstract

The stellar Rossby number, a dimensionless parameter quantifying the influence of Coriolis forces on convective motions, plays a pivotal role in understanding magnetic stellar evolution. In this work, we explore the connection between the Rossby number and potential dynamo mechanisms in Sun-like stars, as well as its dependence on fundamental stellar properties. We present a novel, detailed asteroseismic calibration of the convective turnover time, incorporating for the first time Gaia photometry alongside surface gravity, effective temperature, and stellar metallicity. Our analysis employs an expanded sample of more than 150 stars, including targets from the Kepler LEGACY and KOI surveys, as well as more evolved stars observed by TESS and K2. This sample spans evolutionary stages from the main sequence to the early red giant branch (RGB), enabling a comprehensive investigation of Rossby number trends across stellar evolution.
Paper Structure (19 sections, 16 equations, 10 figures, 6 tables)

This paper contains 19 sections, 16 equations, 10 figures, 6 tables.

Table of Contents

  1. Introduction
  2. The sample
  3. Stellar modeling of the targets
  4. Multi-linear relationships for $\tau_c$
  5. $\tau_c$ vs $\left(G_\mathrm{BP} - G_\mathrm{RP}\right)_0$, $\log g$, $\left[\hbox{Fe/H}\right]$, $T_\mathrm{eff}$
  6. Results
  7. Model comparison
  8. Model $\mathcal{M}_1$ ($\alpha_1 \neq 0$, $\alpha_2 = \alpha_3 = \alpha_4 = 0$)
  9. Model $\mathcal{M}_2$ ($\alpha_1 \neq 0$, $\alpha_2 = \alpha_3 = 0$, $\alpha_4 \neq 0$)
  10. Model $\mathcal{M}_3$ ($\alpha_1 \neq 0$, $\alpha_2 = \alpha_4 = 0$, $\alpha_3 \neq 0$)
  11. Model $\mathcal{M}_4$ ($\alpha_1 \neq 0$, $\alpha_2 \neq 0$, $\alpha_3 = \alpha_4 = 0$)
  12. Model $\mathcal{M}_5$ ($\alpha_1 \neq 0$, $\alpha_2 = 0$, $\alpha_3 \neq 0$, $\alpha_4 \neq 0$)
  13. Model $\mathcal{M}_6$ ($\alpha_1 \neq 0$, $\alpha_2 \neq 0$, $\alpha_3 = 0$, $\alpha_4 \neq 0$)
  14. Model $\mathcal{M}_7$ ($\alpha_1 \neq 0$, $\alpha_2 \neq 0$, $\alpha_3 \neq 0$, $\alpha_4 = 0$)
  15. Model $\mathcal{M}_8$ ($\alpha_1 \neq 0$, $\alpha_2 \neq 0$, $\alpha_3 \neq 0$, $\alpha_4 \neq 0$)
  16. ...and 4 more sections

Figures (10)

  • Figure 1: Convective velocities $v_\mathrm{conv}$ and convective turnover time $\tau_c$ as a function of Gaia DR3 color index $\left(G_\mathrm{BP} - G_\mathrm{RP}\right)_0$, surface gravity $\log g$, metallicity $\left[\hbox{Fe/H}\right]$, and temperature $T_\mathrm{eff}$ for both samples (main sequence and early subgiants from LEGACY + KOI in blue, late subgiants and early RGB from 2024ApJ...965..171L orange). Spearman's rank correlation coefficients are also indicated for each sample using the same color coding. The dashed vertical line represents the cut in $\log g$ applied to distinguish $\mathcal{S}_1$ from $\mathcal{S}_2$, as described in Sect. \ref{['sec:discussion']}.
  • Figure 2: Dispersion plots showing the $\tau_c$ predictions from model $\mathcal{M}_1$. The data points are shown in color (open symbols), while the model predictions are represented by the gray (filled) bullets. A panel showing the residuals of the fit in the form $\ln \tau_c - \ln \tau_c^\mathrm{predict}$ is also shown for each observable. Also indicated are: a polynomial fit with its 1-$\sigma$ confidence region (dotted line with light blue shading), the average value of the residuals (dot-dashed red line), and the indices $\sigma_\mathrm{res}$, $s_\mathrm{dev}$, $D_\mathrm{avg}$, $I_\mathrm{abs}$.
  • Figure 3: Similar description as for Fig. \ref{['fig:m1']} but for model $\mathcal{M}_2$.
  • Figure 4: Similar description as for Fig. \ref{['fig:m1']} but for model $\mathcal{M}_3$.
  • Figure 5: Similar description as for Fig. \ref{['fig:m1']} but for model $\mathcal{M}_4$.
  • ...and 5 more figures