The stellar activity-rotation-age relationship under the lens of asteroseismology

TL;DR

The paper addresses how magnetic activity, rotation, and age interrelate in solar‑like stars by leveraging precise asteroseismic ages and parameters from the Kepler LEGACY sample, combined with X‑ray measurements from eROSITA. It revisits the core relations linking activity to age and to rotation (via the Rossby number), calibrates them with an expanded, high‑quality dataset, and implements the revised relations in a Star‑Planet Interaction model to predict X‑ray tracks and assess planetary atmospheric mass loss. The authors find improved agreement between revised X‑ray tracks and observations for several stars, while noting large scatter and the need for larger samples to robustly characterize the components of the activity–rotation–age relationship; they also observe only modest changes to planetary radius distributions from atmospheric loss when using these revisions. Overall, the work underscores the power of asteroseismology to refine dynamo‑related relationships in evolved solar‑like stars and points to future, larger samples (e.g., with PLATO) to pin down the multi‑parameter dependencies.

Abstract

In low-mass stars, the connection between magnetic activity, rotation period, and age provides key insights into the functioning of dynamos. Fully understanding the activity-rotation-age relationship requires stars with precise fundamental parameters, measured rotation periods, and reliable magnetic activity indicators (e.g. X-ray luminosity). Thanks to space-based photometry, asteroseismology is now the leading method for determining stellar parameters with unprecedented precision and accuracy. The best-characterized solar-like stars compose the Kepler LEGACY sample, with highest-quality asteroseismic data for 66 stars, most of which have measured rotation periods. In the X-ray band, these stars were observed by the ROentgen Survey with an Imaging Telescope Array (eROSITA) telescope on the Russian Spektrum-Roentgen-Gamma (SRG) satellite in the course of its all-sky survey. We reviewed different components of the stellar activity-rotation-age relationship using the largest sample of solar-like stars with highly accurate fundamental parameters from asteroseismology, along with measured rotation periods and X-ray luminosities. We cross-correlated the Kepler LEGACY sample with the SRG/eROSITA source catalogue, finding X-ray detections for 13 of them. We derived their fundamental parameters using the Forward and Inversion COmbination procedure and revisited widely studied activity-age and activity-rotation relationships by consistently incorporating our 13-star subsample with literature samples. By implementing revised activity-rotation-age relationships in a Star-Planet Interaction code to compute X-ray luminosity tracks and comparing the results with observations, we found improved agreement for 7 stars of our subsample. We explored the effect of the revised relationships on the mass loss of planets in the radius valley, finding a modest impact on planet size distributions.

Figures (19)

• Figure 1: Hertzsprung-Russell diagram showing the best-fit models' tracks of the 13 Kepler LEGACY stars with X-ray detections. The location of the Sun in the $\rm L/L_{\odot}$ vs $\rm T_{eff}(K)$ plane is shown as reference.
• Figure 2: Distribution of 13 stars from the Kepler LEGACY (cyan dots) and 7 stars from B17 (orange pentagons) including the Sun (indicated by the usual symbol) in the $\rm Log(L_x/R^2)$-$\rm Log(Age)$ plane. The empty square highlights the position of KIC8006161. The dotted blue and dashed black lines show the fit obtained in B17 and in this work, respectively.
• Figure 3: Stars in the $\rm Log(R_x)$-$\rm Log(Ro)$ plane, with colour coded symbol according to the $\rm (V-Ks)_0$ colour. $\rm Ro$ is computed with $\rm \tau_{conv}$ as in W18. The empty square shows the position of KIC8006161. The black dashed line shows the fit to the stars. Stars with spectral type from M to F are shown in the top panel, while stars from K to F are shown in the bottom one.
• Figure 4: Stars in the $\rm Log(R_x)$-$\rm Log(Ro)$ plane, with colour coded symbol according to $\rm T_{eff}$. The meaning of symbols and lines is the same as for Fig. \ref{['Fig:Rx_Ro_VKs']}
• Figure 5: Evolution of the surface rotation rate (top panel) and X-ray luminosity (bottom panel) of KIC 8006161. The yellow shaded areas indicate the region explored by the tracks across the evolution of the star, for $3.2 \leq \Omega_{\rm in}/\Omega_{\odot} \leq 18$. The gray shaded areas show 20% (top panel) and global one order of magnitude (bottom panel) further variation at the limit of the yellow areas, to account for deviations from more likely rotational histories and fluctuation in the X-ray luminosity due to cyclic or stochastic magnetic activity. The red-dashed line in the top panel shows the evolution of the critical rotation rate, defined as the limit at which the centrifugal acceleration at the equator equals gravity. The blue markers show observational data. For comparison, evolutionary tracks for a $\rm 1~M_{\odot}$ star are showed, with observational data from Table \ref{['Tab:resc_flux']}.