K-dwarf Radius Inflation and a 10-Gyr Spin-down Clock Unveiled through Asteroseismology of HD 219134 from the Keck Planet Finder

TL;DR

This study uses asteroseismology to precisely determine the properties of the K-dwarf star HD 219134, revealing radius inflation, calibrating stellar spin-down, and revising exoplanet parameters, thereby advancing understanding of K-star evolution.

Contribution

First asteroseismic analysis of HD 219134 providing detailed stellar parameters and insights into K-dwarf physics, including radius discrepancy and angular momentum loss calibration.

Findings

Asteroseismic radius is 4% smaller than interferometric measurement.

Confirmed the $(L/M)^{1.5}$ scaling of oscillation amplitude in K dwarfs.

Revised masses and radii of the system's super-Earths, supporting Earth-like compositions.

Abstract

We present the first asteroseismic analysis of the K3\,V planet host HD~219134, based on four consecutive nights of radial velocities collected with the Keck Planet Finder. We applied Gold deconvolution to the power spectrum to disentangle modes from sidelobes in the spectral window, and extracted 25 mode frequencies with spherical degrees $0\leq\ell\leq3$. We derive the fundamental properties using five different evolutionary-modeling pipelines and report a mass of 0.763 $\pm$ 0.020 (stat) $\pm$ 0.007 (sys) M$_\odot$, a radius of 0.748 $\pm$ 0.007 (stat) $\pm$ 0.002 (sys) R$_\odot$, and an age of 10.151 $\pm$ 1.520 (stat) $\pm$ 0.810 (sys) Gyr. Compared to the interferometric radius 0.783 $\pm$ 0.005~R$_\odot$, the asteroseismic radius is 4\% smaller at the 4-$\sigma$ level -- a discrepancy not easily explained by known interferometric systematics, modeling assumptions on atmospheric boundary conditions and mixing lengths, magnetic fields, or tidal heating. HD~219134 is the first main-sequence star cooler than 5000~K with an asteroseismic age estimate and will serve as a critical calibration point for stellar spin-down relations. We show that existing calibrated prescriptions for angular momentum loss, incorporating weakened magnetic braking with asteroseismically constrained stellar parameters, accurately reproduce the observed rotation period. Additionally, we revised the masses and radii of the super-Earths in the system, which support their having Earth-like compositions. Finally, we confirm that the oscillation amplitude in radial velocity scales as $(L/M)^{1.5}$ in K dwarfs, in contrast to the $(L/M)^{0.7}$ relation observed in G dwarfs. These findings provide significant insights into the structure and angular momentum loss of K-type stars.