Asteroseismology of 3,642 Kepler Red Giants: Correcting the Scaling Relations based on Detailed Modeling

TL;DR

This study refines the seismic scaling relations for red giants by using detailed modeling and observations from Kepler, leading to more accurate stellar parameters and addressing biases in previous relations.

Contribution

It introduces corrected scaling relations for red-giant stars based on detailed modeling and observational data, improving accuracy over traditional relations.

Findings

Systematic offset of ~15% in mass between models and scaling relations

Underestimation of Delta nu by ~4% in original scaling relation

Metallicity dependence observed in nu_max scaling relation

Abstract

The paper presents a correction to the scaling relations for red-giant stars using model-based masses and radii. We measure radial-mode frequencies from Kepler observations for 3,642 solar-like oscillators on the red-giant branch and use them to characterise the stars with the grid-based modeling. We determine fundamental stellar parameters with good precision: the typical uncertainty is 4.5% for mass, 16% for age, 0.006 dex for surface gravity, and 1.7% for radius. We also achieve good accuracy for estimated masses and radii, based on comparing with those determined for eclipsing binaries. We find a systematic offset of ~15% in mass and ~7% in radius between the modeling solutions and the scaling relations. Further investigation indicates that these offsets are mainly caused by a systematic bias in the Delta nu scaling relation: the original scaling relation underestimates Delta nu value by ~4%, on average, and it is important to correct for the surface term in the calibration. We find no significant offset in the nu_max scaling relation, although a clear metallicity dependence is seen and we suggest including a metallicity term in the formulae. Lastly, we calibrate new scaling relations for red-giant stars based on observed global seismic parameters, spectroscopic effective temperatures and metallicities, and modeling-inferred masses and radii.