Stellar acoustic radii and ages from seismic inversion techniques

G Buldgen,R Samadi,M A Dupret,D R Reese

doi:10.1051/epjconf/201510106015

Abstract

Determining stellar characteristics such as the radius, mass or age is crucial and asteroseismology is currently the most promising tool to provide these results accurately. We extend the SOLA inversion technique to new global characteristics in addition to the mean density [2] and apply our methodology to the acoustic radius and an age indicator based on the sound speed derivative. The results from SOLA inversions are compared with estimates based on the small and large frequency separations for several test cases. We show that SOLA inversions yield more accurate results than other techniques which are more sensitive to surface effects.

Highlights

The inversion procedure relies on the variational principle and the frequency-structure relation for adiabatic stellar oscillations
Each point gives the result for a given reference model of the grid and the horizontal green line corresponds to the target value
The inversion equations rely on the variational principle, which assumes that the reference model is close to the star

Summary

Theoretical approach

The inversion procedure relies on the variational principle and the frequency-structure relation for adiabatic stellar oscillations. The relative perturbation of a global characteristic A (e.g. ρ, τ, ...) can be related to structural variables as follows: δA A. T and Tcross being the target functions. In the SOLA method, we minimise a cost function related to the target functions and the observational errors to find the optimal frequency combination to reproduce δAobs A. We apply inversion techniques to the acoustic radius, τ, and the age indicator, t, which are defined and related to the large and small frequency separations as follows: τ=. Where is the degree of the mode, Δν the large frequency separation and δν the small frequency separation. SOLA inversions are compared with other techniques based on these asteroseismic indices. The quality of the inversion depends on how well the averaging and cross-term kernels fit their respective targets

Results for a grid of models

Results using forward modelling

Conclusion