Mixed Modes and Asteroseismic Surface Effects. I. Analytic Treatment
Abstract
Normalmode oscillation frequencies computed from stellar models differ from those that would be measured from stars with identical interior structures because of modeling errors in the nearsurface layers. These frequency differences are referred to as the asteroseismic "surface term." The vast majority of solarlike oscillators that have been observed, and that are expected to be observed in the near future, are evolved stars that exhibit mixed modes. For these evolved stars, the inference of stellar properties from these mode frequencies has been shown to depend on how this surface term is corrected for. We show that existing parameterizations of the surface term account for mode mixing only to first order in perturbation theory, if at all, and therefore may not be adequate for evolved stars. Moreover, existing nonparametric treatments of the surface term do not account for mode mixing. We derive both a firstorder construction and a more general approach for one particular class of nonparametric methods. We illustrate the limits of firstorder approximations from both analytic considerations and using numerical injectionrecovery tests on stellar models. Firstorder corrections for the surface term are strictly only applicable where the size of the surface term is much smaller than both the coupling strength between the mixed p and g modes, as well as the local gmode spacing. Our more general matrix construction may be applied to evolved stars, where perturbation theory cannot be relied upon.
 Publication:

The Astrophysical Journal
 Pub Date:
 October 2021
 DOI:
 10.3847/15384357/ac12ca
 arXiv:
 arXiv:2107.03405
 Bibcode:
 2021ApJ...920....8O
 Keywords:

 Asteroseismology;
 Stellar oscillations;
 Computational methods;
 Theoretical techniques;
 73;
 1617;
 1965;
 2093;
 Astrophysics  Solar and Stellar Astrophysics
 EPrint:
 20 pages, 12 figures