Explaining Deviations from the Scaling Relationship of the Large Frequency Separation

Abstract

Asteroseismic large frequency separations possess great diagnostic value. However, their expressions as scaling relations are predicated on homology arguments which may not hold in general, resulting in mass- and temperature-dependent deviations. The first-order asymptotic expressions, which should in principle account for this structural evolution, also deviate more from fitted frequency-separation estimates than do the simple scaling relations, and exhibit qualitatively different behavior. We present a modified asymptotic estimator, and show that these discrepancies can be accounted for by the evolution of the acoustic turning points of the asteroseismic mode cavity, which is typically neglected in first-order asymptotic analysis. This permits us to use a single expression to accurately estimate the large frequency separations of main-sequence, ascending red giant branch, and red clump stellar models, except at transition points between two asymptotic regimes during the subgiant phase of evolution, where the WKB approach fails. The existence of such transition points provides theoretical justification for separately calibrated scaling relations for stars in different evolutionary stages.

arXiv comment12 pages, 9 figures. Accepted for publication in ApJ

References in corpus (17)

• Modules for Experiments in Stellar Astrophysics (MESA): Binaries, Pulsations, and Explosions
• GYRE: An open-source stellar oscillation code based on a new Magnus Multiple Shooting Scheme
• Asteroseismic fundamental properties of solar-type stars observed by the NASA Kepler Mission
• Asteroseismology of old open clusters with Kepler: direct estimate of the integrated RGB mass loss in NGC6791 and NGC6819
• The APOKASC Catalog: An Asteroseismic and Spectroscopic Joint Survey of Targets in the Kepler Fields
• Calculating asteroseismic diagrams for solar-like oscillations
• The underlying physical meaning of the ${\nu }_{\max }-{\nu }_{\mathrm{c}}$ relation
• Stellar population synthesis based modelling of the Milky Way using asteroseismology of 13000 Kepler red giants
• The asteroseismic potential of Kepler: first results for solar-type stars
• Sounding open clusters: asteroseismic constraints from Kepler on the properties of NGC 6791 and NGC 6819
• The First APOKASC Catalog of Kepler Dwarf and Subgiant Stars
• Constraints on the structure of the core of subgiants via mixed modes: the case of HD49385
• Significantly improving stellar mass and radius estimates: A new reference function for the Δν scaling relation
• An Elementary Introduction to the JWKB Approximation
• Nonlinear seismic scaling relations
• Tests of the asymptotic large frequency separation of acoustic oscillations in solar-type and red giant stars
• Mitigating the mass dependence in the $\Delta \nu$ scaling relation of red-giant stars

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• BESTP -- An Automated Bayesian Modeling Tool for Asteroseismology
• Structural and Evolutionary Diagnostics from Asteroseismic Phase Functions
• Unveiling the Structure and Dynamics of Red Giants with Asteroseismology
• Scaling relations for solar-like oscillations: a review