Mixed Modes and Asteroseismic Surface Effects: I. Analytic Treatment

Abstract

Normal-mode oscillation frequencies computed from stellar models differ from those which would be measured from stars with identical interior structures, because of modelling errors in the near-surface layers. These frequency differences are referred to as the asteroseismic "surface term". The vast majority of solar-like oscillators which have been observed, and which are expected to be observed in the near future, are evolved stars which 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 parametrisations 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 first-order construction, and a more general approach, for one particular class of nonparametric methods. We illustrate the limits of first-order approximations from both analytic considerations and using numerical injection-recovery tests on stellar models. First-order 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 g-mode spacing. Our more general matrix construction may be applied to evolved stars, where perturbation theory cannot be relied upon.

arXiv comment20 pages, 12 figures; accepted for publication in ApJ

References in corpus (28)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Array Programming with NumPy
• Astropy: A Community Python Package for Astronomy
• Modules for Experiments in Stellar Astrophysics (MESA)
• Binary companions of evolved stars in APOGEE DR14: Search method and catalog of ~5,000 companions
• Modules for Experiments in Stellar Astrophysics (MESA): Giant Planets, Oscillations, Rotation, and Massive Stars
• Modules for Experiments in Stellar Astrophysics (MESA): Convective Boundaries, Element Diffusion, and Massive Star Explosions
• GYRE: An open-source stellar oscillation code based on a new Magnus Multiple Shooting Scheme
• Correcting stellar oscillation frequencies for near-surface effects
• A new correction of stellar oscillation frequencies for near-surface effects
• Surface-effect corrections for solar-like oscillations using 3D hydrodynamical simulations
• Age dating of an early Milky Way merger via asteroseismology of the naked-eye star $\nu$ Indi
• Modelling Kepler Red Giants in Eclipsing Binaries:Calibrating the Mixing Length Parameter with Asteroseismology
• Asteroseismic modelling of solar-type stars: internal systematics from input physics and surface correction methods
• Asteroseismology of 36 \emph{Kepler} subgiants -- I. Oscillation frequencies, linewidths and amplitudes
• Semi-analytic Expressions for the Isolation and Coupling of Mixed Modes
• Masses of subgiant stars from asteroseismology using the coupling strengths of mixed modes
• Surface effects on the red giant branch
• The Helium Abundance of NGC 6791 from Modeling of Stellar Oscillations
• Investigating surface correction relations for RGB stars
• Modeling the Asteroseismic Surface Term across the HR Diagram
• Asteroseismology of 19 low-luminosity red giant stars from Kepler
• Surface correction of main sequence solar-like oscillators with the $Kepler$ LEGACY sample
• The robustness of asteroseismic estimates of global stellar parameters to surface term corrections
• Wave propagation in semi-convective regions of giant planets
• Surface layer independent model fitting by phase matching: theory and application to HD49933 an HD177153 (aka Perky)
• Differential Modelling Systematics across the HR Diagram from Asteroseismic Surface Corrections
• Structural and Evolutionary Diagnostics from Asteroseismic Phase Functions

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• Detectability of axisymmetric magnetic fields from the core to the surface of oscillating post-main sequence stars
• Asteroseismology of the G8 subgiant beta Aquilae with SONG-Tenerife, SONG-Australia and TESS
• The robustness of inferred envelope and core rotation rates of red-giant stars from asteroseismology
• Asteroseismology and Buoyancy Glitch Inversion with Fourier Spectra of Gravity Mode Period Spacings
• Impact of near-degeneracy effects on linear rotational inversions for red-giant stars