A new correction of stellar oscillation frequencies for near-surface effects

Abstract

Context. Space-based observations of solar-like oscillations present an opportunity to constrain stellar models using individual mode frequencies. However, current stellar models are inaccurate near the surface, which introduces a systematic difference that must be corrected. Aims. We introduce and evaluate two parametrizations of the surface corrections based on formulae given by Gough (1990, LNP, 367, 283). The first we call a cubic term proportional to ν 3 /I and the second has an additional inverse term proportional to ν −1 /I, where ν and I are the frequency and inertia of an oscillation mode. Methods. We first show that these formulae accurately correct model frequencies of two different solar models (Model S and a calibrated MESA model) when compared to observed BiSON frequencies. In particular, even the cubic form alone fits significantly better than a power law. We then incorporate the parametrizations into a modelling pipeline that simultaneously fits the surface effects and the underlying stellar model parameters. We apply this pipeline to synthetic observations of a Sun-like stellar model, solar observations degraded to typical asteroseismic uncertainties, and observations of the well-studied CoRoT target HD 52265. For comparison, we also run the pipeline with the scaled power-law correction proposed by Kjeldsen et al. (2008, ApJ, 683, L175). Results. The fits to synthetic and degraded solar data show that the method is unbiased and produces best-fit parameters that are consistent with the input models and known parameters of the Sun. Our results for HD 52265 are consistent with previous modelling efforts and the magnitude of the surface correction is similar to that of the Sun. The fit using a scaled power-law correction is significantly worse but yields consistent parameters, suggesting that HD 52265 is sufficiently Sun-like for the same power-law to be applicable. Conclusions. We find that the cubic term alone is suitable for asteroseismic applications and it is easy to implement in an existing pipeline. It reproduces the frequency dependence of the surface correction better than a power-law fit, both when comparing calibrated solar models to BiSON observations and when fitting stellar models using the individual frequencies. This parametrization is thus a useful new way to correct model frequencies so that observations of individual mode frequencies can be exploited.

A seismic and gravitationally bound double star observed byKepler

“…GN93: Grevesse & Noels (1993); GS98: Grevesse & Sauval (1998). KBC08: Kjeldsen et al (2008); BG14: Ball & Gizon (2014).…”

“…These 11 initial guesses were then optimised using a downhill simplex optimisation (Nelder & Mead 1965), with all models with a χ 2 < 1000 being recorded. In this latter case, we optimised the merit function without Δν and ν max , instead using the individual oscillation frequencies, corrected according to the cubic correction given by Ball & Gizon (2014).…”

Keplerobservations of the asteroseismic binary HD 176465

“…Oscillation mode frequencies were computed by internal calls to adipls. Model frequencies were corrected for surface effects using the two-term (or combined) correction described by Ball & Gizon (2014). For a given choice of mass M, initial metal abundance Z i , initial helium abundance Y i and mixing-length parameter α, mesa evolved a stellar model from a pre-main-sequence model with central temperature T c = 9 × 10 6 K and found the bestfitting age and surface correction parameters for those input parameters.…”

Differential Rotation in Sun-like Stars from Surface Variability and Asteroseismology

“…The P N values are averages over several sets of oscillation modes. The gyrochronology ages are calculated from Barnes and Kim (2010), Mamajek and Hillenbrand (2008), and 4.5 Gyrochronology with the same input physics as in Ball and Gizon (2014). Initial fits were determined using the SEEK method (Quirion et al 2010) to compare a grid of models to observed spectroscopic and global asteroseismic parameters.…”

“…The 11 initial guesses were optimized in five parameters (age, mass, metallicity, helium abundance, and mixing length) using a downhill simplex (Nelder and Mead 1965) to match spectroscopic data ) and individual oscillation frequencies, computed with ADIPLS (Christensen-Dalsgaard 2008) and corrected according to the cubic correction by Ball and Gizon (2014). As in Ball and Gizon (2014), the seismic and nonseismic observations are weighted only by their respective measurement uncertainties. Best-fit parameters and uncertainties are estimated from ellipses bounding surfaces of constant χ 2 for all the models determined during the optimizations, corresponding to a total of about 3000 models for each star.…”