# Forward asteroseismic modeling of stars with a convective core from gravity-mode oscillations: parameter estimation and stellar model selection

**Authors:** C. Aerts, G. Molenberghs, M. Michielsen, M. G. Pedersen, R. Björklund, C. Johnston, J. S. G. Mombarg, D. M. Bowman, B. Buysschaert, P. I. Pápics, S. Sekaran, J. O. Sundqvist, A. Tkachenko, K. Truyaert, T. Van Reeth, E. Vermeyen  
**arXiv:** [1806.06869](https://arxiv.org/abs/1806.06869)  
**Date:** 2018-06-18  
**Summary page:** https://www.summarizepaper.com/en/paper/1806.06869v1/

## Key points

- C. Aerts et al. propose a methodological framework for forward asteroseismic modeling of stars with a convective core using gravity-mode oscillations.
- The paper discusses major uncertainties in theoretically predicted gravity-mode oscillation frequencies based on linear pulsation theory.
- The authors provide a global methodological scheme to achieve forward asteroseismic modeling while properly taking into account correlations amongst free parameters included in stellar models.
- Major parameters to be estimated are the near-core rotation rate, amount of convective core overshooting, and level of chemical mixing in radiative zones.
- This modeling scheme allows for maximum likelihood estimation of stellar parameters for fixed input physics of equilibrium models followed by stellar model selection considering various choices of input physics.
- The approach uses Mahalanobis distance instead of often-used $\chi^2$ statistic and includes heteroscedasticity while providing an estimation of unknown variance in theoretically predicted oscillation frequencies.

## Summary

In their paper, "Forward asteroseismic modeling of stars with a convective core from gravity-mode oscillations: parameter estimation and stellar model selection," C. Aerts et al. propose a methodological framework for forward asteroseismic modeling of stars with a convective core using gravity-mode oscillations to probe the near-core region in the deep stellar interior. The authors rely on a set of observed high-precision oscillation frequencies of low-degree coherent gravity modes with long lifetimes and their observational uncertainties, assuming identification of the mode degree and azimuthal order is achieved from rotational splitting and/or period spacing patterns. The paper has two major outcomes: first, it provides a comprehensive list and discussion of the major uncertainties of theoretically predicted gravity-mode oscillation frequencies based on linear pulsation theory caused by fixing choices of input physics for evolutionary models; second, guided by a hierarchy among these uncertainties of theoretical frequencies, the authors provide a global methodological scheme to achieve forward asteroseismic modeling while properly taking into account correlations amongst free parameters included in stellar models. Aside from the stellar mass, metallicity, and age, the major parameters to be estimated are the near-core rotation rate, amount of convective core overshooting, and level of chemical mixing in radiative zones. This modeling scheme allows for maximum likelihood estimation of stellar parameters for fixed input physics of equilibrium models followed by stellar model selection considering various choices of input physics. The approach uses Mahalanobis distance instead of often-used $\chi^2$ statistic and includes heteroscedasticity while providing an estimation of unknown variance in theoretically predicted oscillation frequencies. Overall, this paper presents an important contribution to our understanding and ability to model stars with convective cores using gravity-mode oscillations as probes into their deep interiors.