# High-precision asteroseismology in Slowly Pulsating B star: HD 50230

## TL;DR

This study conducts high-precision asteroseismology on the SPB star HD 50230, revealing detailed internal structure and pulsation characteristics through 8 observed modes and advanced modeling techniques.

## Contribution

It provides a detailed seismic analysis of HD 50230, accurately measuring the buoyancy radius and constraining stellar parameters including mass, metallicity, and core properties.

## Key findings

- Buoyancy radius measured as 245.78±0.59 μHz with 0.24% precision
- HD 50230 is a metal-rich star with a mass of 6.15-6.27 solar masses
- Core overshooting and extra mixing are essential for modeling the observed period spacing

## Abstract

SPB star HD 50230, in fact a hybrid B-type pulsator, has been observed by CoRoT least 137 days. A nearly equidistant period spacing pattern are found among 8 modes which are extracted from the oscillation spectrum with more than 500 frequencies. However, it is thought to be most likely accidental by Szewczuk et al. (2014). In the present work, we analyze the 8 modes in depth with the $\chi^2$-matching method. Based on the best fitting model (model MA), we find that they can be well explained as a sequences of consecutive dipolar $(l,~m)=(1,~0)$. The period discrepancies between observations and the best fitting model are within 100 s except for the outlier which is up to 300 s. Based on the calculated CMMs, we find that, for pure g-mode oscillations, the buoyancy radius $\Lambda_{0}$ can be precisely measured with the $\chi^2$-matching method between observations and calculations. It represents the "Propagation time" of the g-mode from stellar surface to center. It is of $\Lambda_{0}=245.78\pm0.59~\mu$Hz with a precision of 0.24\%. In addition, we also find that HD 50230 is a metal-rich ($Z_{\rm init}=0.034-0.043$) star with a mass of $M=6.15-6.27~{\rm M_{\odot}}$. It is still located on hydrogen-burning phase with central hydrogen $X_{\rm C}=0.298-0.316$ (or $X_{\rm C}=0.306^{+0.010}_{-0.008}$), therefore has a convective core with a radius of $R_{\rm cc}=0.525-0.536~{\rm R_{\odot}}$ (or $R_{\rm cc}=0.531^{+0.005}_{-0.006}~{\rm R_{\odot}}$). In order to well interpret the structure of observed period spacing pattern, the convective core overshooting ($f_{\rm ov}=0.0175-0.0200$) and the extra diffusion mixing ($\log D_{\rm mix}=3.7-3.9$) should be taken into account in theoretical models.