Is a 1D perturbative method sufficient for asteroseismic modelling of $β$ Cephei pulsators? Implications for measurements of rotation and internal magnetic fields

TL;DR

The paper investigates whether a 1D perturbative approach to rotation (via StORM) suffices for asteroseismic modelling of β Cephei pulsators or whether full 2D modelling (ESTER/TOP) is required for reliable inferences of internal rotation and magnetic fields. By comparing 1D and 2D predictions for a $12\,M_\odot$ ZAMS model across rotation up to $0.20\,Ω_{\rm c, Kep}$ and low-order g/p modes, the authors find generally good frequency agreement but notable differences in rotational mode asymmetries, which can severely bias magnetic-field measurements if not properly accounted for. They show that magnetic-field inferences are particularly sensitive to the choice of rotation treatment, with significant errors for many $n_{\rm pg}$ values unless conditions such as $n_{\rm pg}\ge2$ and moderate rotation are met; evolution to more advanced main-sequence stages enhances magnetic asymmetries and can improve measurability. Overall, while StORM offers fast and accurate rotational modelling suitable for large samples, 2D methods remain essential for robust magnetic-field determinations in β Cephei stars, guiding the use of 1D versus 2D approaches in seismic diagnostics.

Abstract

Asymmetries in the observed rotational splittings of a multiplet contain information about the star's rotation profile and internal magnetic field. However, to exploit this information, highly accurate theoretical predictions are needed. We aim to quantify the difference in the predicted mode asymmetries between a 1D perturbative method, and a 2D method that includes a 2D stellar structure model, which takes rotation into account. We then put these differences in the context of asteroseismic measurements of internal magnetic fields. We couple the 1D pulsation codes GYRE and StORM to the 2D stellar structure code ESTER and compare the oscillation predictions with the results from the 2D TOP pulsation code. We focus on ZAMS models representative of rotating $β$~Cephei pulsators, going up to 20% of the critical rotation rate. We find a generally good agreement between the oscillation frequencies resulting from the 1D and 2D pulsation codes. Since the magnetic asymmetries are small compared to the differences in the rotational asymmetries resulting from the 1D and 2D predictions, accurate measurements of the magnetic field are in most cases challenging. Differences in the predicted mode asymmetries between 1D perturbative methods and 2D non-perturbative methods can greatly hinder accurate measurements of internal magnetic fields in main-sequence pulsators with low-order modes. Nevertheless, reasonably accurate measurements could be possible with $n_{pg} \ge 2$ modes if the internal rotation is roughly below 10% of the critical rotation frequency for (aligned) magnetic fields on the order of a few hundred kG. While the differences between the 1D and 2D predictions are mostly too large for internal magnetic field detections, the rotational asymmetries predicted by StORM are in general accurate enough for asteroseismic modelling of the stellar rotation in main-sequence stars.

Figures (10)

• Figure 1: Differential rotation profiles of a 12 M$_{\odot}$ stars computed with ESTER at ZAMS (top panel) and $X_{\rm c} = 0.4$ (bottom panel), normalized by the critical rotation frequency at the equator.
• Figure 2: Frequency differences for different radial resolutions of the ESTER/TOP grid. Frequency differences between 30 and 60 radial points per domain (in black), and differences between 60 and 90 points per domain (in red).
• Figure 3: Frequency spectra of a non-rotating ESTER model computed with TOP (top panel) and StORM (bottom) panel. The GYRE frequency spectrum is indicated with red dotted lines. The ordinate corresponds to the value of $\ell$. The radial modes are indicated with black dashed lines.
• Figure 4: Predicted asymmetry parameters (dimensionless) for $\ell = 1$ computed with TOP (in black) and StORM (in red) as a function of radial order.
• Figure 5: Predicted asymmetry parameters for $\ell = 2$ computed with TOP (in black) and StORM (in red) as a function of radial order.