Asteroseismic detection of a predominantly toroidal magnetic field in the deep interior of the main-sequence F star KIC 9244992

TL;DR

Using four years of Kepler data, this work detects a strong internal magnetic field in the main-sequence F star KIC 9244992 by analyzing the asymmetry of high-order gravity-mode splittings. The authors develop a tripartite model incorporating rotation, magnetic effects, and an aspherical glitch, and show that rotation alone cannot explain the observed asymmetries. The inferred field is predominantly toroidal (B_φ^min ≈ 92 kG) with a much weaker radial component (B_r^min ≈ 3.5 kG) confined near the core, and the glitch localizes to a layer just outside the convective core where the chemical gradient is steep. These results imply efficient angular-momentum transport inconsistent with several radiative-dynamo scenarios and point to fossil fields or merger-related origins, marking the first seismic detection of a deep interior magnetic field in a main-sequence star.

Abstract

An asteroseismic analysis has revealed a magnetic field in the deep interior of a slowly-rotating main-sequence F star KIC9244992, which was observed by the Kepler spacecraft for four years. The star shows clear asymmetry of frequency splittings of high-order dipolar gravity modes, which cannot be explained by rotation alone, but are fully consistent with a model with rotation, a magnetic field and a discontinuous structure (glitch). Careful examination of the frequency dependence of the asymmetry allows us to put constraints on not only the radial component of the magnetic field, but also its azimuthal (toroidal) component. The lower bounds of the root-mean-squares of the radial and azimuthal components in the radiative region within 50 per cent in radius, which have the highest sensitivity in the layers just outside the convective core with a steep gradient of chemical compositions, are estimated to be $\mathsf{B}_{\mathrm{r}}^{\min}=3.5 \pm 0.1$ kG and $\mathsf{B}_φ^{\min}=92 \pm 7$ kG, respectively. The much stronger azimuthal component than the radial one is consistent with the significant contribution of the differential rotation although the star has almost uniform rotation at present. The estimated field strengths are too strong to be explained by dynamo mechanisms in the radiative zone associated with the magnetic Tayler instability. The aspherical glitch is found to be located in the innermost radiative layers where there is a steep gradient of chemical composition. The first detection of magnetic fields in the deep interior of a main-sequence star sheds new light on the problem of stellar magnetism, for which there remain many uncertainties.

Figures (12)

• Figure 1: Asymmetry of frequency splittings $\mathfrak{a}_n$ (see equation \ref{['eq:t_n_obs']}) for high-order gravity modes in KIC 9244992. Errors are smaller than the symbol size for the points without error bars.
• Figure 2: Profiles of $K_{\mathrm{r}}$ (solid curve) and $K_{\phi}$ (dashed curve) multiplied by the total radius $R$ for the best evolutionary model (model A in Table \ref{['tab:models']}) with the upper limit of $\text{G}_{B}$ set at 50 per cent of the total radius. The gradual increase of $R K_{\phi}$ towards larger $r/R$ actually complicates the interpretation, which is treated in Section \ref{['sec:mag_strength']} in detail.
• Figure 3: Asymmetry of frequency splittings caused by the second-order effect of rotation for the modes of our best evolutionary model (model A in Table \ref{['tab:models']}). The total effects $\mathfrak{a}_n^{(\mathrm{rot})}$ and the asymptotic estimates $\mathfrak{a}_n^{(\mathrm{rot,asymp})}$ (see equation (\ref{['eq:t_n_C1_asymp']})) are shown by the filled dots and the dashed curve, respectively.
• Figure 4: Residuals of the fitting in period, $-\nu_{n,1}^{-2}\left(\mathfrak{a}_n - \mathfrak{a}_n^{(\mathrm{rot})} - \mathfrak{a}_n^{(\mathrm{mag})}\right)$, as a function of the mode period. The fitting is performed based on equation (\ref{['eq:t_n_mag']}) for model A (see Table \ref{['tab:fitting']}) using only the eight modes with periods longer than $0.8\,\mathrm{d}$. The residuals are computed for not only those modes but also the modes with shorter periods. The solid curve represents the best fit to the residuals by a sinusoidal function of constant amplitude, neglecting the data point at $0.83\,\mathrm{d}$. There is another rejected point at $0.88\,\mathrm{d}$, whose ordinate is outside the plot range. This corresponds to the outlier at $1.13\,\mathrm{d}^{-1}$ in Fig. \ref{['fig:asymmetry']} (see Section \ref{['subsec:outlier']}).
• Figure 5: Asymmetry of frequency splittings $\mathfrak{a}_n$ of KIC 9244992 fitted with the model that takes account of rotation, a magnetic field and a glitch (upper part of each panel) and the residuals (lower part). The results for the two cases, 1 and 2 (see Table \ref{['tab:best_fit_params']}), with different positions of the glitch (see Fig. \ref{['fig:N_XH']}), are presented in the left and right panels, respectively. The rotation effect is estimated based on our best evolutionary model (model A in Table \ref{['tab:models']}). In each panel, there are two data points excluded from the fitting, one at $1.20\,\mathrm{d}^{-1}$ indicated by the filled circle and the other at $1.13\,\mathrm{d}^{-1}$, whose ordinate is outside the plot range (Fig. \ref{['fig:asymmetry']}). See Section \ref{['subsec:outlier']} for the possible origins of these points.