Asteroseismology Can Reveal Strong Internal Magnetic Fields in Red Giant Stars

Published in Science
10/23/2015

Abstract

*This is the author’s version of the work. It is posted here by permission of the AAAS for personal use, not for redistribution. The definitive version was published in Science on Vol. 350 no. 6259 pp. 423-426 , DOI: 10.1126/science.aac6933*

Internal stellar magnetic fields are inaccessible to direct observations and little is known about their amplitude, geometry and evolution. We demonstrate that strong magnetic fields in the cores of red giant stars can be identified with asteroseismology. The fields can manifest themselves via depressed dipole stellar oscillation modes, which arises from a magnetic greenhouse effect that scatters and traps oscillation mode energy within the core of the star. The *Kepler* satellite has observed a few dozen red giants with depressed dipole modes which we interpret as stars with strongly magnetized cores. We find field strengths larger than \(\sim\! 10^5 \,{\rm G}\) may produce the observed depression, and in one case we infer a minimum core field strength of \(\approx \! \! 10^7 \,{\rm G}\).

\label{main}

Despite rapid progress in the discovery and characterization of magnetic fields at the surfaces of stars, very little is known about internal stellar magnetic fields. This has prevented the development of a coherent picture of stellar magnetism and the evolution of magnetic fields within stellar interiors.

After exhausting hydrogen in their cores, most main sequence stars evolve up the red giant branch (RGB). During this phase, the stellar structure is characterized by an expanding convective envelope and a contracting radiative core. Acoustic waves (p modes) in the envelope can couple to gravity waves (g modes) in the core (Bedding 2014). Consequently, non-radial stellar oscillation modes become mixed modes that probe both the envelope (the p mode cavity) and the core (the g mode cavity), as illustrated in Fig. \ref{fig:cartoon}. Mixed modes (Beck 2011) have made it possible to distinguish between hydrogen and helium-burning red giants (Bedding 2011, Mosser 2014) and have been used to measure the rotation rate of red giant cores (Beck 2012, Mosser 2012).

A group of red giants with depressed dipole modes were identified using *Kepler* observations (Mosser 2012a), see also Fig. \ref{fig:moneyplot}. These stars show normal radial modes (spherical harmonic degree \(\ell=0\)), but exhibit dipole (\(\ell=1\)) modes whose amplitude is much lower than usual. Until now, the suppression mechanism was unknown (García 2014). Below, we demonstrate that dipole mode suppression may result from strong magnetic fields within the cores of these red giants.

Red giant oscillation modes are standing waves that are driven by stochastic energy input from turbulent near-surface convection (Goldreich 1977, Dupret 2009). Waves excited near the stellar surface propagate downward as acoustic waves until their angular frequency \(\omega\) is less than the local Lamb frequency for waves of angular degree \(\ell\), i.e., until \(\omega = L_{\ell} = \sqrt{\ell(\ell+1)} v_s/r\), where \(v_s\) is the local sound speed and \(r\) is the radial coordinate. At this boundary, part of the wave flux is reflected, and part of it tunnels into the core.

The wave resumes propagating inward as a gravity wave in the radiative core where \(\omega < N\), where \(N\) is the local buoyancy frequency. In normal red giants, wave energy that tunnels into the core eventually tunnels back out to produce the observed oscillation modes. We show here that suppressed modes can be explained if wave energy leaking into the core never returns back to the stellar envelope.

The degree of wave transmission between the core and envelope is determined by the tunneling integral through the intervening evanescent zone. The transmission coefficient is

\[\label{eqn:integral2} T \sim \bigg( \frac{r_1}{r_2} \bigg)^{\sqrt{\ell(\ell+1)}} \, ,\]

where \(r_1\) and \(r_2\) are the lower and upper boundaries of the evanescent zone, respectively. The fraction of wave energy transmitted through the evanescent zone is \(T^2\). For waves of the same frequency, larger values of \(\ell\) have larger values of \(r_2\), thus Eqn. \ref{eqn:integral2} demonstrates that high \(\ell\) waves have much smaller transmission coefficients through the evanescent zone.

The visibility of stellar oscillations depends on the interplay between driving and damping of the modes (Dupret 2009, Benomar 2014). To estimate the reduced mode visibility due to energy loss in the core, we assume that all mode energy which leaks into the g mode cavity is completely lost. The mode then loses a fraction \(T^2\) of its energy in a time \(2 t_{\rm cross}\), where \(t_{\rm cross}\) is the wave