Co-existence of Internal Gravity Waves and Tayler-Spruit Magnetic Fields in the Radiative Core of Low-mass Stars

TL;DR

This work investigates how a Tayler-Spruit dynamo (TSD)–generated magnetic field coexists with internal gravity waves (IGW) in the radiative cores of solar-type, low-mass stars. Using the STAREVOL evolutionary code, the authors implement the TSD to map regions where IGW convert to magneto-gravity waves and to assess the impact on standing modes and angular-momentum transport across evolutionary stages from the pre-main sequence to the red-giant branch. They find that, for Spruit2002-like TSD fields, standing gravity modes are largely unaffected because the Alfvén frequencies remain below the mode-cutoff, while progressive low-frequency IGW can be converted to MGW during the main sequence and especially on the red giant branch, potentially altering core rotation. The study provides a first self-consistent framework to quantify IGW transmission in the presence of rotation and magnetism and highlights the evolution- and mass-dependent role of TSD in angular-momentum transport, setting the stage for future coupled MGW–TSD modeling in a broader stellar-mass range.

Abstract

The Tayler-Spruit dynamo (TSD) is able to generate a small-scale magnetic field in the differentially rotating stably stratified layers of stars and was recently observed in numerical simulations. In parallel, the propagation of internal gravity waves in stars can be modified in the presence of a magnetic field. Here we first want to estimate the interaction between a magnetic field generated by the TSD and internal gravity waves in the radiative core of low-mass stars. This allows us to then characterise the effect of this interplay on the observed standing modes spectrum and on the internal transport of angular momentum by progressive waves. To do this, we use the STAREVOL evolution code to compute the structure of low-mass rotating stars along their evolution. In particular, we implement a formalism to describe the TSD and estimate the regions where the generated magnetic field is strong enough to change the identity of internal gravity waves to magneto-gravity waves. In addition, we evaluate the possible limitation of angular momentum transport by the combined action of rotation and magnetism. We show that along the pre-main sequence and main-sequence evolution, the lowest frequencies of the excited gravity wave spectrum could be converted to magneto-gravity waves by the magnetic field generated by the TSD. During the red-giant branch we find that most of the excited spectrum of progressive internal gravity waves could be converted into magneto-gravity waves in the very central region.

Figures (6)

• Figure 1: Wave spectrum in a magnetised rotating star
• Figure 2: Top. Rotation profile at the age of the Sun for the 1M$_\odot$ model. The points and their error bars are from EffDarwich2008. Bot. Rotation profile evolution of the 1M$_\odot$ model through the ages as indicated on each plot.
• Figure 3: Top left : Location of each selected profile on the Hertzsprung-Russel diagram of the 1M$_\odot$ model. The next diagrams show the variations of the relevant characteristic frequencies along the evolution. From top center to bottom right : Early PMS (5 Myr), Henyey track (25 Myr), ZAMS (52 Myr), Solar age (4.57 Gyr), TAMS (9.61 Gyr), sub-giant branch (10.53 Gyr), base of the RGB (10.97 Gyr), and middle of the RGB (11.38 Gyr). The light blue region indicates the frequency range of standing gravity modes.
• Figure 4: Colour maps of the transmission function $\mathcal{P}_m$ from MDB2012 with $m=-1$ as a function of frequency and time for a 1M$_\odot$ star. The left (central) panel shows $\mathcal{P}_m$ when only the rotation (toroidal magnetism) is taken into account, the right panel presents the case with the full contribution of $\mathcal{P}_m$. White regions show where the angular momentum flux carried by the wave is unaffected by the rotation and magnetic field while black regions indicate where it is. The dashed part of the diagram present the region where the waves are completely trapped vertically and therefore do not propagate. The red line shows the convective turnover frequency as a function of time, which acts as a proxy for the peak of excitation. The blue and the green lines are the inertial frequency ($2\Omega$) and the Alfvén frequency integrated over the upper 5% of the radiative core, respectively.
• Figure 5: Same as fig. \ref{['fig:allfreq']} for a 0.6M$_\odot$ (top line), 0.8M$_\odot$ (middle), and 1.2M$_\odot$ (bottom) star.