On the Temporal Variability in the Magnetic Dichotomy of Late M Dwarf Stars

TL;DR

This work investigates how thermal convective flux modulates magnetic polarity reversals in fully convective late M dwarfs within an $\alpha^2$ dynamo framework. It introduces a low-dimensional magnetohydrodynamic shell model that couples velocity $u_n$, magnetic $b_n$, and temperature $\theta_n$ under the Boussinesq approximation, incorporating nonlocal interactions and an $\alpha$-quenching term $\alpha=\mu\left(1-\frac{b_1^2}{B_0^2}\right)$ to enable reversals. Numerical simulations across wide ranges of $\tilde{\alpha}$, $\nu$, $\eta$, and $\chi$ show that stronger convective driving and lower diffusivities increase reversal frequency and shorten persistence times, with persistence-time PDFs exhibiting power-law tails similar to Earth's reversal record CK95; this supports a link between heat flux and magnetic variability. The study suggests that differences in global heat transport efficiency could underlie the observed magnetic dichotomy in late-M dwarfs, while acknowledging the model’s idealizations and the need for more realistic simulations that include stratification and rotation.

Abstract

Rapidly rotating late M dwarfs are observed in two different branches of magnetic activity, although they operate in the same stellar parameter range. Current empirical evidence indicates that M dwarfs with spectral types ranging from M3 / M4 to late-type M dwarfs, stellar masses smaller than 0.15 M$_\odot$, and rotational period shorter than four days display either a stable dipolar magnetic field or magnetic structures with significant time variability. The magnetic activity of fully convective M dwarfs is known to be regulated by a mechanism named the $α^2$ dynamo. To further constrain the physics of this mechanism, we use a low-dimensional model for thermally driven magnetoconvection producing an $α^2$ dynamo, specifically a modified magnetohydrodynamic (MHD) shell model. Although the model neglects density stratification, it captures the essential nonlinear dynamics of an $α^2$ dynamo. Therefore, the results should be interpreted in a qualitative sense, highlighting possible trends rather than providing direct quantitative predictions for fully convective stars. The model is validated by comparing the statistical properties of magnetic polarity reversals with paleomagnetic data, since the geodynamo provides the only natural $α^2$ dynamo with sufficiently rich reversal statistics. Our findings reveal that increased convective heat transport correlates with more frequent magnetic-polarity reversals, resulting in enhanced magnetic variability. This suggests that the observed magnetic dichotomy in late M dwarfs could be interpreted in terms of differences in global heat transport efficiency. However, additional models and observations of M dwarfs are needed to further constrain this interpretation.

Figures (1)

• Figure 1: Sensitivity of the system with respect to the thermal diffusivity $\chi$ (i.e., Rayleigh number $\textrm{Ra} = {\tilde{\alpha}}{\theta_0}L^3/(\nu \chi))$, keeping constant the other parameters; in particular $\tilde{\alpha} =0.5$, $\eta = 10^{-2}$, and $\nu = 10^{-4}$.