Retarded Stellar Dynamo in Tidally Deformed M Dwarfs

Abstract

Current studies of stellar dynamos primarily focus on spherical stars, leaving their behavior in distorted stars largely unexplored. We utilize stars of varying distortions to examine the relation between stellar cycle periods ($P_{\rm cyc}$) and rotational periods ($P_{\rm rot}$), which are closely linked to dynamo processes. By analyzing a sample of tidally distorted M dwarfs in cataclysmic variables, we identify an anti-correlation between $P_{\rm cyc}$ and $P_{\rm rot}$, in contrast to the lack of such a relation in single M dwarfs. This means that stars with greater deformation have longer cycle periods, suggesting variations in dynamo behavior under non-spherical geometries. Our numerical simulations further reveal that, the thermal convection weakens in highly distorted stars, and subsequently, the differential rotation is also reduced. These effects may lengthen the conversion timescale between poloidal and toroidal magnetic fields, potentially explaining the newly discovered $P_{\rm cyc}$-$P_{\rm rot}$ relation in cataclysmic variables.

Figures (8)

• Figure 1: $P_{\rm cyc}$ versus $P_{\rm rot}$ in log--log scale for M dwarfs. Filled dots represent stars in close binaries (i.e., CVs), while filled squares represent stars in wide binaries. Open pentagons represent single stars. The two horizontal dashed lines represent stars with cycle periods of 1 and 2 years, respectively.
• Figure 2: $P_{\rm cyc}$/$P_{\rm rot}$ versus 1/$P_{\rm rot}$ in log--log scale for M stars. Open pentagons represent single stars. Filled dots represent stars in close binaries (i.e., CVs), while filled squares represent stars in wide binaries. The solid black line is the fitting from literature 2019AA...621A.126D for single M dwarfs with a slope of 1.01$\pm$0.06. The blue line represents our fitting using M dwarfs in close binaries, with a slope of 1.59$\pm$0.05, and the shaded blue region indicates the 1$\sigma$ uncertainty of the linear fit. The shaded gray region denotes the 1$\sigma$ uncertainty of the polynomial fit to the whole sample.
• Figure 3: Sketch of a binary system under the asymmetrical deformation. Star A of mass $M$ and the companion B of mass $m_s$ are tidally locked to each other. The dashed circle denotes the original spherically symmetric shape of star A of radius $R$, while the solid curve represents its asymmetrically deformed figure due to its fast rotation and the tidal forcing from the companion B. In this physical model the companion B is simplified as a mass point. The distance between the barycenters of A and B is $r_s$.
• Figure 4: Contours of the azimuthal component $\boldsymbol{\hat{\phi}}\cdot\boldsymbol{u}$ of flows at the onset of thermal convection computed via direct numerical simulation. The top row represents the numerical results in the slightly deformed figure with $q_{\text{rot}}=0.015$, while the bottom row demonstrates the numerical results in the heavily deformed figure with $q_{\text{rot}}=0.051$. The panels (a) and (d) are sliced in the $xOy$ plane, (b) and (e) in the $xOz$ plane, and (c) and (f) in the $yOz$ plane. Other physical parameters are referred to Table \ref{['table1.tab']}.
• Figure 5: Contours of the time-averaged azimuthal velocity $\boldsymbol{\hat{\phi}}\cdot\boldsymbol{\mathop{\overline{U}}\nolimits}$ of turbulent flows via simulation. The top panels represent the numerical results in the slightly deformed figure with $q_{\text{rot}}=0.015$, while the bottom panels describe the numerical results in the heavily deformed figure with $q_{\text{rot}}=0.051$. The unit of velocity is $R\Omega$, with $R$ and $\Omega$ being the spherical radius and strength of angular velocity of rotation, respectively. The Rayleigh number is fixed at $\hbox{Ra}=10\hbox{Ra}_c$, respetively, in these numerical results. Other physical parameters are referred to Table \ref{['table1.tab']}. The panels (a) and (d) are sliced in the $xOy$ plane, (b) and (e) in the $xOz$ plane, and (c) and (f) in the $yOz$ plane.