Radial differential rotation leading to dipole collapse in pre-main-sequence stars

TL;DR

This paper demonstrates that radial differential rotation developed during the pre-main-sequence phase can destabilize inherited dipolar magnetic fields in low-mass stars. Using 3D anelastic DNS with imposed shear in convective spherical shells, anchored to PMS structure profiles from Cesam2k20, the authors show that dipole collapse to weaker, oscillatory states occurs when the shear-to-convection ratio $Ro_{sh}/Ro_{conv}^{\ell}$ crosses a threshold that depends on the radiative-core size and magnetic diffusivity. A practical criterion is derived to connect 3D DNS results to 1D stellar evolution models, enabling predictions of dipole survival or collapse along PMS evolution and linking magnetic topology to angular-momentum transport. The findings suggest that the observed diversity of magnetism on the main sequence may reflect the history of PMS angular momentum redistribution and differential rotation, with implications for magnetospheric processes and planet formation.

Abstract

Despite progress in the observations of stellar magnetic fields, their physical mechanisms remain poorly understood. During the pre-main sequence (PMS) phase, the inner layers of stars contract and a radiative core gradually develops. In contrast, the convective envelope is gradually braked through magnetic interactions with the accretion disk and winds. With developing differential rotation inside the star, PMS phase is thus a critical period for magnetic properties of stars when strong initial dipoles can get perturbed, leading to the observed diversity in the magnetism on the main sequence (MS). In this work, we study the impact of differential rotation on such fields. We perform three-dimensional anelastic convective dynamo simulations of rotating spherical shells with an imposed differential rotation (shear) between the boundaries. Density, gravity profiles and convective zone thicknesses were set close to those predicted in PMS low-mass stars by one-dimensional stellar evolution code Cesam2k20. Our results show that radial differential rotation can induce dipole collapse leading to weaker, oscillatory magnetic fields. Differential rotation seems to perturb $α^2$ dynamo mechanism, responsible for dipolar magnetic fields, by shearing poloidal field lines and by affecting turbulent magnetic transport processes. This collapse is moderated by the relative importance of shear compared to the vigor of convective motions, with exact stability criterion depending on the field strength and the size of the radiative core. Applying DNS-based stability criterion in PMS stellar evolution models, we qualitatively reproduce the trends observed in the magnetic topologies of low-mass stars when assuming an efficient internal angular momentum redistribution. This suggests that stellar magnetic properties are intimately related to the PMS angular momentum evolution.

Figures (16)

• Figure 1: Evolution of a $0.55M_\odot$ model. Top: Kippenhahn diagram. Radius of interfaces in solar unit as a function of the model's age. Convective zones (resp. radiative zones) are represented as dark (resp. light) grey areas. Middle: Aspect ratio (left axis) and density contrast (right axis). Inner radius $r_{\rm i}$ is the bottom radius of the convective envelope, while the outer radius $r_{\rm o}$ is $90\%$ of the photospheric radius. Bottom: Kelvin-Helmholtz (blue) and convection (green) timescales and surface rotation period (red). The shaded areas correspond to the classical T Tauri phase (CTTS; light green) which coincides in our case with the disc-locking phase, and weak T Tauri phase (WTTS; green).
• Figure 2: Normalized gravitational acceleration $g/g_{\rm max}$ (top panel) and normalized angular velocity $\Omega/\Omega_{\rm surf}$ (bottom panel) as a function of the radius. These profiles are shown at the beginning (blue), middle (orange) and end (green) of the WTTS phase. Same model as in Fig. \ref{['fig:kippenhahn']}.
• Figure 3: (a) Normalized gravity profiles from stellar evolution code Cesam2k20 for a star of $0.8 M_\odot$ at an early stage of stellar evolution ($1$ Myr, in light gray) and at the MS ($4.9 \cdot 10^3$ Myrs, dark gray). Example of imposed gravity profiles in DNS: $g\propto 1/r^2$ for radii ratio $\xi = 0.35$ (in red), $g\propto r$ and $\xi = 0.2$ (in dashed light blue) and a typical profile from Cesam2k20 with $\xi=0.35$ (in magenta, see Eq. \ref{['eq:g_r_cesam']} for detail). (b) Local convective Rossby number, normalized with its maximum, as a function of $r/r_{\rm o}$ for the runs gr2_2, gr_1, gc_2, associated with the gravity profiles of panel (a) (same color code), and for the run gr2_3with $g \propto 1/r^2$ and $\xi = 0.2$ (in dashed red). See details of the runs in Table \ref{['tab:sim_param']}. (c) Equatorial cut of instantaneous radial velocity for $g\propto 1/r^2$, $\xi = 0.35$ (run gr2_2). (d) Same for $g\propto r$, $\xi =0.2$ (run gr_1) (e) Same for $g \propto 1/r^2$, $\xi = 0.2$ (run gr2_3). Velocities in panels (c-e) were normalized with $\nu/(r_o - r_i)$, i.e. kinematic viscosity $\nu$ and the thickness of convective zone.
• Figure 4: Local convective Rossby number as a function of normalized radius $r/r_{\rm o}$ for typical values of $\operatorname{{R o}}_{\rm sh}$ considered in this work. The gravity profile is taken from Cesam2k20, approximated by Eq. \ref{['eq:g_r_cesam']}. See run gc_1 in Table \ref{['tab:sim_param']} for more details on the parameters.
• Figure 5: Butterfly diagrams of the axisymmetric radial magnetic field component, $\langle B_r \rangle_\phi$, together with the dipolarity. $\Omega_s t$ corresponds to the rotation time, and follows the uniform rotation of a meridional plane. (a) Stable dipole for $g\propto 1/r^2$, $\operatorname{{R a}}=5\times10^6$, $\xi = 0.35$, $\operatorname{{R o}}_{\rm sh} =0.005$. (b) Equatorially propagating dipolar waves for the same parameters, except for $\operatorname{{R o}}_{\rm sh} =0.02$. (c) Aperiodic dynamos for $g\propto 1/r^2$, $\operatorname{{R a}}=5\times10^5$, $\xi = 0.1$, $\operatorname{{R o}}_{\rm sh} = 0.015$. (d) Steady quadrupolar dynamos for $g\propto r$, $\operatorname{{R a}}=1.6\times10^7$, $\xi = 0.2$, $\operatorname{{R o}}_{\rm sh} = 0.3$. Magnetic field was normalized with $(\rho_o \mu_0 \lambda_i \Omega_s^{1/2})$, where $\rho_o$ is the density at the outer boundary, $\lambda_i$ is magnetic diffusivity at the inner boundary, and $\mu_0$ is the free space permeability.