Exploring hydrodynamical stellar tachoclines along stellar evolution

TL;DR

The paper addresses how hydrodynamical tachoclines respond to evolving latitudinal differential rotation in solar-type stars. It applies the MathisZahn2004 formalism in a thin-layer approximation to couple tachocline dynamics with a 1 solar-mass evolutionary model across cylindrical, conical solar-like, and conical anti-solar-like envelope rotation histories. Key findings show that the tachocline extension and top forcing are governed by $\alpha=(\Omega_{bar}/N)^{1/2}(\kappa_v/\nu_h)^{1/4}$ and $\Delta_Omega$, with thick, highly mixed tachoclines in early MS and increasingly confined, less-mixed tachoclines later. The work suggests overshoot-dominated mixing may prevail in the confined tachocline, reshaping estimates of transport and offering a self-consistent method to study evolution-driven tachocline dynamics.

Abstract

Stellar tachoclines are thin regions located between the radiative core and the convective envelope of solar-type stars. They are defined as layers where the rotation of the radiative interior transitions to the differential rotation of the convective envelope, generating strong shear and turbulence. As such, understanding the dynamics of the transport and mixing inside stellar tachoclines would shed light on how the dynamical processes of the convection zone might affect the secular transport of the radiative zone. In particular, we investigate how the change of the latitudinal differential rotation in the convection zone with stellar evolution would affect the dynamics of the tachocline. Indeed, as solar-type stars are braked on the Main Sequence, the differential rotation in the convection zone is expected to evolve from a cylindrical rapidly-rotating regime (columns of varying velocities, aligned with the rotation axis) to a conical solar-like regime (with an equatorial acceleration as in the case of the Sun) and finally to a conical anti-solar-like regime (with a polar acceleration). However, stellar evolutionary codes currently only consider at best the solar conical regime to study the dynamics of stellar tachoclines throughout the evolution of stars. We discuss different possibilities to model hydrodynamical tachoclines and we show that Mathis Zahn 2004's formalism is able to treat coherently hydrodynamical stellar tachoclines when taken in the thin layer approximation. We use it to model the differential rotation, meridional circulation, and mixing coefficients inside the tachocline in order to examine the effect of the different rotation regimes on the transport.

Figures (3)

• Figure 1: Illustration of the temporal evolution of the mean surface rotation $\Omega$ of solar-type stars, normalised to that of the Sun $\Omega_{\odot}$. $\Omega_{i}$ is the rotation of the initial proto-star. After the "Zero Age Main Sequence" (ZAMS), the differential rotation in the convective envelope evolves from cylindrical to conical solar-like and conical anti solar-like, at values of the Rossby fluid number $\textrm{Ro}_{\textrm{f}}$ normalized by the solar value $\textrm{Ro}_{\textrm{f},{\odot}}$ around $0.15$ and $1$ respectively Brunetal2022Norazetal2024.
• Figure 2: Differential rotation in the tachocline $\Omega_2Q_2$ as a function of the colatitude $\theta$ and of the distance to the base of the convective layer (located at $(r_{cz}-r)/R_{\odot}=0)$, computed using the prescription of Mathisetal2004 for the turbulent horizontal eddy-viscosity. Left:$t=1.0\times10^{8}$ years associated with a cylindrical forcing from the convective zone. Middle:$t=1.0\times10^{9}$ years and a conical solar-like forcing. Right:$t=6.7\times10^{9}$ years and a conical anti-solar-like forcing.
• Figure 3: Effective turbulent diffusion coefficient $D_{\textrm{eff}}$ as a function of the distance to the base of the convection zone $((r_{cz}-r)/R_{\odot}=0)$ for the three times considered in figure \ref{['fig_rot_diff']}.