Axisymmetric investigation of differential rotation in contracting stellar radiative zones

Abstract

Context. Stars experience rapid contraction or expansion at different phases of their evolution. Modelling the angular momentum and chemical elements transport occurring during these phases remains an unsolved problem. Aims. We study a stellar radiative zone undergoing radial contraction and investigate the induced differential rotation and meridional circulation. Methods. We consider a rotating spherical layer crossed by an imposed radial velocity field that mimics the contraction and solve numerically the axisymmetric hydrodynamical equations in both the Boussinesq and anelastic approximations. An extensive parametric study is conducted to cover regimes of contraction, rotation, stable stratification and density stratification that are relevant for stars. Results. The differential rotation and the meridional circulation result from a competition between the contraction-driven inward transport of angular momentum and an outward transport dominated by either viscosity or an Eddington-Sweet type circulation, depending on the value of the $P_r{\left(N_0/{\Omega }_0\right)}^2$ parameter, where $P_r$ is the Prandtl number, $N_0$ the Brunt-Väisäilä frequency and ${\Omega }_0$ the rotation rate. Taking the density stratification into account is important to study more realistic radial contraction fields but also because the resulting flow is less affected by unwanted effects of the boundary conditions. In these different regimes and for a weak differential rotation, we derive scaling laws that relate the amplitude of the differential rotation to the contraction timescale.

arXiv comment24 pages, 16 figures, 8 tables

References in corpus (32)

• Dynamo action by differential rotation in a stably stratified stellar interior
• Fast core rotation in red-giant stars revealed by gravity-dominated mixed modes
• Stellar evolution with rotation VII: Low metallicity models and the blue to red supergiant ratio in the SMC
• Seismic evidence for a rapidly rotating core in a lower-giant-branch star observed with Kepler
• Influence of gravity waves on the internal rotation and Li abundance of solar-type stars
• Improved angular momentum evolution model for solar-like stars
• Slowing the Spins of Stellar Cores
• Seismic constraints on the radial dependence of the internal rotation profiles of six Kepler subgiants and young red giants
• Seismic diagnostics for transport of angular momentum in stars 1. Rotational splittings from the PMS to the RGB
• Angular Momentum Transport in Stellar Interiors
• A high-resolution spectropolarimetric survey of Herbig Ae/Be stars - I. Observations and measurements
• Hydrodynamical stellar models including rotation, internal gravity waves and atomic diffusion. I. Formalism and tests on Pop I dwarfs
• Angular momentum transport in stellar interiors constrained by rotational splittings of mixed modes in red giants
• Effects of compressibility on driving zonal flow in gas giants
• Angular momentum extraction by gravity waves in the Sun
• Understanding angular momentum transport in red giants: the case of KIC 7341231
• Self-consistent 2D models of fast rotating early-type star
• Discovery of the pre-main sequence progenitors of the magnetic Ap/Bp stars?
• Energy Conservation and Gravity Waves in Sound-proof Treatments of Stellar Interiors: Part I Anelastic Approximations
• Asteroseismology of evolved stars to constrain the internal transport of angular momentum II. Test of a revised prescription for transport by the Tayler instability
• Can plume-induced internal gravity waves regulate the core rotation of subgiant stars?
• The dynamics of the radiative envelope of rapidly rotating stars. I. A spherical Boussinesq model
• A high-resolution spectropolarimetric survey of Herbig Ae/Be stars - II. Rotation
• The angular momentum transport by unstable toroidal magnetic fields
• Excitation of gravity waves by fingering convection, and the formation of compositional staircases in stellar interiors
• Asteroseismology of evolved stars to constrain the internal transport of angular momentum. III. Using the rotation rates of intermediate-mass stars to test the Fuller-formalism
• Penetrative Convection in Partly Stratified Rapidly Rotating Spherical Shells
• Interplay between magnetic fields and differential rotation in a stably stratified stellar radiative zone
• Evolution of a magnetic field in a differentially rotating radiative zone
• The dichotomy between strong and ultra-weak magnetic fields among intermediate-mass stars
• Dynamics of the radiative envelope of rapidly rotating stars: Effects of spin-down driven by mass loss
• Dynamics of the envelope of a rapidly rotating star or giant planet in gravitational contraction

Cited by in corpus (1)

• MRI-driven $\alpha -\Omega$ dynamos in protoneutron stars