# On differential rotation and overshooting in solar-like stars

## TL;DR

This study uses numerical simulations to explore how changes in rotation rate affect the dynamics, differential rotation states, and overshooting in the convective envelopes of solar-like stars across spectral types, revealing multiple rotation regimes.

## Contribution

It introduces a comprehensive analysis of differential rotation states and overshooting in stars with varying rotation rates, using 3D simulations and scaling laws to map stellar behavior.

## Key findings

- Identification of three main rotation states: anti-solar, solar-like, and cylindrical.
- Discovery of a transition to Jupiter-like rotation profiles under strict rotational constraints.
- Proposal of a Rossby number threshold for the existence of anti-solar differential rotation.

## Abstract

We seek to characterize how the change of global rotation rate influences the overall dynamics and large scale flows arising in the convective envelopes of stars covering stellar spectral types from early G to late K. We do so through numerical simulations with the ASH code, where we consider stellar convective envelopes coupled to a radiative interior with various global properties. As solar-like stars spin down over the course of their main sequence evolution, such change must have a direct impact on their dynamics and rotation state. We indeed find that three main states of rotation may exist for a given star: anti-solar-like (fast poles, slow equator), solar-like (fast equator, slow poles), or a cylindrical rotation profile. Under increasingly strict rotational constraints, the latter profile can further evolve into a Jupiter-like profile, with alternating prograde and retrograde zonal jets. We have further assessed how far the convection and meridional flows overshoot into the radiative zone and investigated the morphology of the established tachocline. Using simple mixing length arguments, we are able to construct a scaling of the fluid Rossby number $R_{of} = \tilde{\omega}/2\Omega_* \sim \tilde{v}/2\Omega_* R_*$, which we calibrate based on our 3-D ASH simulations. We can use this scaling to map the behavior of differential rotation versus the global parameters of stellar mass and rotation rate. Finally, we isolate a region on this map ($R_{of} \gtrsim 1.5-2$) where we posit that stars with an anti-solar differential rotation may exist in order to encourage observers to hunt for such targets.