# Accounting for Differential Rotation in Calculations of the Sun's Angular Momentum-loss Rate

## TL;DR

This study investigates how surface differential rotation affects the Sun's angular momentum-loss rate, finding a small variation (~10-15%) during solar cycles, with potential larger effects in faster-rotating stars.

## Contribution

It quantifies the influence of surface differential rotation on the Sun's wind-braking torque using magnetic field models, a factor previously largely unexplored.

## Key findings

- Differential rotation causes a 10-15% decrease in torque during solar minimum.
- Torque varies by a few percent between solar minimum and maximum.
- Differential rotation may be more significant in faster-rotating Sun-like stars.

## Abstract

Sun-like stars shed angular momentum due to the presence of magnetised stellar winds. Magnetohydrodynamic models have been successful in exploring the dependence of this "wind-braking torque" on various stellar properties, however the influence of surface differential rotation is largely unexplored. As the wind-braking torque depends on the rotation rate of the escaping wind, the inclusion of differential rotation should effectively modulate the angular momentum-loss rate based on the latitudinal variation of wind source regions. In order to quantify the influence of surface differential rotation on the angular momentum-loss rate of the Sun, we exploit the dependence of the wind-braking torque on the effective rotation rate of the coronal magnetic field. This quantity is evaluated by tracing field lines through a Potential Field Source Surface (PFSS) model, driven by ADAPT-GONG magnetograms. The surface rotation rates of the open magnetic field lines are then used to construct an open-flux weighted rotation rate, from which the influence on the wind-braking torque can be estimated. During solar minima, the rotation rate of the corona decreases with respect to the typical solid-body rate (the Carrington rotation period is 25.4 days), as the sources of the solar wind shift towards the slowly-rotating poles. With increasing activity, more solar wind emerges from the Sun's active latitudes which enforces a Carrington-like rotation. The effect of differential rotation on the Sun's current wind-braking torque is found to be small. The wind-braking torque is ~10-15% lower during solar minimum, than assuming solid body rotation, and a few percent larger during solar maximum. For more rapidly-rotating Sun-like stars, differential rotation may play a more significant role, depending on the configuration of the large-scale magnetic field.