Effect of Differential Rotation on the Magnetic Braking of Low-mass and Solar-like Stars: A Proof-of-concept Study

Abstract

On the main sequence, low-mass and solar-like stars are observed to spin down over time, and magnetized stellar winds are thought to be predominantly responsible for this significant angular momentum loss. Previous studies have demonstrated that the wind torque can be predicted via formulations dependent on stellar properties, such as magnetic field strength and geometry, stellar radius and mass, wind mass-loss rate, and stellar rotation rate. Although these stars are observed to experience surface differential rotation, torque formulations so far have assumed solid-body rotation. Surface differential rotation is expected to affect the rotation of the wind and thus the angular momentum loss. To investigate how differential rotation affects the torque, we use the PLUTO code to perform 2.5D magnetohydrodynamic, axisymmetric simulations of stellar winds, using a colatitude-dependent surface differential rotation profile that is solar-like (i.e., rotation is slower at the poles than the equator). We demonstrate that the torque is determined by the average rotation rate in the wind so that the net torque is less than that predicted by assuming solid-body rotation at the equatorial rate. The magnitude of the effect is essentially proportional to the magnitude of the surface differential rotation, for example, resulting in a torque for the Sun that is ∼20% smaller than predicted by the solid-body assumption. We derive and fit a semianalytic formulation that predicts the torque as a function of the equatorial spin rate, magnitude of differential rotation, and wind magnetization (depending on the dipolar magnetic field strength and mass-loss rate, combined).

COCONUT, a Novel Fast-converging MHD Model for Solar Corona Simulations: I. Benchmarking and Optimization of Polytropic Solutions

“…However, we recall that we use here the polytropic approximation for this first version of the model, which means that we do not reproduce accurately the heating of the corona, and hence a number of structures that are typically used for validation such as bimodal distribution of solar wind velocity or EUV coronal hole dimming. We however would like to suggest broad validation metrics that can be used for polytropic wind models, which are usually the first step for coronal models, and are still largely used for solar wind comparisons (Karageorgopoulos et al 2021) and by the stellar community (Ireland et al 2022). For this reason, we will focus mostly on magnetic field quantities, as they are the ones best described by our MHD model for the moment.…”

Accounting for differential rotation in calculations of the Sun’s angular momentum-loss rate

“…In the recent work of Ireland et al (2022), the value of Ω e f f was allowed to vary in latitude in order to model the influence of differential rotation on the wind-braking torques from their 2.5D stellar wind models (see also Pinto et al 2021). This has the effect of anchoring the field lines at different latitudes to different rotation rates.…”

“…The technique described here could also be used to correct the wind-braking torques from MHD wind simulations performed Article number, page 4 of 16 with solid-body rotation. The form of Ω wind is motivated by insights from the scaling of the wind-braking torque in Ireland et al (2022). It is left for future work to truly validate this relation.…”

“…Finley & Matt 2018;Hazra et al 2021;Ireland et al 2022). In the slowly rotating regime, where centrifugal ef-Article number, page 7 of 16…”

Magnetic Braking with MESA Evolutionary Models in the Single Star and Low-mass X-Ray Binary Regimes

“…It may seem obvious that a phenomenon involving such interrelated physical processes should vary by stellar class, but understanding why and how has remained elusive for low-mass stars. Models have explored the ideas of a "saturated" braking state (MacGregor & Brenner 1991;Chaboyer et al 1995;Sills et al 2000;Spada et al 2011;Gallet & Bouvier 2013van Saders & Pinsonneault 2013;Matt et al 2015), core-envelope coupling (Bouvier 2008;Irwin & Bouvier 2009;Denissenkov et al 2010;Spada et al 2011;Lanzafame & Spada 2015;Spada & Lanzafame 2020), and recent explorations of magnetic field geometry (Garraffo et al 2015(Garraffo et al , 2018bGarraffo & Drake 2016;Réville et al 2015;Finley et al 2019;See et al 2019aSee et al , 2020 and differential rotation (Ireland et al 2022).…”