The rotational evolution of accreting pre-main-sequence stars is influenced by its magnetic interaction with its surrounding circumstellar disk. Using the PLUTO code, we perform 2.5D magnetohydrodynamic, axisymmetric, time-dependent simulations of star-disk interaction-with an initial dipolar magnetic field structure, and a viscous and resistive accretion disk-in order to model the three mechanisms that contribute to the net stellar torque: accretion flow, stellar wind, and magnetospheric ejections (periodic inflation and reconnection events). We investigate how changes in the stellar magnetic field strength, rotation rate, and mass accretion rate (changing the initial disk density) affect the net stellar torque. All simulations are in a net spin-up regime. We fit semi-analytic functions for the three stellar torque contributions, allowing for the prediction of the net stellar torque for our parameter regime, and the possibility of investigating spin-evolution using 1D stellar evolution codes. The presence of an accretion disk appears to increase the efficiency of stellar torques compared to isolated stars, for cases with outflow rates much smaller than accretion rates, because the star-disk interaction opens more of the stellar magnetic flux compared to that from isolated stars. In our parameter regime, a stellar wind with a mass loss rate of ≈ 1% of the mass accretion rate is capable of extracting 50% of the accreting angular momentum. These simulations suggest that achieving spin-equilibrium in a representative T Tauri case within our parameter regime, e.g., BP Tau, would require a wind mass loss rate of ≈ 25% of the mass accretion rate.

Some low-mass stars appear to have larger radii than predicted by standard 1D structure models; prior work has suggested that inefficient convective heat transport, due to rotation and/or magnetism, may ultimately be responsible. We examine this issue using 1D stellar models constructed using Modules for Experiments in Stellar Astrophysics (MESA). First, we consider standard models that do not explicitly include rotational/magnetic effects, with convective inhibition modeled by decreasing a depth-independent mixing length theory (MLT) parameter α MLT (following Cox et al. 1981;Chabrier et al. 2007). We provide formulae linking changes in α MLT to changes in the interior specific entropy, and hence to the stellar radius. Next, we modify the MLT formulation in MESA to mimic explicitly the influence of rotation and magnetism, using formulations suggested by Stevenson (1979) and MacDonald & Mullan (2014) respectively. We find rapid rotation in these models has a negligible impact on stellar structure, primarily because a star's adiabat, and hence its radius, is predominantly affected by layers near the surface; convection is rapid and largely uninfluenced by rotation there. Magnetic fields, if they influenced convective transport in the manner described by MacDonald & Mullan (2014), could lead to more noticeable radius inflation. Finally, we show that these non-standard effects on stellar structure can be fabricated using a depth-dependent α MLT : a non-magnetic, non-rotating model can be produced that is virtually indistinguishable from one that explicitly parameterizes rotation and/or magnetism using the two formulations above. We provide formulae linking the radially-variable α MLT to these putative MLT reformulations.

The magnetic interaction between a classical T Tauri star and its surrounding accretion disk is thought to influence its rotational evolution. We use 2.5D magnetohydrodynamic, axisymmetric simulations of star-disk interaction, computed via the PLUTO code, to calculate the net torque acting on these stars. We divide the net torque into three contributions: accretion (spin-up), stellar winds (spin-down), and magnetospheric ejections (MEs) (spin-up or down). In Paper I, we explored interaction regimes in which the stellar magnetosphere truncates the inner disk at a location spinning faster than the star, resulting in a strong net spin-up contribution from accretion and MEs (“steady accretion” regime). In this paper, we investigate interaction regimes in which the truncation radius gets closer to and even exceeds corotation, where it is possible for the disk material to gain angular momentum and be periodically ejected by the centrifugal barrier (“propeller” regime). This reduces the accretion torque, can change the sign of the ME torque, and can result in a net stellar spin-down configuration. These results suggest it is possible to have a net spin-down stellar torque even for truncation radii within the corotation radius (R t ≳ 0.7R co). We fit semi-analytic functions for the truncation radius, and the torque associated with star-disk interaction (i.e., the sum of accretion and ME torques) and stellar wind, allowing for the prediction of the net stellar torque for a parameter regime covering both net spin-up and spin-down configurations, as well as the possibility of investigating rotational evolution via 1D stellar evolution codes.

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).

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