Alfvén-wave driven magnetic rotator winds from low-mass stars I: rotation dependences of magnetic braking and mass-loss rate

Abstract

Observations of stellar rotation show that low-mass stars lose angular momentum during the main sequence. We simulate the winds of Sun-like stars with a range of rotation rates, covering the fast and slow magneto-rotator regimes, including the transition between the two. We generalize an Alfvén-wave driven solar wind model that builds on previous works by including the magneto-centrifugal force explicitly. In this model, the surface-averaged open magnetic flux is assumed to scale as $B_{\ast }{f}_{\ast }^{\mathrm{open}}\propto {\mathrm{Ro}}^{-1.2}$, where $f_{\ast }^{\mathrm{open}}$ and $\mathrm{Ro}$ are the surface open-flux filling factor and Rossby number, respectively. We find that, 1. the angular momentum loss rate (torque) of the wind is described as $\ddot{I}{„}_w\approx 2.59\times 10^{30}\mathrm{erg}{\left(\hat{I}{\text{c◯}}_{\ast }/\hat{I}{\text{c◯}}_{\odot }\right)}^{2.82}$, yielding a spin-down law $\hat{I}{\text{c◯}}_{\ast }\propto t^{-0.55}$. 2. the mass-loss rate saturates at ${\dot{M}}_w\sim 3.4\times 10^{-14}{M}_{\odot }\mathrm{y}{\mathrm{r}}^{-1}$, due to the strong reflection and dissipation of Alfvén waves in the chromosphere. This indicates that the chromosphere has a strong impact in connecting the stellar surface and stellar wind. Meanwhile, the wind ram pressure scales as $P_w\propto \hat{I}{\text{c◯}}_{\ast }^{0.57}$, which is able to explain the lower-envelope of the observed stellar winds by Wood et al. 3. the location of the Alfvén radius is shown to scale in a way that is consistent with 1D analytic theory. Additionally, the precise scaling of the Alfvén radius matches previous works which used thermally-driven winds. Our results suggest that the Alfvén-wave driven magnetic rotator wind plays a dominant role in the stellar spin-down during the main-sequence.

accepted for publication in The Astrophysical Journal