Alfvén-wave-driven Magnetic Rotator Winds from Low-mass Stars. I. Rotation Dependences of Magnetic Braking and Mass-loss Rate

Observations of stellar rotation show that low-mass stars lose angular momentum during the main sequence. We simulate the winds of sunlike 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 ${B}_{* }{f}_{* }^{\mathrm{open}}\propto {\mathrm{Ro}}^{-1.2}$ , where ${f}_{* }^{\mathrm{open}}$ and 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 ${\tau }_{{\rm{w}}}\approx 2.59\times {10}^{30}\ \mathrm{erg}\ {\left({{\rm{\Omega }}}_{* }/{{\rm{\Omega }}}_{\odot }\right)}^{2.82}$ , yielding a spin-down law ${{\rm{\Omega }}}_{* }\propto {t}^{-0.55}$ . (2) The mass-loss rate saturates at ${\dot{M}}_{{\rm{w}}}\sim 3.4\times {10}^{-14}{M}_{\odot }\ {\mathrm{yr}}^{-1}$ , 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 ${P}_{{\rm{w}}}\propto {{\rm{\Omega }}}_{* }^{0.57}$ , 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 one-dimensional 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.