The optically thick rotating magnetic wind from a massive white dwarf merger product -- II. axisymmetric magnetohydrodynamic simulations

We numerically construct a series of axisymmetric rotating magnetic wind solutions, aiming at exploring the observation properties of massive white dwarf (WD) merger remnants with a strong magnetic field, a fast spin, and an intense mass loss, as inferred for WD J005311. We investigate the magnetospheric structure and the resultant spin-down torque exerted to the merger remnant with respect to the surface magnetic flux $\Phi_*$, spin angular frequency $\Omega_*$ and the mass loss rate $\dot M$. We confirm that the wind properties for $\sigma \equiv \Phi^2_* \Omega_*^2/\dot M v_\mathrm{esc}^3 \gtrsim 1$ significantly deviate from those of the spherical Parker wind, where $v_\mathrm{esc}$ is the escape velocity at stellar surface. For such a rotating magnetic wind sequence, we find: (i) quasi-periodic mass eruption triggered by magnetic reconnection along with the equatorial plane (ii) a scaling relation for the spin-down torque $T \approx (1/2) \times \dot{M} \Omega_* R^2_* \sigma^{1/4}$. We apply our results to discuss the spin-down evolution and wind anisotropy of massive WD merger remnants, the latter of which could be probed by a successive observation of WD J005311 using Chandra.