Proto-neutron Star Winds with Magnetic Fields and Rotation

We solve the one-dimensional neutrino-heated non-relativistic magnetohydrodynamic (MHD) wind problem for conditions that range from slowly rotating (spin period P & 10 ms) protoneutron stars (PNSs) with surface field strengths typical of radio pulsars (B . 1013 G), to "proto-magnetars" with B ≈ 1014 − 1015 G in their hypothesized rapidly rotating initial states (P ≈ 1 ms). We use the relativistic axisymmetric simulations of Bucciantini et al. (2006) to map our split-monopole results onto a more physical dipole geometry and to estimate the spindown of PNSs when their winds are relativistic. We then quantify the effects of rotation and magnetic fields on the mass loss, energy loss, and thermodynamic structure of PNS winds. The latter is particularly important in assessing PNS winds as the astrophysical site for the r-process. We describe the evolution of PNS winds through the Kelvin-Helmholtz cooling epoch, emphasizing the transition between (1) thermal neutrino-driven, (2) non-relativistic magnetically-dominated, and (3) relativistic magnetically-dominated outflows. In the last of these stages, the spindown is enhanced relative to the canonical force-free rate because of additional open magnetic flux caused by neutrino-driven mass loss. We find that proto-magnetars with P ≈ 1 ms and B & 1015 G drive relativistic winds with luminosities, energies, and Lorentz factors (magnetization σ ∼ 0.1 − 1000) consistent with those required to produce long duration gamma-ray bursts and hyper-energetic supernovae (SNe). A significant fraction of the rotational energy may be extracted in only a few seconds, sufficiently rapidly to alter the asymptotic energy of the SN remnant, its morphology, and, potentially, its nucleosynthetic yield. We find that winds from PNSs with somewhat more modest rotation periods (≈ 2 − 10 ms) and with magnetar-strength fields produce conditions significantly more favorable for the r-process than winds from slowly rotating, non-magnetized PNSs. Lastly, we argue that energy and momentum deposition by convectively-excited waves may be important in PNS winds. We show that this further increases the likelihood of successful r-process, relatively independent of the PNS rotation rate and magnetic field strength. Subject headings: stars: neutron — stars: winds, outflows — supernovae: general — gamma rays: bursts — stars: magnetic fields — nuclear reactions, nucleosynthesis, abundances