Proto-neutron star winds with magnetic fields and rotation

We solve the one-dimensional neutrino-heated nonrelativistic magnetohydrodynamic (MHD) wind problem for conditions that range from slowly rotating (spin period P ≳ 10 ms) proto-neutron stars (PNSs) with field strengths typical of radio pulsars (B ≲ 10¹³ G) to "protomagnetars" with B ≈ 10¹⁴-10¹⁵ G in their hypothesized rapidly rotating initial states (P ≈ 1 ms). We use the relativistic axisymmetric simulations of Bucciantini and coworkers to map our split-monopole results onto a more physical dipole geometry and to estimate the spin-down of PNSs when their winds are relativistic. We then quantify the effects of rotation and magnetic fields on the mass loss, energy loss, and r-process nucleosynthesis in PNS winds. We describe the evolution of PNS winds through the Kelvin-Helmholtz cooling epoch, emphasizing the transition between (1) thermal neutrino-driven, (2) nonrelativistic magnetically dominated, and (3) relativistic magnetically dominated outflows. In the latter, spin-down is enhanced relative to the canonical force-free rate because of additional open magnetic flux caused by neutrino-driven mass loss. We find that protomagnetars with P ≈ 1 ms and B ≳ 10¹⁵ G drive 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 energy of the SN remnant, its morphology, and potentially its nucleosynthesis. We show that winds from protomagnetars with P ≈ 2-10 ms produce conditions more favorable for the r-process than winds from slowly rotating, nonmagnetized PNSs; in addition, energy and momentum deposition by convectively excited waves further increase the likelihood of a successful r-process.