Conservative Moment Equations for Neutrino Radiation Transport with Limited Relativity

We derive conservative, multidimensional, energy-dependent moment equations for neutrino transport in core-collapse supernovae and related astrophysical systems, with particular attention to the consistency of conservative four-momentum and lepton number transport equations. After taking angular moments of conservative formulations of the general relativistic Boltzmann equation, we specialize to a conformally flat spacetime, which also serves as the basis for four further limits. Two of these---the multidimensional special relativistic case, and a conformally flat formulation of the spherically symmetric general relativistic case---are given in appendices for the sake of comparison with extant literature. The third limit is a weak-field, `pseudo-Newtonian approach citep{kim_etal_2009,kim_etal_2012} in which the source of the gravitational potential includes the trace of the stress-energy tensor (rather than just the mass density), and all orders in fluid velocity $v$ are retained. Our primary interest here is in the fourth limit: `$mathcal{O}(v)$ moment equations for use in conjunction with Newtonian self-gravitating hydrodynamics. We show that the concept of `$mathcal{O}(v)$ transport requires care when dealing with both conservative four-momentum and conservative lepton number transport, and present two self-consistent options: `$mathcal{O}(v)$-plus transport, in which an $mathcal{O}(v^2)$ energy equation combines with an $mathcal{O}(v)$ momentum equation to give an $mathcal{O}(v^2)$ number equation; and `$mathcal{O}(v)$-minus transport, in which an $mathcal{O}(v)$ energy equation combines with an $mathcal{O}(1)$ momentum equation to give an $mathcal{O}(v)$ number equation.

Generation of Magnetic Fields by the Stationary Accretion Shock Instability

We begin an exploration of the capacity of the stationary accretion shock instability (SASI) to generate magnetic fields by adding a weak, stationary, and radial (but bipolar) magnetic field, and in some cases rotation, to an initially spherically symmetric fluid configuration that models a stalled shock in the post-bounce supernova environment. In axisymmetric simulations we find that cycles of latitudinal flows into and radial flows out of the polar regions amplify the field parallel to the symmetry axis, typically increasing the total magnetic energy by about two orders of magnitude. Nonaxisymmetric calculations result in fundamentally different flows and a larger magnetic energy increase: shearing associated with the SASI spiral mode contributes to a widespread and turbulent field amplification mechanism, boosting the magnetic energy by almost four orders of magnitude (a result which remains very sensitive to the spatial resolution of the numerical simulations). While the SASI may contribute to neutron star magnetization, these simulations do not show qualitatively new features in the global evolution of the shock as a result of SASI-induced magnetic field amplification.