The First X-Ray Proper-Motion Measurements of the Forward Shock in the Northeastern Limb of SN 1006

We report on the first X-ray proper-motion measurements of the nonthermally-dominated forward shock in the northeastern limb of SN 1006, based on two Chandra observations taken in 2000 and 2008. We find that the proper motion of the forward shock is about 0.48 arcsec/yr and does not vary around the rim within the ~10% measurement uncertainties. The proper motion measured is consistent with that determined by the previous radio observations. The mean expansion index of the forward shock is calculated to be ~0.54 which matches the value expected based on an evolutionary model of a Type Ia supernova with either a power-law or an exponential ejecta density profile. Assuming pressure equilibrium around the periphery from the thermally-dominated northwestern rim to the nonthermally-dominated northeastern rim, we estimate the ambient density to the northeast of SN 1006 to be about 0.085/cm^3.Comment: Accepted for publication in The Astrophysical Journal Letter

Fully-Coupled Simulation of Cosmic Reionization. I: Numerical Methods and Tests

We describe an extension of the Enzo code to enable fully-coupled radiation hydrodynamical simulation of inhomogeneous reionization in large $\sim (100 Mpc)^3$ cosmological volumes with thousands to millions of point sources. We solve all dynamical, radiative transfer, thermal, and ionization processes self-consistently on the same mesh, as opposed to a postprocessing approach which coarse-grains the radiative transfer. We do, however, employ a simple subgrid model for star formation which we calibrate to observations. Radiation transport is done in the grey flux-limited diffusion (FLD) approximation, which is solved by implicit time integration split off from the gas energy and ionization equations, which are solved separately. This results in a faster and more robust scheme for cosmological applications compared to the earlier method. The FLD equation is solved using the hypre optimally scalable geometric multigrid solver from LLNL. By treating the ionizing radiation as a grid field as opposed to rays, our method is scalable with respect to the number of ionizing sources, limited only by the parallel scaling properties of the radiation solver. We test the speed and accuracy of our approach on a number of standard verification and validation tests. We show by direct comparison with Enzo's adaptive ray tracing method Moray that the well-known inability of FLD to cast a shadow behind opaque clouds has a minor effect on the evolution of ionized volume and mass fractions in a reionization simulation validation test. We illustrate an application of our method to the problem of inhomogeneous reionization in a 80 Mpc comoving box resolved with $3200^3$ Eulerian grid cells and dark matter particles.Comment: 32 pages, 23 figures. ApJ Supp accepted. New title and substantial revisions re. v

Magnetic-Field Amplification in the Thin X-ray Rims of SN1006

Several young supernova remnants (SNRs), including SN1006, emit synchrotron X-rays in narrow filaments, hereafter thin rims, along their periphery. The widths of these rims imply 50 to 100 $\mu$G fields in the region immediately behind the shock, far larger than expected for the interstellar medium compressed by unmodified shocks, assuming electron radiative losses limit rim widths. However, magnetic-field damping could also produce thin rims. Here we review the literature on rim width calculations, summarizing the case for magnetic-field amplification. We extend these calculations to include an arbitrary power-law dependence of the diffusion coefficient on energy, $D \propto E^{\mu}$. Loss-limited rim widths should shrink with increasing photon energy, while magnetic-damping models predict widths almost independent of photon energy. We use these results to analyze Chandra observations of SN 1006, in particular the southwest limb. We parameterize the full widths at half maximum (FWHM) in terms of energy as FWHM $\propto E^{m_E}_{\gamma}$. Filament widths in SN1006 decrease with energy; $m_E \sim -0.3$ to $-0.8$, implying magnetic field amplification by factors of 10 to 50, above the factor of 4 expected in strong unmodified shocks. For SN 1006, the rapid shrinkage rules out magnetic damping models. It also favors short mean free paths (small diffusion coefficients) and strong dependence of $D$ on energy ($\mu \ge 1$).Comment: Accepted by ApJ, 49 pages, 10 figure