The Evolution of Adiabatic Supernova Remnants in a Turbulent, Magnetized Medium

(Abridged) We present the results of three dimensional calculations for the MHD evolution of an adiabatic supernova remnant in both a uniform and turbulent interstellar medium using the RIEMANN framework of Balsara. In the uniform case, which contains an initially uniform magnetic field, the density structure of the shell remains largely spherical, while the magnetic pressure and synchrotron emissivity are enhanced along the plane perpendicular to the field direction. This produces a bilateral or barrel-type morphology in synchrotron emission for certain viewing angles. We then consider a case with a turbulent external medium as in Balsara & Pouquet, characterized by $v_{A}(rms)/c_{s}=2$. Several important changes are found. First, despite the presence of a uniform field, the overall synchrotron emissivity becomes approximately spherically symmetric, on the whole, but is extremely patchy and time-variable, with flickering on the order of a few computational time steps. We suggest that the time and spatial variability of emission in early phase SNR evolution provides information on the turbulent medium surrounding the remnant. The shock-turbulence interaction is also shown to be a strong source of helicity-generation and, therefore, has important consequences for magnetic field generation. We compare our calculations to the Sedov-phase evolution, and discuss how the emission characteristics of SNR may provide a diagnostic on the nature of turbulence in the pre-supernova environment.Comment: ApJ, in press, 5 color figure

Direct Evidence for Two-Fluid Effects in Molecular Clouds

We present a combination of theoretical and simulation-based examinations of the role of two-fluid ambipolar drift on molecular line widths. The dissipation provided by ion-neutral interactions can produce a significant difference between the widths of neutral molecules and the widths of ionic species, comparable to the sound speed. We demonstrate that Alfven waves and certain families of magnetosonic waves become strongly damped on scales comparable to the ambipolar diffusion scale. Using the RIEMANN code, we simulate two-fluid turbulence with ionization fractions ranging from 10^{-2} to 10^{-6}. We show that the wave damping causes the power spectrum of the ion velocity to drop below that of the neutral velocity when measured on a relative basis. Following a set of motivational observations by Li & Houde (2008), we produce synthetic line width-size relations that shows a difference between the ion and neutral line widths, illustrating that two-fluid effects can have an observationally detectable role in modifying the MHD turbulence in the clouds.Comment: 18 pages, 4 figures, submitted to MNRA

Divergence-Free Adaptive Mesh Refinement for Magnetohydrodynamics

In this paper we present a full-fledged scheme for the second order accurate, divergence-free evolution of vector fields on an adaptive mesh refinement (AMR) hierarchy. We focus here on adaptive mesh MHD. The scheme is based on making a significant advance in the divergence-free reconstruction of vector fields. In that sense, it complements the earlier work of Balsara and Spicer (1999) where we discussed the divergence-free time-update of vector fields which satisfy Stoke's law type evolution equations. Our advance in divergence-free reconstruction of vector fields is such that it reduces to the total variation diminishing (TVD) property for one-dimensional evolution and yet goes beyond it in multiple dimensions. Divergence-free restriction is also discussed. An electric field correction strategy is presented for use on AMR meshes. The electric field correction strategy helps preserve the divergence-free evolution of the magnetic field even when the time steps are sub-cycled on refined meshes. The above-mentioned innovations have been implemented in Balsara's RIEMANN framework for parallel, self-adaptive computational astrophysics which supports both non-relativistic and relativistic MHD. Several rigorous, three dimensional AMR-MHD test problems with strong discontinuities have been run with the RIEMANN framework showing that the strategy works very well.Comment: J.C.P., figures of reduced qualit

A Two-Fluid Method for Ambipolar Diffusion

We present a semi-implicit method for isothermal two-fluid ion-neutral ambipolar drift that is second-order accurate in space and time. The method has been implemented in the RIEMANN code for astrophysical fluid dynamics. We present four test problems that show the method works and correctly tracks the propagation of MHD waves and the structure of two-fluid C-shocks. The accurate propagation of MHD waves in the two-fluid approximation is shown to be a stringent test of the algorithm. We demonstrate that highly accurate methods are required in order to properly capture the MHD wave behaviour in the presence of ion-neutral friction.Comment: 29 pages, 16 figures, accepted to MNRA

A Two-dimensional HLLC Riemann Solver for Conservation Laws : Application to Euler and MHD Flows

In this paper we present a genuinely two-dimensional HLLC Riemann solver. On logically rectangular meshes, it accepts four input states that come together at an edge and outputs the multi-dimensionally upwinded fluxes in both directions. This work builds on, and improves, our prior work on two-dimensional HLL Riemann solvers. The HLL Riemann solver presented here achieves its stabilization by introducing a constant state in the region of strong interaction, where four one-dimensional Riemann problems interact vigorously with one another. A robust version of the HLL Riemann solver is presented here along with a strategy for introducing sub-structure in the strongly-interacting state. Introducing sub-structure turns the two-dimensional HLL Riemann solver into a two-dimensional HLLC Riemann solver. The sub-structure that we introduce represents a contact discontinuity which can be oriented in any direction relative to the mesh. The Riemann solver presented here is general and can work with any system of conservation laws. We also present a second order accurate Godunov scheme that works in three dimensions and is entirely based on the present multidimensional HLLC Riemann solver technology. The methods presented are cost-competitive with traditional higher order Godunov schemes

The accretion and spreading of matter on white dwarfs

For a slowly rotating non-magnetized white dwarf the accretion disk extends all the way to the star. Here the matter impacts and spreads towards the poles as new matter continuously piles up behind it. We have solved the 3d compressible Navier-Stokes equations on an axisymmetric grid to determine the structure of this boundary layer for different viscosities corresponding to different accretion rates. The high viscosity cases show a spreading BL which sets off a gravity wave in the surface matter. The accretion flow moves supersonically over the cusp making it susceptible to the rapid development of gravity wave and/or Kelvin-Helmholtz instabilities. This BL is optically thick and extends more than 30 degrees to either side of the disk plane after 3/4 of a Keplerian rotation period (t=19s). The low viscosity cases also show a spreading BL, but here the accretion flow does not set off gravity waves and it is optically thin.Comment: 6 pages, 5 figures, requires autart.cl

Multidimensional HLLE Riemann solver; Application to Euler and Magnetohydrodynamic Flows

In this work we present a general strategy for constructing multidimensional Riemann solvers with a single intermediate state, with particular attention paid to detailing the two-dimensional Riemann solver. This is accomplished by introducing a constant resolved state between the states being considered, which introduces sufficient dissipation for systems of conservation laws. Closed form expressions for the resolved fluxes are also provided to facilitate numerical implementation. The Riemann solver is proved to be positively conservative for the density variable; the positivity of the pressure variable has been demonstrated for Euler flows when the divergence in the fluid velocities is suitably restricted so as to prevent the formation of cavitation in the flow. We also focus on the construction of multidimensionally upwinded electric fields for divergence-free magnetohydrodynamical flows. A robust and efficient second order accurate numerical scheme for two and three dimensional Euler and magnetohydrodynamic flows is presented. The scheme is built on the current multidimensional Riemann solver. The number of zones updated per second by this scheme on a modern processor is shown to be cost competitive with schemes that are based on a one-dimensional Riemann solver. However, the present scheme permits larger timesteps

A Simple and Accurate Riemann Solver for Isothermal MHD

A new approximate Riemann solver for the equations of magnetohydrodynamics (MHD) with an isothermal equation of state is presented. The proposed method of solution draws on the recent work of Miyoshi and Kusano, in the context of adiabatic MHD, where an approximate solution to the Riemann problem is sought in terms of an average constant velocity and total pressure across the Riemann fan. This allows the formation of four intermediate states enclosed by two outermost fast discontinuities and separated by two rotational waves and an entropy mode. In the present work, a corresponding derivation for the isothermal MHD equations is presented. It is found that the absence of the entropy mode leads to a different formulation which is based on a three-state representation rather than four. Numerical tests in one and two dimensions demonstrates that the new solver is robust and comparable in accuracy to the more expensive linearized solver of Roe, although considerably faster.Comment: 19 pages, 9 figure