Two-dimensional, Time-dependent, Multi-group, Multi-angle Radiation Hydrodynamics Test Simulation in the Core-Collapse Supernova Context

We have developed a time-dependent, multi-energy-group, and multi-angle (S$_n$) Boltzmann transport scheme for radiation hydrodynamics simulations, in one and two spatial dimensions. The implicit transport is coupled to both 1D (spherically-symmetric) and 2D (axially-symmetric) versions of the explicit Newtonian hydrodynamics code VULCAN. The 2D variant, VULCAN/2D, can be operated in general structured or unstructured grids and though the code can address many problems in astrophysics it was constructed specifically to study the core-collapse supernova problem. Furthermore, VULCAN/2D can simulate the radiation/hydrodynamic evolution of differentially rotating bodies. We summarize the equations solved and methods incorporated into the algorithm and present results of a time-dependent 2D test calculation. A more complete description of the algorithm is postponed to another paper. We highlight a 2D test run that follows for 22 milliseconds the immediate post-bounce evolution of a collapsed core. We present the relationship between the anisotropies of the overturning matter field and the distribution of the corresponding flux vectors, as a function of energy group. This is the first 2D multi-group, multi-angle, time-dependent radiation/hydro calculation ever performed in core collapse studies. Though the transport module of the code is not gray and does not use flux limiters (however, there is a flux-limited variant of VULCAN/2D), it still does not include energy redistribution and most velocity-dependent terms.Comment: 19 pages, plus 13 figures in JPEG format. Submitted to the Astrophysical Journa

A Refined Scaling Law for Spatially Coupled LDPC Codes Over the Binary Erasure Channel

We propose a refined scaling law to predict the finite-length performance in the waterfall region of spatially coupled low-density parity-check codes over the binary erasure channel. In particular, we introduce some improvements to the scaling law proposed by Olmos and Urbanke that result in a better agreement between the predicted and simulated frame error rate. We also show how the scaling law can be extended to predict the bit error rate performance.Comment: Paper accepted to IEEE Information Theory Workshop (ITW) 201

Storm‐time configuration of the inner magnetosphere: Lyon‐Fedder‐Mobarry MHD code, Tsyganenko model, and GOES observations

[1] We compare global magnetohydrodynamic (MHD) simulation results with an empirical model and observations to understand the magnetic field configuration and plasma distribution in the inner magnetosphere, especially during geomagnetic storms. The physics-based Lyon-Fedder-Mobarry (LFM) code simulates Earth\u27s magnetospheric topology and dynamics by solving the equations of ideal MHD. Quantitative comparisons of simulated events with observations reveal strengths and possible limitations and suggest ways to improve the LFM code. Here we present a case study that compares the LFM code to both a semiempirical magnetic field model and to geosynchronous measurements from GOES satellites. During a magnetic cloud event, the simulation and model predictions compare well qualitatively with observations, except during storm main phase. Quantitative statistical studies of the MHD simulation shows that MHD field lines are consistently under-stretched, especially during storm time (Dst \u3c −20 nT) on the nightside, a likely consequence of an insufficient representation of the inner magnetosphere current systems in ideal MHD. We discuss two approaches for improving the LFM result: increasing the simulation spatial resolution and coupling LFM with a ring current model based on drift physics (i.e., the Rice Convection Model (RCM)). We show that a higher spatial resolution LFM code better predicts geosynchronous magnetic fields (not only the average Bz component but also higher-frequency fluctuations driven by the solar wind). An early version of the LFM/RCM coupled code, which runs so far only for idealized events, yields a much-improved ring current, quantifiable by decreased field strengths at all local times compared to the LFM-only code

Evolution equations for slowly rotating stars

We present a hyperbolic formulation of the evolution equations describing non-radial perturbations of slowly rotating relativistic stars in the Regge--Wheeler gauge. We demonstrate the stability preperties of the new evolution set of equations and compute the polar w-modes for slowly rotating stars.Comment: 27 pages, 2 figure

General relativistic neutrino transport using spectral methods

We present a new code, Lorene's Ghost (for Lorene's gravitational handling of spectral transport) developed to treat the problem of neutrino transport in supernovae with the use of spectral methods. First, we derive the expression for the nonrelativistic Liouville operator in doubly spherical coordinates (r, theta, phi, epsilon, Theta, Phi)$, and further its general relativistic counterpart. We use the 3 + 1 formalism with the conformally flat approximation for the spatial metric, to express the Liouville operator in the Eulerian frame. Our formulation does not use any approximations when dealing with the angular arguments (theta, phi, Theta, Phi), and is fully energy-dependent. This approach is implemented in a spherical shell, using either Chebyshev polynomials or Fourier series as decomposition bases. It is here restricted to simplified collision terms (isoenergetic scattering) and to the case of a static fluid. We finish this paper by presenting test results using basic configurations, including general relativistic ones in the Schwarzschild metric, in order to demonstrate the convergence properties, the conservation of particle number and correct treatment of some general-relativistic effects of our code. The use of spectral methods enables to run our test cases in a six-dimensional setting on a single processor.Comment: match published versio

Evolution equations for the perturbations of slowly rotating relativistic stars

We present a new derivation of the equations governing the oscillations of slowly rotating relativistic stars. Previous investigations have been mostly carried out in the Regge-Wheeler gauge. However, in this gauge the process of linearizing the Einstein field equations leads to perturbation equations which as such cannot be used to perform numerical time evolutions. It is only through the tedious process of combining and rearranging the perturbation variables in a clever way that the system can be cast into a set of hyperbolic first order equations, which is then well suited for the numerical integration. The equations remain quite lengthy, and we therefore rederive the perturbation equations in a different gauge, which has been first proposed by Battiston et al. (1970). Using the ADM formalism, one is immediately lead to a first order hyperbolic evolution system, which is remarkably simple and can be numerically integrated without many further manipulations. Moreover, the symmetry between the polar and the axial equations becomes directly apparent.Comment: 13 pages, no figures, MSRAS typesetting, cleaning of the inadvertently disfigured equation