arXiv subjects

Christian Y. Cardall

Publications and source records attributed to Christian Y. Cardall.

At least 37 records · Page 2Linked to original sources

arXiv2012

Turbulent Magnetic Field Amplification from Spiral SASI Modes: Implications for Core-Collapse Supernovae and Proto-Neutron Star Magnetization

We extend our investigation of magnetic field evolution in three-dimensional flows driven by the stationary accretion shock instability (SASI) with a suite of higher-resolution idealized models of the post-bounce core-collapse supernova environment. Our magnetohydrodynamic simulations vary in initial magnetic field strength, rotation rate, and grid resolution. Vigorous SASI-driven turbulence inside the shock amplifies magnetic fields exponentially; but while the amplified fields reduce the kinetic energy of small-scale flows, they do not seem to affect the global shock dynamics. The growth rate and final magnitude of the magnetic energy are very sensitive to grid resolution, and both are underestimated by the simulations. Nevertheless our simulations suggest that neutron star magnetic fields exceeding $10^{14}$ G can result from dynamics driven by the SASI, \emph{even for non-rotating progenitors}.

astro-ph.SR↗

arXiv2011

Parallel FFT-based Poisson Solver for Isolated Three-dimensional Systems

We describe an implementation to solve Poisson's equation for an isolated system on a unigrid mesh using FFTs. The method solves the equation globally on mesh blocks distributed across multiple processes on a distributed-memory parallel computer. Test results to demonstrate the convergence and scaling properties of the implementation are presented. The solver is offered to interested users as the library PSPFFT.

physics.comp-ph↗

arXiv2010

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.

astro-ph↗

arXiv2009

Towards neutrino transport with flavor mixing in supernovae: the Liouville operator

The calculation of neutrino decoupling from nuclear matter requires a transport formalism capable of handling both collisions and flavor mixing. The first steps towards such a formalism are the construction of neutrino and antineutrino "distribution matrices," and a determination of the Liouville equations they satisfy in the noninteracting case. These steps are accomplished through study of a Wigner-transformed "density function," the mean value of paired neutrino quantum field operators.

astro-ph.HE↗

arXiv2008

Degeneracy, the virial theorem, and stellar collapse

Formulae for the energies of degenerate non-relativistic and ultra-relativistic Fermi gases play multiple roles in simple arguments related to the collapse of a stellar core to a neutron star. These formulae, deployed in conjunction with the virial theorem and a few other basic physical principles, provide surprisingly good estimates of the temperature, mass, and radius (and therefore also density and entropy) of the core at the onset of collapse; the final radius and composition of the cold compact remnant; and the total energy lost to neutrino emission during collapse.

astro-ph↗

arXiv2008

Liouville equations for neutrino distribution matrices

The classical notion of a single-particle scalar distribution function or phase space density can be generalized to a matrix in order to accommodate superpositions of states of discrete quantum numbers, such as neutrino mass/flavor. Such a `neutrino distribution matrix' is thus an appropriate construct to describe a neutrino gas that may vary in space as well as time and in which flavor mixing competes with collisions. The Liouville equations obeyed by relativistic neutrino distribution matrices, including the spatial derivative and vacuum flavor mixing terms, can be explicitly but elegantly derived in two new ways: from a covariant version of the familiar simple model of flavor mixing, and from the Klein-Gordon equations satisfied by a quantum `density function' (mean value of paired quantum field operators). Associated with the latter derivation is a case study in how the joint position/momentum dependence of a classical gas (albeit with Fermi statistics) emerges from a formalism built on quantum fields.

astro-ph↗

arXiv2007

Supernova neutrinos

A nascent neutron star resulting from stellar collapse is a prodigious source of neutrinos of all flavors. While the most basic features of this neutrino emission can be estimated from simple considerations, the detailed simulation of the neutrinos' decoupling from the hot neutron star is not yet computationally tractable in its full glory, being a time-dependent six-dimensional transport problem. Nevertheless, supernova neutrino fluxes are of great interest in connection with the core-collapse supernova explosion mechanism and supernova nucleosynthesis, and as a potential probe of the supernova environment and of some of the neutrino mixing parameters that remain unknown; hence a variety of approximate transport schemes have been used to obtain results with reduced dimensionality. However, none of these approximate schemes have addressed a recent challenge to the conventional wisdom that neutrino flavor mixing cannot impact the explosion mechanism or r-process nucleosynthesis.

astro-ph↗

arXiv2007

Supernova neutrinos, from back of the envelope to supercomputer

While an understanding of supernova explosions will require sophisticated large-scale simulations, it is nevertheless possible to outline the most basic features of the neutrino emission resulting from stellar core collapse with a pedestrian account that, through reliance upon broadly accessible physical ideas, remains simple and largely self-contained.

astro-ph↗

arXiv2005

Toward Five-dimensional Core-collapse Supernova Simulations

The computational difficulty of six-dimensional neutrino radiation hydrodynamics has spawned a variety of approximations, provoking a long history of uncertainty in the core-collapse supernova explosion mechanism. Under the auspices of the Terascale Supernova Initiative, we are honoring the physical complexity of supernovae by meeting the computational challenge head-on, undertaking the development of a new adaptive mesh refinement code for self-gravitating, six-dimensional neutrino radiation magnetohydrodynamics. This code--called {\em GenASiS,} for {\em Gen}eral {\em A}strophysical {\em Si}mulation {\em S}ystem--is designed for modularity and extensibility of the physics. Presently in use or under development are capabilities for Newtonian self-gravity, Newtonian and special relativistic magnetohydrodynamics (with `realistic' equation of state), and special relativistic energy- and angle-dependent neutrino transport--including full treatment of the energy and angle dependence of scattering and pair interactions.

astro-ph↗

arXiv2005

Conservative special relativistic radiative transfer for multidimensional astrophysical simulations: motivation and elaboration

Many astrophysical phenomena exhibit relativistic radiative flows. While velocities in excess of $v \sim 0.1c$ can occur in these systems, it has been common practice to approximate radiative transfer to $\cO(v/c)$. In the case of neutrino transport in core-collapse supernovae, this approximation gives rise to an inconsistency between the lepton number transfer and lab frame energy transfer, which have different $\cO(v/c)$ limits. A solution used in spherically symmetric $\cO(v/c)$ simulations has been to retain, for energy accounting purposes, the $\cO(v^2/c^2)$ terms in the lab frame energy transfer equation that arise from the $\cO(v/c)$ neutrino number transport equation. Avoiding the proliferation of such ``extra'' $\cO(v^2/c^2)$ terms in the absence of spherical symmetry motivates a special relativistic formalism, which we exhibit in coordinates sufficiently general to encompass Cartesian, spherical, and cylindrical coordinate systems.

astro-ph↗

arXiv2005

The Long Term: Six-dimensional Core-collapse Supernova Models

The computational difficulty of six-dimensional neutrino radiation hydrodynamics has spawned a variety of approximations, provoking a long history of uncertainty in the core-collapse supernova explosion mechanism. Under the auspices of the Terascale Supernova Initiative, we are honoring the physical complexity of supernovae by meeting the computational challenge head-on, undertaking the development of a new adaptive mesh refinement code for self-gravitating, six-dimensional neutrino radiation magnetohydrodynamics. This code--called {\em GenASiS}, for {\em Gen}eral {\em A}strophysical {\em Si}mulation {\em S}ystem--is designed for modularity and extensibility of the physics. Presently in use or under development are capabilities for Newtonian self-gravity, Newtonian and special relativistic magnetohydrodynamics (with `realistic' equation of state), and special relativistic energy- and angle-dependent neutrino transport--including full treatment of the energy and angle dependence of scattering and pair interactions.

astro-ph↗

arXiv2005

Supernova neutrino challenges

A principal `supernova neutrino challenge' is the computational difficulty of six-dimensional neutrino radiation hydrodynamics. The variety of resulting approximations has provoked a long history of uncertainty in the core-collapse supernova explosion mechanism, but recent work highlighting low-mode convection and a newly-recognized instability in spherical accretion shocks may signal (yet another) resolution. As part of its goal of elucidating the explosion mechanism, the Terascale Supernova Initiative is committed to meeting the full complexity of the computational challenge. The understanding of supernova neutrino emission gained in detailed simulations provides a potential basis for learning about two major remaining unknowns in neutrino flavor mixing: the value of the mixing angle $θ_{13}$, and distinguishing between ``normal'' and ``inverted'' mass hierarchies.

astro-ph↗

arXiv2004

General Relativity and Neutrino-driven Supernova Winds

To date, detailed core-collapse supernova simulations have not succeeded in elucidating the explosion mechanism. But whatever the mechanism turns out to be, there will be a neutrino-heated outflow between the hot, newly-born neutron star and the outgoing supernova shock wave whose neutron richness, low density, and high temperature could provide promising conditions for the synthesis of heavy nuclei via rapid neutron capture (the r-process). General relativistic effects improve the prospects for this outflow as an r-process site. Among relativistic effects, the enhanced "gravitational potential" is more important than the gravitational redshift or trajectory bending of neutrinos.

astro-ph↗

arXiv2004

An Approach to Neutrino Radiative Transfer in Supernova Simulations

Neutrinos dominate the energetics of core-collapse supernovae, and are believed to play an important role in driving the explosion. The development of a spatially multidimensional neutrino radiative transfer code is a key part of the Terascale Supernova Initiative, a multi-year effort aimed at understanding the supernova explosion mechanism through supercomputer simulations. I will describe the conservative formulations of general relativistic radiative transfer we have developed for this application, and the algorithm we are implementing in our parallel code.

astro-ph↗

arXiv2004

Conservative Formulations of General Relativistic Radiative Transfer

Accurate accounting of particle number and 4-momentum in radiative transfer may be facilitated by the use of transport equations that allow transparent conversion between volume and surface integrals in both spacetime and momentum space. Such conservative formulations of general relativistic radiative transfer in multiple spatial dimensions are presented, and their relevance to core-collapse supernova simulations described.

astro-ph↗

arXiv2004

Core-collapse supernovae and gravitational waves

Core-collapse supernovae are dramatic events with a rich phenomenology, including gravitational radiation. Simulations of these events in multiple spatial dimensions with energy- and angle-dependent neutrino transport are still in their infancy. Core collapse and bounce in a supernova in our galaxy may well be visible by first-generation LIGO, but detailed understanding waits on improvements in modeling both stellar progenitors and the supernova process.

astro-ph↗

arXiv2002

Conservative formulations of general relativistic kinetic theory

Experience with core-collapse supernova simulations shows that accurate accounting of total particle number and 4-momentum can be a challenge for computational radiative transfer. This accurate accounting would be facilitated by the use of particle number and 4-momentum transport equations that allow transparent conversion between volume and surface integrals in both configuration and momentum space. Such conservative formulations of general relativistic kinetic theory in multiple spatial dimensions are presented in this paper, and their relevance to core-collapse supernova simulations is described.

astro-ph↗

arXiv2002

The Status of Core-collapse Supernova Simulations

Core-collapse supernovae can be used to place limits on dark matter candidate particles, but the strength of these limits depends on the depth of our theoretical understanding of these astrophysical events. To date, limitations on computing power have prevented inclusion of all the physics that would constitute a realistic simulation. The TeraScale Supernova Initiative (TSI) will overcome these obstacles in the next few years, elucidating the explosion mechanism and other phenomena closely associated with the core collapse of massive stars.

astro-ph↗