T. W. Jones

Cosmological Shock Waves and Their Role in the Large-Scale Structure of the Universe

We study the properties of cosmological shock waves identified in high-resolution, N-body/hydrodynamic simulations of a ΛCDM universe and their role on thermalization of gas and acceleration of nonthermal, cosmic-ray (CR) particles. External shocks form around sheets, filaments, and knots of mass distribution when the gas in void regions accretes onto them. Within those nonlinear structures, internal shocks are produced by infall of previously shocked gas to filaments and knots and during subclump mergers, as well as by chaotic flow motions. Due to the low temperature of the accreting gas, the Mach number of external shocks is high, extending up to M ~ 100 or higher. In contrast, internal shocks have mostly low Mach numbers. For all shocks of M ≥ 1.5, the mean distance between shock surfaces over the entire computed volume is ~4 h-1 Mpc at present, or ~1 h-1 Mpc for internal shocks within nonlinear structures. Identified external shocks are more extensive, with their surface area ~2 times larger than that of identified internal shocks at present. However, especially because of higher preshock densities but also due to higher shock speeds, internal shocks dissipate more energy. Hence, the internal shocks are mainly responsible for gas thermalization as well as CR acceleration. In fact, internal shocks with 2 M 4 contribute about one-half of the total dissipation. Using a nonlinear diffusive shock acceleration model for CR protons, we estimate the ratio of CR energy to gas thermal energy dissipated at cosmological shock waves to be about one-half through the history of the universe. Our result supports scenarios in which the intracluster medium contains energetically significant populations of CRs.

Properties of cosmic shock waves in large scale structure formation

We have examined the properties of shock waves in simulations of large-scale structure formation. Two cosmological scenarios have been considered: a standard cold dark matter model with ΩM = 1 (SCDM), and a cold dark matter model with cosmological constant and ΩM + ΩΛ = 1 (ΛCDM) having ΩΛ = 0.55. Large-scale shocks result from accretion onto sheets, filaments, and knots of mass distribution on a scale of the order of ~5 h-1 Mpc in both scenarios. Energetic motions, partly residuals of past accretion processes and partly caused by current asymmetric inflow along filaments, end up generating additional shocks. These extend on a scale of the order of ~1 h-1 Mpc and envelop and penetrate deep inside the clusters. Collisions between substructures inside clusters also form merger shocks. Consequently, the topology of the shocks is very complex and highly connected. During cosmic evolution the comoving shock surface density decreases, reflecting the ongoing structure merger process in both scenarios. Accretion shocks have very high Mach numbers, typically between 10 and a few ×103, when photoheating of the preshock gas is not included. The characteristic shock velocity is of the order of vsh(z) = H(z)λnl(z), where λnl(z) is the wavelength scale of the nonlinear perturbation at the given epoch. However, the Mach number for merger and flow shocks (which occur within clusters) is usually smaller, in the range of ~3-10, corresponding to the fact that the intracluster gas is hot (i.e., already shock heated). Statistical fits of shock velocities around clusters as a function of cluster temperature give power-law functions in accord with those predicted by one-dimensional solutions. On the other hand, a very different result is obtained for the shock radius, reflecting extremely complex shock structures surrounding clusters of galaxies in three-dimensional simulations. The amount of inflowing kinetic energy across the shocks around clusters, which represents the power available for cosmic-ray acceleration, is comparable to the cluster X-ray luminosity emitted from a central region of radius 0.5 h-1 Mpc. Considering their large size and long lifetimes, those shocks are potentially interesting sites for cosmic-ray acceleration, if modest magnetic fields exist within them.

COSMIC RAYS IN GALAXY CLUSTERS AND THEIR NONTHERMAL EMISSION

Radio observations prove the existence of relativistic particles and magnetic field associated with the intra-cluster-medium (ICM) through the presence of extended synchrotron emission in the form of radio halos and peripheral relics. This observational evidence has fundamental implications on the physics of the ICM. Nonthermal components in galaxy clusters are indeed unique probes of very energetic processes operating within clusters that drain gravitational and electromagnetic energy into cosmic rays (CRs) and magnetic fields. These components strongly affect the (micro-)physical properties of the ICM, including viscosity and electrical conductivities, and have also potential consequences on the evolution of clusters themselves. The nature and properties of CRs in galaxy clusters, including the origin of the observed radio emission on cluster-scales, have triggered an active theoretical debate in the last decade. Only recently we can start addressing some of the most important questions in this field, t...

A divergence-free upwind code for multidimensional magnetohydrodynamic flows

A description is given for preserving ∇ = 0 in a magnetohydrodynamic (MHD) code that employs the upwind, total variation diminishing (TVD) scheme and Strang type operator splitting for multidimensionality. The method is based on the staggered mesh technique to constrain the transport of magnetic field: the magnetic field components are defined at grid interfaces with their advective fluxes on grid edges, while other quantities are defined at grid centers. The magnetic field at grid centers for the upwind step is calculated by interpolating the values from grid interfaces. The advective fluxes on grid edges for the magnetic field evolution are calculated from the upwind fluxes at grid interfaces. Then the magnetic field can be maintained with ∇ = 0 exactly, if this is so initially, while the upwind scheme is used for the update of fluid quantities. The correctness of the code is demonstrated through tests comparing numerical solutions either with analytic solutions or with numerical solutions from a code using an explicit divergence-cleaning method. Also, the robustness is shown through tests involving realistic astrophysical problems.

Magnetohydrodynamic Simulations of Relic Radio Bubbles in Clusters

In order to better understand the origin and evolution of relic radio bubbles in clusters of galaxies, we report on an extensive set of two-dimensional MHD simulations of hot buoyant bubbles evolving in a realistic intracluster medium (ICM). Our bubbles are inflated near the base of the ICM over a finite time interval from a region whose magnetic field is isolated from the ICM. We confirm both the early conjecture from linear analysis and the later results based on preformed MHD bubbles, namely, that very modest ICM magnetic fields can stabilize the rising bubbles against disruption by Rayleigh-Taylor and Kelvin-Helmholtz instabilities. We find in addition that amplification of the ambient fields as they stretch around the bubbles can be sufficient to protect the bubbles or their initial fragments even if the fields are initially much too weak to play a significant role early in the evolution of the bubbles. Indeed, even with initial fields less than 1 μG and values of β = Pg/Pb approaching 105, magnetic stresses in our simulations eventually became large enough to influence the bubble evolution. Magnetic field influence also depends significantly on the geometry of the ICM field and on the topology of the field at the bubble/ICM interface. For example, reconnection of antiparallel fields across the bubble top greatly reduced the ability of the magnetic field to inhibit disruptive instabilities. Our results confirm earlier estimates of 108 yr for relic radio bubble lifetimes and show that magnetic fields can account for the long-term stability of these objects against disruption by surface instabilities. In addition, these calculations show that lifting and mixing of the ambient ICM may be a critical function of field geometries in both the ICM and the bubble interior.

TURBULENCE-INDUCED MAGNETIC FIELDS AND STRUCTURE OF COSMIC RAY MODIFIED SHOCKS

We propose a model for diffusive shock acceleration (DSA) in which stochastic magnetic fields in the shock precursor are generated through purely fluid mechanisms of a so-called small-scale dynamo. This contrasts with previous DSA models that considered magnetic fields amplified through cosmic ray (CR) streaming instabilities, i.e., either by way of individual particles resonant scattering in the magnetic fields, or by macroscopic electric currents associated with large-scale CR streaming. Instead, in our picture, the solenoidal velocity perturbations that are required for the dynamo to work are produced through the interactions of the pressure gradient of the CR precursor and density perturbations in the inflowing fluid. Our estimates show that this mechanism provides fast growth of magnetic field and is very generic. We argue that for supernovae shocks the mechanism is capable of generating upstream magnetic fields that are sufficiently strong for accelerating CRs up to around 1016 eV. No action of any other mechanism is necessary.

Simulating Magnetohydrodynamical Flow with Constrained Transport and Adaptive Mesh Refinement: Algorithms and Tests of the AstroBEAR Code

A description is given of the algorithms implemented in the AstroBEAR adaptive mesh-refinement code for ideal magnetohydrodynamics. The code provides several high-resolution shock-capturing schemes which are constructed to maintain conserved quantities of the flow in a finite-volume sense. Divergence-free magnetic field topologies are maintained to machine precision by collating the components of the magnetic field on a cell-interface staggered grid and utilizing the constrained transport approach for integrating the induction equations. The maintenance of magnetic field topologies on adaptive grids is achieved using prolongation and restriction operators which preserve the divergence and curl of the magnetic field across collocated grids of different resolutions. The robustness and correctness of the code is demonstrated by comparing the numerical solution of various tests with analytical solutions or previously published numerical solutions obtained by other codes.

A multidimensional code for isothermal magnetohydrodynamic flows in astrophysics

We present a multidimensional numerical code to solve isothermal magnetohydrodynamic (IMHD) equations for use in modeling astrophysical flows. First we have built a one-dimensional code which is based on an explicit finite-difference method on an Eulerian grid, called the total variation diminishing (TVD) scheme. The TVD scheme is a second-order-accurate extension of the Roe-type upwind scheme. Recipes for building the one-dimensional IMHD code, including the normalized right and left eigenvectors of the IMHD Jacobian matrix, are presented. Then we have extended the one-dimensional code to a multidimensional IMHD code through a Strang-type dimensional splitting. In the multidimensional code, an explicit cleaning step has been included to eliminate nonzero ∇B at every time step. To test the code, IMHD shock tube problems, which encompass all the physical IMHD structures, have been constructed. One-dimensional and two-dimensional shock tube tests have shown that the code captures all the structures correctly without producing noticeable oscillations. Strong shocks are resolved sharply, but weaker shocks spread more. Numerical dissipation (viscosity and resistivity) has been estimated through the decay test of a two-dimensional Alfven wave. It has been found to be slightly smaller than that of the adiabatic magnetohydrodynamic code based on the same scheme. As an example of astrophysical applications, we have simulated the nonlinear evolution of the two-dimensional Parker instability under a uniform gravity.

Numerical Studies of Diffusive Shock Acceleration at Spherical Shocks

Abstract We have developed a cosmic ray (CR) shock code in one-dimensional spherical geometry with which the particle distribution, the gas flow and their nonlinear interaction can be followed numerically in a frame comoving with an expanding shock. In order to accommodate a very wide dynamic range of diffusion length scales in the CR shock problem, we have incorporated subzone shock tracking and adaptive mesh refinement techniques. We find the spatial grid resolution required for numerical convergence is less stringent in this code compared to typical, fixed-grid Eulerian codes. The improved convergence behavior derives from maintaining the shock discontinuity inside the same grid zone in the comoving code. That feature improves numerical estimates of the compression rate experienced by CRs crossing the subshock compared to codes that allow the subshock to drift on the grid. Using this code with a Bohm-like diffusion model we have calculated the CR acceleration and the nonlinear feedback at supernova remnant shocks during the Sedov–Taylor stage. Similarly to plane-parallel shocks, with an adopted thermal leakage injection model, about 10 −3 of the particles that pass through the shock and up to 60% of the explosion energy are transferred to the CR component. These results are in good agreement with previous nonlinear spherical CR shock calculations of Berezhko and collaborators.

The morbidity and utility of periaortic radiotherapy in cervical carcinoma

From 1971 through 1981, 81 women received 4350 to 5075 rad to the periaortic lymph nodes as part of their primary management for carcinoma of the uterine cervix. While two patients developed chronic small bowel damage, only one required surgical intervention. Five-year disease-free survival was 40%. Approximately one-third of the first recurrences were within the pelvic and periaortic radiation portals, with the remainder in the lungs, liver, bones, abdomen, and supraclavicular lymph nodes. Radiation dose and volume guidelines are presented in order to minimize enteric morbidity.