arXiv subjects

T. W. Jones

Publications and source records attributed to T. W. Jones.

95 records · Page 6Linked to original sources

arXiv1995

Cluster Accretion Shocks as Possible Acceleration Sites for Ultra High Energy Protons below the Greisen Cutoff

Three-dimensional hydrodynamic simulations of large scale structure in the Universe have shown that accretion shocks form during the gravitational collapse of one-dimensional caustics, and that clusters of galaxies formed at intersections of the caustics are surrounded by these accretion shocks. Estimated speed and curvature radius of the shocks are 1000-3000 \kms and about 5 Mpc, respectively, in the $Ω=1$ CDM universe. Assuming that energetic protons are accelerated by these accretion shocks via the first-order Fermi process and modeling particle transport around the shocks through Bohm diffusion, we suggest that protons can be accelerated up to the {\it Greisen cutoff energy} near $6\times 10^{19}$ eV, provided the mean magnetic field strength in the region around the shocks is at least of order a microgauss. We have also estimated the proton flux at earth from the Virgo cluster. Assuming a few (1-10) \% of the ram pressure of the infalling matter would be transferred to the cosmic-rays, the estimated flux for $ E \sim 10^{19}$eV is consistent with observations, so that such clusters could be plausible sources of the UHE CRs.

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arXiv1995

Numerical Magnetohydrodynamics in Astrophysics: Algorithm and Tests for Multi-Dimensional Flow

We present for astrophysical use a multi-dimensional numerical code to solve the equations for ideal magnetohydrodynamics (MHD). It is based on an explicit finite difference method on an Eulerian grid, called the Total Variation Diminishing (TVD) scheme, which is a second-order-accurate extension of the Roe-type upwind scheme. Multiple spatial dimensions are treated through a Strang-type operator splitting. The constraint of a divergence-free field is enforced exactly by calculating a correction via a gauge transformation in each time step. Results from two-dimensional shock tube tests show that the code captures correctly discontinuities in all three MHD waves families as well as contact discontinuities. The numerical viscosities and resistivity in the code, which are useful in order to understand simulations involving turbulent flows, are estimated through the decay of two-dimensional linear waves. Finally, the robustness of the code in two-dimensions is demonstrated through calculations of the Kelvin-Helmholtz instability and the Orszag-Tang vortex.

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arXiv1995

Diffusive Shock Acceleration Simulations: Comparison with Particle Methods and Bow Shock Measurements

Direct comparisons of diffusive particle acceleration numerical simulations have been made against Monte Carlo and hybrid plasma simulations by Ellison {\it et. al.} (1993) and against observations at the earth's bow shock presented by Ellison {\it et. al.} (1990). Toward this end we have introduced a new numerical scheme for injection of cosmic-ray particles out of the thermal plasma, modeled by way of the diffusive scattering process itself; that is, the diffusion and acceleration across the shock front of particles out of the suprathermal tail of the Maxwellian distribution. We find that all of these computational methods (diffusion-advection, two-fluid, Monte Carlo and hybrid) are in substantial agreement on the issues they can simultaneously address, so that the essential physics of diffusive particle acceleration is adequately contained within each. This is despite the fact that each makes what appear to be very different assumptions or approximations.

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arXiv1994

Numerical Magnetohydrodynamics in Astrophysics: Algorithm and Tests for One-Dimensional Flow

We describe a numerical code to solve the equations for ideal magnetohydrodynamics (MHD). It is based on an explicit finite difference scheme on an Eulerian grid, called the Total Variation Diminishing (TVD) scheme, which is a second-order-accurate extension of the Roe-type upwind scheme. We also describe a nonlinear Riemann solver for ideal MHD, which includes rarefactions as well as shocks and produces exact solutions for two-dimensional magnetic field structures as well as for the three-dimensional ones. The numerical code and the Riemann solver have been used to test each other. Extensive tests encompassing all the possible ideal MHD structures with planar symmetries (\ie ~one-dimensional flows) are presented. These include those for which the field structure is two-dimensional ({\it i.e.}, those flows often called ``$1 + 1/2$ dimensional'') as well as those for which the magnetic field plane rotates ({\it i.e.,}, those flows often called ``$1 + 1/2 + 1/2$ dimensional''). Results indicate that the code can resolve strong fast, slow, and magnetosonic shocks within 2-4 cells while more cells are required if shocks become weak. With proper stiffening, rotational discontinuities are resolved within 3-5 cells. Contact discontinuities are also resolved within 3-5 cells with stiffening and 6-8 cells without stiffening, while the stiffening on contact discontinuities in some cases generates numerical oscillations. Tangential discontinuities spread over more than 10 cells. Our tests confirm that slow compound structures with two-dimensional magnetic field are composed of intermediate shocks (so called ``2-4''

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arXiv1994

The Evolution and Efficiency of Oblique MHD Cosmic-Ray Shocks: Two-Fluid Simulations

Using a new, second-order accurate numerical method we present dynamical simulations of oblique MHD cosmic ray (CR) modified plane shock evolution using the two-fluid model for diffusive particle acceleration. The numerical shocks evolve to published analytical steady state properties. In order to probe the dynamical role of magnetic fields we have explored for these time asymptotic states the parameter space of upstream fast mode Mach number, $M_f$, and plasma $β$, compiling the results into maps of dynamical steady state CR acceleration efficiency, $ε_c$. These maps, along with additional numerical experiments, show that $ε_c$ is reduced through the action of compressive work on tangential magnetic fields in CR-MHD shocks. Thus $ε_c$ in low $β$, moderate $M_f$ shocks tends to be smaller in quasi perpendicular shocks than it would be high $β$ shocks of the same $M_f$. This result supports earlier conclusions that strong, oblique magnetic fields inhibit diffusive shock acceleration. For quasi parallel shocks with $β< 1$, on the other hand, $ε_c$ seems to be increased at a given $M_f$ when compared to high $β$ shocks. The apparent contradiction to the first conclusion results, however, from the fact that for small $β$ quasi parallel shocks, the fast mode Mach number is not a good measure of compression through the shock. That is better reflected in the sonic Mach number, which is greater. Acceleration efficiencies for high and low $β$ having comparable sonic Mach numbers are more similar. Time evolution of CR-MHD shocks is qualitatively similar to CR-gasdynamical shocks. However, several potentially interesting differences are apparent.

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