arXiv subjects

Dongsu Ryu

Publications and source records attributed to Dongsu Ryu.

154 records · Page 9Linked to original sources

arXiv1995

The MHD Kelvin-Helmholtz Instability: A Two-Dimensional Numerical Study

Using a new numerical code we have carried out two-dimensional simulations of the nonlinear evolution of unstable sheared magnetohydrodynamic flows. We considered two cases: a strong magnetic field (Alfven Mach number, M_a = 2.5) and a weak field (M_a =5). Each flow rapidly evolves until it reaches a nearly steady condition, which is fundamentally different from the analogous gasdynamic state. Both MHD flows relax to a stable, laminar flow on timescales less than or of the order of 15 linear growth times, measured from saturation of the instability. That timescale is several orders of magnitude less than the nominal dissipation time for these simulated flows, so this condition represents an quasi-steady relaxed state. The strong magnetic field case reaches saturation as magnetic tension in the displaced flow boundary becomes sufficient to stabilize it. That flow then relaxes in a straightforward way to the steady, laminar flow condition. The weak magnetic field case, on the other hand, begins development of the vortex expected for gasdynamics, but that vortex is destroyed by magnetic stresses that locally become strong. Magnetic topologies lead to reconnection and dynamical alignment between magnetic and velocity fields. Together these processes produce a sequence of intermittent vortices and subsequent relaxation to a nearly laminar flow condition in which the magnetic cross helicity is nearly maximized. Remaining irregularities consist of a pair of flux tubes straddling the shear layer. Fluctuations within those features are closely aligned, representing Alfvén waves propagating locally downstream.

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arXiv1995

Global Aspects of Elliptical Instability in Tidally Distorted Accretion Disks

Tidally distorted accretion disks in binary star systems are subject to a local hydrodynamic instability which excites $m=1$ internal waves. This instability is three dimensional and approximately incompressible. We study the global aspects of this local instability using equations derived under the shearing sheet approximation, where the effects of the azimuthal variation along distorted orbital trajectories are included in source terms which oscillate with local orbital phase. Linear analyses show that the excitation of the instability is essentially local, i.e. insensitive to radial boundary conditions. The region of rapid growth feeds waves into the region of slow or negligible growth, allowing the instability to become global. The global growth rate depends the maximum local growth rate, the size of the rapid growth region, and the local group velocity. We present an empirical expression for the global growth rate. We note that the local nature of the instability allows the excitation of waves with $m\ne 1$ when the local growth rate is large.

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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

Background X-ray Emission from Hot Gas in CDM and CDM+Lambda Universes: Spectral Signatures

We present a new treatment of two popular models for the growth of structure, examining the X-ray emission from hot gas with allowance for spectral line emission from various atomic species, primarily ``metals". The X-ray emission from the bright cluster sources is not significantly changed from prior work and, as noted earlier, shows the CDM$+Λ$ model (LCDM) to be consistent but the standard, COBE normalized model (SCDM) to be inconsistent with existing observations --- after allowance for still the considerable numerical modelling uncertainties. But we find one important new result. Radiation in the softer band 0.5-1.0keV is predominantly emitted by gas far from cluster centers (hence ``background"). This background emission dominates over the cluster emission below 1keV and observations of it should show clear spectral signatures indicating its origin. In particular the ``iron blend" should be seen prominantly in this spectral bin from cosmic background hot gas at high galactic latitudes and should show shadowing against the SMC indicating its extragalactic origin. Certain OVII lines also provide a signature of this gas which emits a spectrum characteristic of $10^{6.6\pm 0.6}$K gas. Recent ASCA observations of the X-ray background tentatively indicate the presence of component with exactly the spectral features we predict here.

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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

Stable and Unstable Accretion Flows with Angular Momentum near a Point Mass

The properties of axisymmetric accretion flows of cold adiabatic gas with zero total energy in the vicinity of a Newtonian point mass are characterized by a single dimensionless parameter, the thickness of incoming flow. In the limit of thin accretion flows with vanishing thickness, we show that the governing equations become self-similar, involving no free parameters. We study numerically thin accretion flows with finite thickness as well as those with vanishing thickness. Mass elements of the incoming flow enter the computational regime as thin rings. In the case with finite thickness, after a transient period of initial adjustment, an almost steady-state accretion shock with a small oscillation amplitude forms, confirming the previous work by Molteni, Lanzafame, \& Chakrabarti (1994). The gas in the region of vorticity between the funnel wall and the accretion shock follows closed streamlines, forming a torus. This torus, in turn, behaves as an effective barrier to the incoming flow and supports the accretion shock which reflects the incoming gas away from the equatorial plane. The postshock flow, which is further accelerated by the pressure gradient behind the shock, goes through a second shock which then reflects the flow away from the symmetry axis to form a conical outgoing wind. As the thickness of the inflowing layer decreases (or if the ratio of the half thickness to the distance to the funnel wall along the equatorial plan is smaller than $\sim0.1$), the flow becomes unstable. In the case with vanishing thickness, the accretion shock formed to stop the incoming flow behind the funnel wall oscillates quasi-periodically with an amplitude comparable to the thickness. The structure between the funnel wall and the accretion shock is destroyed as the shock moves inwards toward the central mass and re-generated

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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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arXiv1994

Hot Gas in the CDM Scenario: X-Ray Clusters from a High Resolution Numerical Simulation

We exmaine the distribution of hot gas in a standard CDM model of the universe using high resolution hydrodynamic simulations. Adopting standard parameters determined from COBE and light element nucleosynthesis, $σ_8=1.05$, $Ω_b=0.06$ and assuming $h=0.5$, we find the X-ray emitting clusters, compute the luminosity function at several wavelengths, the temperature distribution and estimated sizes as well as the evolution of these quantities with redshift. This standard CDM model, normalized to COBE, produces approximately 5 times too much emission from clusters having $L_x>10^{43}$erg/s, a not unexpected result. If all other parameters were unchanged, we would expect adequate agreement for $σ_8=0.6$. This provides a new and independent argument for lower small scale power than standard CDM at the $8h^{-1}$Mpc scale. The background radiation field at 1keV due to clusters in this model is approximately $1/3$ of the observed background which, after correction for numerical effects, again indicates approximately 5 times too much emission and the appropriateness of $σ_8=0.6$. If we had used the observed ratio of gas to total mass in clusters, rather than basing the mean density on light element nucleosynthesis, then the computed luminosity of each cluster would have increased still further, by a factor of approximately ten. Examining the ratio of gas to total mass in the clusters (which we find to be anti-biased by a factor of approximately 0.6), normalized to $Ω_b h^2=0.015$, and comparing to observations, we conclude, in agreement with S. White, that the cluster observations argue for an open universe.

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arXiv1994

A Comparison of Cosmological Hydrodynamic Codes

We present a detailed comparison of the simulation results of various cosmological hydrodynamic codes. Starting with identical initial conditions based on the Cold Dark Matter scenario for the growth of structure, we integrate from redshift $z=20$ to $z=0$ to determine the physical state within a representative volume of size $L^3$ where $L=64 h^{-1} {\rm Mpc}$. Five independent codes are compared: three of them Eulerian mesh based and two variants of the Smooth Particle Hydrodynamics "SPH" Lagrangian approach. The Eulerian codes were run at $N^3=(32^3,~64^3,~128^3,~{\rm and},~256^3)$ cells, the SPH codes at $N^3= 32^3$ and $64^3$ particles. Results were then rebinned to a $16^3$ grid with the expectation that the rebinned data should converge, by all techniques, to a common and correct result as $N \rightarrow \infty$. We find that global averages of various physical quantities do, as expected, tend to converge in the rebinned model, but that uncertainties in even primitive quantities such as $\langle T \rangle$, $\langle ρ^2\rangle^{1/2}$ persists at the 3\%-17\% level after completion of very large simulations. The two SPH codes and the two shock capturing Eulerian codes achieve comparable and satisfactory accuracy for comparable computer time in their treatment of the high density, high temperature regions as measured in the rebinned data; the variance among the five codes (at highest resolution) for the mean temperature (as weighted by $ρ^2$) is only 4.5\%. Overall the comparison allows us to better estimate errors, it points to ways of improving this current generation of hydrodynamic codes and of suiting their use to problems which exploit their individually best features.

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