A Divergence-Free Upwind Code for Multidimensional Magnetohydrodynamic Flows

A description is given for preserving {\bmsy\nabla}\cdot{\vec B}=0 in a magnetohydrodynamic (MHD) code that employs the upwind, Total Variation Diminishing (TVD) scheme and the Strang-type operator splitting for multi-dimensionality. 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 {\bmsy\nabla}\cdot{\vec B}=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 the code using an explicit divergence-cleaning method. Also the robustness is shown through tests involving realistic astrophysical problems.Comment: 15 pages of text, 8 figures (in degraded gif format), to appear in The Astrophysical Journal (Dec. 10, 1998), original quality figures available via anonymous ftp at ftp://ftp.msi.umn.edu/pub/users/twj/mhddivb5.uu or ftp://canopus.chungnam.ac.kr/ryu/mhddivb5.u

Three-Dimensional Simulations of the Parker Instability in a Uniformly-rotating Disk

We investigate the nonlinear effects of uniform rotation on the Parker instability in an exponentially-stratified disk through high-resolution simulations. During the linear stage, the speed of gas motion is subsonic and the evolution with the rotation is not much different from that without the rotation. This is because the Coriolis force is small. During the nonlinear stage, oppositely-directed supersonic flows near a magnetic valley are under the influence of the Coriolis force with different directions, resulting in twisted magnetic field lines near the valley. Sheet-like structures, which are tilted with respect to the initial field direction, are formed with an 1.5 enhancement of column density with respect to its initial value. Even though uniform rotation doesn't give much impact on density enhancement, it generates helically twisted field lines, which may become an additional support mechanism of clouds.Comment: 3 pages, uses rmaa.cls, to appear in Proc. of the Conference on "Astrophysical Plasmas: Codes, Models and Observations", Eds. J. Franco, J. Arthur, N. Brickhouse, Rev.Mex.AA Conf. Serie

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 $\Omega=1$ 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.Comment: 14 pages, uuencoded compressed postscript file. Accepted for Jan. 1, 1996 issue of Ap

Simulating Electron Transport and Synchrotron Emission in Radio Galaxies: Shock Acceleration and Synchrotron Aging in Three-Dimensional Flows

We present the first three-dimensional MHD radio galaxy simulations that explicitly model transport of relativistic electrons, including diffusive acceleration at shocks as well as radiative and adiabatic cooling in smooth flows. We discuss three simulations of light Mach 8 jets, designed to explore the effects of shock acceleration and radiative aging on the nonthermal particle populations that give rise to synchrotron and inverse-Compton radiations. We also conduct detailed synthetic radio observations of our simulated objects. We have gained several key insights from this approach: 1. The jet head in these multidimensional simulations is extremely complex. The classical jet termination shock is often absent, but motions of the jet terminus spin a ``shock-web complex'' within the backflowing jet material of the head. 2. Understanding the spectral distribution of energetic electrons in these simulations relies partly upon understanding the shock-web complex, for it can give rise to distributions that confound interpretation in terms of the standard model for radiative aging of radio galaxies. 3. The magnetic field outside of the jet itself becomes very intermittent and filamentary in these simulations, yet adiabatic expansion causes most of the cocoon volume to be occupied by field strengths considerably diminished below the nominal jet value. Thus population aging rates vary considerably from point to point.Comment: 44 pages, 6 figures; to be published in the Astrophysical Journal (August 2001); higher-quality figures can be found at http://www.msi.umn.edu/Projects/twj/radjet/radjet.htm

Quasiscarred modes and their branching behavior at an exceptional point

We study quasiscarring phenomenon and mode branching at an exceptional point (EP) in typically deformed microcavities. It is shown that quasiscarred (QS) modes are dominant in some mode group and their pattern can be understood by short-time ray dynamics near the critical line. As cavity deformation increases, high-Q and low-Q QS modes are branching in an opposite way, at an EP, into two robust mode types showing QS and diamond patterns, respectively. Similar branching behavior can be also found at another EP appearing at a higher deformation. This branching behavior of QS modes has its origin on the fact that an EP is a square-root branch point.Comment: 5 pages, 5 figure

Hydrodynamics of Cloud Collisions in 2D: The Fate of Clouds in a Multi-phase Medium

We have studied head-on collisions between equal-mass, mildly supersonic (Mach number 1.5) HI clouds, in a standard Two-phase ISM (T_cl = 74 K, n_cl = 22 cm^-3, \chi = 100). We explore the role of various factors, including the radiative cooling parameter \eta = t_rad/t_coll (t_coll=R_c/v_c), evolutionary modifications on the cloud structure (by colliding clouds ``evolved'' through independent motion within the intercloud medium (WIM)), and the symmetry of the problem (by colliding initially identical clouds, evolved to different ages before impact). The presence of bow shocks and ram pressure from material in the cloud wake, developed during such evolution through the WIM, significantly alters these interactions with respect to the standard case of non-evolved clouds. In general, in our adiabatic collisions the clouds are disrupted and convert their gas into a few low density contrast clumps. By contrast, for symmetric radiative cases we find that the two clouds coalesce, with almost all the initial kinetic energy radiated away. On the other hand, for both adiabatic and radiative collisions, asymmetric collisions have a much greater tendency to disrupt the two clouds. Fragmentation of the clouds may occur, and instabilities are in general enhanced. In addition, radiative cooling is less efficient in our asymmetric interactions, so that those parts of the clouds that initially seem to merge are more likely to re-expand and fade into the WIM. Since the majority of real cloud collisions should be asymmetric for one reason or another, we conclude that most gasdynamical diffuse cloud collisions will be disruptive, at least in the absence of significant self-gravity or of a significant magnetic field.Comment: Revised version, published in The Astrophysical Journal; 26 pages Latex + 9 figures, mpeg animations available at http://www.msi.umn.edu/Projects/twj/Cloud-Collision.htm

Winds and Shocks in Galaxy Clusters: Shock Acceleration on an Intergalactic Scale

We review the possible roles of large scale shocks as particle accelerators in clusters of galaxies. Recent observational and theoretical work has suggested that high energy charged particles may constitute a substantial pressure component in clusters. If true that would alter the expected dynamical evolution of clusters and increase the dynamical masses consistent with hydrostatic equilibrium. Moderately strong shocks are probably common in clusters, through the actions of several agents. The most obvious of these agents include winds from galaxies undergoing intense episodes of starbursts, active galaxies and cosmic inflows, such as accretion and cluster mergers. We describe our own work derived from simulations of large scale structure formation, in which we have, for the first time, explicitly included passive components of high energy particles. We find, indeed that shocks associated with these large scale flows can lead to nonthermal particle pressures big enough to influence cluster dynamics. These same simulations allow us also to compute nonthermal emissions from the clusters. Here we present resulting predictions of gamma-ray fluxes.Comment: 12 pages, uses aipproc.cls and aipproc.sty, to appear in Proc. of the International Symposium on "High Energy Gamma-Ray Astrophysics" (published as a volume of AIP Conference Series) eds. F. Aharonian and H. Voel