David A. Clarke

A consistent method of characteristics for multidimensional magnetohydrodynamics

This paper introduces a previously unaddressed problem with performing multidimensional numerical MHD characterized by {open_quote}{open_quote}explosive{close_quote}{close_quote} growth (within a single time step) of weak magnetic fields to possibly dynamic strengths in the vicinity of strong velocity shear. This problem has been observed to occur in numerical algorithms which rely on the solution of the characteristic equations at the mesh interfaces. The solution to this problem is the subject of this paper and has led to an algorithm fundamentally different from those discussed previously. Specifically, at every point on the mesh, the magnetic induction terms are determined from the characteristic velocities which are evaluated by solving {ital implicitly} (in space) the characteristic equations for incompressible MHD (although the algorithm is perfectly suitable for compressible MHD). The implicit treatment of the characteristic equations sets this algorithm apart from previous efforts and is shown to be a necessary condition for multidimensional accuracy. It amounts to replacing the usual directional-split treatment of the induction and transport operators with a planar-split scheme. {copyright} {ital 1996 The American Astronomical Society.}

Numerical simulations of a magnetically confined jet

Preliminary results of two-dimensional, axisymmetric numerical simulations of a propagating jet which possesses a dominating toroidal magnetic field are presented. Unlike its pure hydrodynamical (HD) counterpart, the magnetohydrodynamical (MHD) jet presented here possesses no substantial backflowing cocoon. Rather, most of the material is collected between the HD working surface (terminal Mach disk) and the leading bow shock, forming what is called a nose cone. The nature of the nose cone and other features peculiar to this jet are discussed, along with possible observational implications. 18 references.

VLA observations of the inner lobes of Centaurus A

Scaled-array VLA observations of the closest active radio galaxy Centaurus A at 1.4, 1.6, and 4.9 GHz with 4.5 ″ × 1.2″ resolution have been used to derive the spectral and polarimetric properties of the inner radio lobes of the source. The extended emission of the lobes is filamentary, similar to other well-resolved radio galaxies. Two compact radio features have been detected in the southern lobe which are roughly aligned with the axis of the main jet. This may be the first indication of a counterjet in Centaurus A

Dynamics and Structure of Three-dimensional Poloidally Magnetized Supermagnetosonic Jets

A set of three-dimensional magnetohydrodynamical simulations of supermagnetosonic magnetized jets has been performed. The jets contain an equipartition primarily poloidal magnetic field, and the effect of jet density on jet dynamics and structure is evaluated. The jet is precessed at the origin to break the symmetry and to excite Kelvin-Helmholtz-unstable helical modes. In the linear limit, observed structures are similar in all simulations and can be produced by structures predicted to arise as a result of instability. The amplitude of various unstable modes is evaluated. Most unstable modes do not reach the maximum amplitudes estimated from the linear theory by computing displacement surfaces associated with the modes. Surprisingly, even these large-amplitude distortions are fitted reasonably well by displacement surfaces computed from the linear theory. Large-amplitude helical and elliptical distortions lead to significant differences in the nonlinear development of the jets as a function of the jet density. Jets less dense than the surrounding medium entrain material, lose energy through shock heating, and slow down relatively rapidly once large-amplitude distortions develop as a result of instability. Jets more dense than the surrounding medium lose much less energy as they entrain and accelerate the surrounding medium. The dense jet maintains a high-speed spine that exhibits large-amplitude helical twisting and elliptical distortion over considerable distance without disruption of internal jet structures as happens for the less dense jets. This dense high-speed spine is surrounded by a less dense sheath consisting of slower moving jet fluid and magnetic field mixed with the external medium. Simulated synchrotron intensity and fractional polarization images from these calculations provide a considerably improved connection between simulation results and jet observations than do images made using the fluid variables alone. Intensity structure in the dense jet simulation appears remarkably similar to structure observed in the Cygnus A jet. These simulations suggest that the extended jets in high-power radio sources propagate to such large distances without disruption by entrainment because they are surrounded by a lobe or cocoon whose density is less than the jet density.

Effects of Magnetic Fields on Mass Entrainment of Supermagnetosonic Jets

We have performed three-dimensional MHD equilibrium jet simulations that have been designed to excite the Kelvin-Helmholtz (K-H) instability and allow us to investigate the spatial growth of the mixing layer between a magnetized jet and an initially unmagnetized external medium. These simulations differ in the magnetic field strength and orientation, in the jet-to-ambient density ratio, and in the amplitude of the initial (velocity) perturbation. We calculate as a direct measure of mass entrainment the mass of magnetized or high axial velocity material and compare the growth of entrained mass with dynamical and potentially observable properties of a jet. An equipartition toroidal field (whose magnetic pressure is approximately equal to the jets thermal pressure) can inhibit the growth of the K-H instability and reduce mass entrainment significantly. An equipartition axial field has a slight stabilizing effect and reduces mass entrainment relative to a weak field for comparable magnetosonic Mach number. As the jet and ambient medium are mixed, the width of simulated total synchrotron intensity images increases and the fractional polarization of the jet decreases. In these simulations the jet evolves to a fast-moving magnetized spine surrounded by a slower moving, less magnetized sheath. These centralized spines are more easily disrupted in jets less dense than the surrounding medium. As a consequence of their greater instability, simulations with axial magnetic fields are more likely than simulations with toroidal magnetic fields to filament into axial (matter) streams. In both the width of the simulated intensity images and in the mass of magnetized material, we see evidence for a linear growth stage, a nonlinear growth stage, and a final saturation stage. Results from a normal-mode analysis suggest that the initial linear stage of mixing coincides with growth of the K-H-unstable normal surface modes and a spatial progression from higher to lower order modes. The nonlinear stage coincides with large-amplitude elliptical distortion to the jet cross section and filamentation of the jet. A subset of simulations was run at lower (9 zones/jet radius) and higher (25 zones/jet radius) spatial resolutions than the typical moderate spatial resolution of 15 zones/jet radius. We find that the instability saturates at approximately the same amount of entrained mass (relative to the jet mass) in the moderate- and high-resolution cases, although the transition between the linear and nonlinear stages is closer to the inlet in the higher resolution simulations.

Origin of the structures and polarization in the classical double 3C 219

Scaled-array VLA observations of the classical double radio galaxy 3C 219 at 1.4, 1.5, 1.7, and 4.9 GHz with 1.4″ resolution have been used to derive the spectral and polarimetric properties of the source. The extended emission of the lobes is filamentary, as in other well-resolved radio galaxies. A second type of filamentation, spatially independent of the total intensity filaments, is found in the depolarization distribution of the source. The depolarization filaments are associated with strong local gradients in the rotation measure and may indicate that a clumpy magnetoionic medium surrounds the radio galaxy

Numerical simulations of a restarting jet

The first self-consistent two-dimensional numerical simulation of an axisymmetric intermittent jet is presented. It is found that if the jet parameters at the jet nozzle do not vary widely from one duty cycle to the next, the restarted jet will always be overdense if the original jet is underdense relative to the quiescent intergalactic medium. Although the working surface advance speed of the restarted jet is greater than that of the original jet, the Mach number of the advance speed is less. Because the advance speed Mach number of the new working surface is relatively low, the bow shock excited by the new jet is weak regardless of the strength of the original bow shock in the quiescent ambient medium. Because the bow shock and terminal Mach disk must have comparable strengths, the brightness contrast of emission features associated with the shock should be roughly the same. Without the momentum flux of the jet, the hot spot expands in a time short compared with the duty cycle. 27 refs.

Hierarchical numerical cosmology with hydrodynamics: Methods and code tests

HierarchicalNumericalCosmologywithHydro dynamics:Metho dsandCo deTestsPeter Anninos, Michael L. NormanLaboratory forComputationalAstrophysicsNational Center forSupercomputing ApplicationsUniversity ofIl linois at Urbana-Champaign405N. MathewsAve., Urbana, IL 61801andDavid A. ClarkeHarvard-Smithsonian CFA60Garden St., Cambridge, MA 02138We describ e a two-level hierarchical three-dimensional numerical co de designedto simulate the formation of galaxies and other larger scale structures in an expandinguniverse with Newtonian gravity and radiative co oling.The basis of the hierarchicalco de is a standard particle-mesh (PM) algorithm used to evolve the dark matter con-stituents and an ideal nonrelativistic MHD uid solver to evolve the gas comp onentson a cubical Cartesian grid with variable timesteps.Within the parent cub ewe canconstruct a smaller subgrid ( xed in space) to resolve ner scale structures, provid-ing a larger dynamical rangeover standard single grid co deswithout the enormousdemand for memory and execution time.The elds from the parent grid are treatedasexternal eldsinthesubgridevolutionandarepasseddownonlyb oundary1

ON THE RELIABILITY OF ZEUS-3D

Recent and not-so-recent critiques of the widely used magnetohydrodynamics (MHD) code, ZEUS-3D, challenge its reliability and efficiency suggesting that its MHD algorithm is capable of “significant errors” in some simple one-dimensional shock-tube problems. I show that these concerns are either inapplicable in multi-dimensional astrophysical applications, or result from a misuse of the code rather than “flaws” in its design. I also describe a few multi-dimensional test problems including one for super-Alfv´ enic turbulence, and highlight some recent innovations and improvements to the code now available online.

Ram-pressure confinement of a hypersonic jet

The results of a high-resolution, hydrodynamical simulation of an extremely supersonic jet with a Mach number (relative to the undisturbed ambient medium) of 4650 are presented. Both the Mach number and the final length of the jet are greater than those of any previously published simulation. It is found that the hypersonic jet is highly dynamic in nature with varying head velocity and shape; the importance of the back action of the cocoon upon the jet is also clearly seen. Such hypersonically moving jets can account for the observations of luminous extragalactic radio jets, associated with classical double radio sources, which appear to be overpressured with respect to the surrounding ambient medium