The Numerical Simulation of Radiative Shocks I: The elimination of numerical shock instabilities using a localized oscillation filter

We address a numerical instability that arises in the directionally split computation of hydrodynamic flows when shock fronts are parallel to a grid plane. Transverse oscillations in pressure, density and temperature are produced that are exacerbated by thermal instability when cooling is present, forming post--shock `stripes'. These are orthogonal to the classic post--shock 'ringing' fluctuations. The resulting post--shock `striping' substantially modifies the flow. We discuss three different methods to resolve this problem. These include (1) a method based on artificial viscosity; (2) grid--jittering and (3) a new localized oscillation filter that acts on specific grid cells in the shock front. These methods are tested using a radiative wall shock problem with an embedded shear layer. The artificial viscosity method is unsatisfactory since, while it does reduce post--shock ringing, it does not eliminate the stripes and the excessive shock broadening renders the calculation of cooling inaccurate, resulting in an incorrect shock location. Grid--jittering effectively counteracts striping. However, elsewhere on the grid, the shear layer is unphysically diffused and this is highlighted in an extreme case. The oscillation filter method removes stripes and permits other high velocity gradient regions of the flow to evolve in a physically acceptable manner. It also has the advantage of only acting on a small fraction of the cells in a two or three dimensional simulation and does not significantly impair performance.Comment: 20 pages, 6 figures, revised version submitted to ApJ Supplement Serie

The Evolution of Shocks in Blazar Jets

We consider the shock structures that can arise in blazar jets as a consequence of variations in the jet flow velocity. There are two possible cases: (1) A double shock system consisting of both a forward and reverse shock (2) A single shock (either forward or reverse) together with a rarefaction wave. These possibilities depend upon the relative velocity of the two different sections of jet. Using previously calculated spherical models for estimates of the magnetic field and electron number density of the emission region in the TeV blazar Markarian 501, we show that this region is in the form of a thin disk, in the plasma rest frame. It is possible to reconcile spectral and pair opacity constraints for MKN 501 for Doppler factors in the range of 10--20. This is easiest if the corrections for TeV absorption by the infrared background are not as large as implied by recent models.Comment: 19 pages, 8 figures, accepted for publication in PASA, 19, No.1, AGN Variability across the Electromagnetic Spectru

Instability of toroidal magnetic field in jets and plerions

Jets and pulsar-fed supernova remnants (plerions) tend to develop highly organized toroidal magnetic field. Such a field structure could explain the polarization properties of some jets, and contribute to their lateral confinement. A toroidal field geometry is also central to models for the Crab Nebula - the archetypal plerion - and leads to the deduction that the Crab pulsar's wind must have a weak magnetic field. Yet this `Z-pinch' field configuration is well known to be locally unstable, even when the magnetic field is weak and/or boundary conditions slow or suppress global modes. Thus, the magnetic field structures imputed to the interiors of jets and plerions are unlikely to persist. To demonstrate this, I present a local analysis of Z-pinch instabilities for relativistic fluids in the ideal MHD limit. Kink instabilities dominate, destroying the concentric field structure and probably driving the system toward a more chaotic state in which the mean field strength is independent of radius (and in which resistive dissipation of the field may be enhanced). I estimate the timescales over which the field structure is likely to be rearranged and relate these to distances along relativistic jets and radii from the central pulsar in a plerion. I conclude that a concentric toroidal field is unlikely to exist well outside the Crab pulsar's wind termination shock. There is thus no dynamical reason to conclude that the magnetic energy flux carried by the pulsar wind is much weaker than the kinetic energy flux. Abandoning this inference would resolve a long-standing puzzle in pulsar wind theory.Comment: 28 pages, plain TeX. Accepted for publication in Ap

Numerical wave optics and the lensing of gravitational waves by globular clusters

We consider the possible effects of gravitational lensing by globular clusters on gravitational waves from asymmetric neutron stars in our galaxy. In the lensing of gravitational waves, the long wavelength, compared with the usual case of optical lensing, can lead to the geometrical optics approximation being invalid, in which case a wave optical solution is necessary. In general, wave optical solutions can only be obtained numerically. We describe a computational method that is particularly well suited to numerical wave optics. This method enables us to compare the properties of several lens models for globular clusters without ever calling upon the geometrical optics approximation, though that approximation would sometimes have been valid. Finally, we estimate the probability that lensing by a globular cluster will significantly affect the detection, by ground-based laser interferometer detectors such as LIGO, of gravitational waves from an asymmetric neutron star in our galaxy, finding that the probability is insignificantly small.Comment: To appear in: Proceedings of the Eleventh Marcel Grossmann Meetin