Shocks, Outflows and Bubbles: New Views on Pulsars and their Winds

A typical young pulsar slows down at an imperceptible rate, its spin period increasing by less than 10 microseconds over the course of a year. However, the inertia of a pulsar is so extreme that to effect this tiny change in rotation rate, the star must dissipate about 10^46 ergs of kinetic energy. Observations of pulsars and their surroundings demonstrate that this ``spin-down energy'' is expelled into the pulsar's surroundings in spectacular fashion, in the form of a relativistic wind of charged particles and magnetic fields. In this review I highlight some recent observational results on pulsar winds at radio, X-ray and optical wavelengths, and explain what we can learn from these data about shock structure, particle acceleration and the interstellar medium.Comment: 8 pages, 4 embedded EPS figures, uses ws-procs9x6.cls. To appear in proceddings of "Texas in Tuscany" (XXI Symposium on Relativistic Astrophysics

Analytical shock solutions at large and small Prandtl number

Exact one-dimensional solutions to the equations of fluid dynamics are derived in the large-Pr and small-Pr limits (where Pr is the Prandtl number). The solutions are analogous to the Pr = 3/4 solution discovered by Becker and analytically capture the profile of shock fronts in ideal gases. The large-Pr solution is very similar to Becker's solution, differing only by a scale factor. The small-Pr solution is qualitatively different, with an embedded isothermal shock occurring above a critical Mach number. Solutions are derived for constant viscosity and conductivity as well as for the case in which conduction is provided by a radiation field. For a completely general density- and temperature-dependent viscosity and conductivity, the system of equations in all three limits can be reduced to quadrature. The maximum error in the analytical solutions when compared to a numerical integration of the finite-Pr equations is O(1/Pr) for large Pr and O(Pr) for small Pr.Comment: 11 pages, 6 figures. Accepted for publication in Journal of Fluid Mechanics Rapid

Wind tunnel model damper

Damper system for alleviating air flow shock loads on wind tunnel models

Buoyancy instability of homologous implosions

I consider the hydrodynamic stability of imploding gases as a model for inertial confinement fusion capsules, sonoluminescent bubbles and the gravitational collapse of astrophysical gases. For oblate modes under a homologous flow, a monatomic gas is governed by the Schwarzschild criterion for buoyant stability. Under buoyantly unstable conditions, fluctuations experience power-law growth in time, with a growth rate that depends upon mean flow gradients and is independent of mode number. If the flow accelerates throughout the implosion, oblate modes amplify by a factor (2C)^(|N0| ti)$, where C is the convergence ratio of the implosion, N0 is the initial buoyancy frequency and ti is the implosion time scale. If, instead, the implosion consists of a coasting phase followed by stagnation, oblate modes amplify by a factor exp(pi |N0| ts), where N0 is the buoyancy frequency at stagnation and ts is the stagnation time scale. Even under stable conditions, vorticity fluctuations grow due to the conservation of angular momentum as the gas is compressed. For non-monatomic gases, this results in weak oscillatory growth under conditions that would otherwise be buoyantly stable; this over-stability is consistent with the conservation of wave action in the fluid frame. By evolving the complete set of linear equations, it is demonstrated that oblate modes are the fastest-growing modes and that high mode numbers are required to reach this limit (Legendre mode l > 100 for spherical flows). Finally, comparisons are made with a Lagrangian hydrodynamics code, and it is found that a numerical resolution of ~30 zones per wavelength is required to capture these solutions accurately. This translates to an angular resolution of ~(12/l) degrees, or < 0.1 degree to resolve the fastest-growing modes.Comment: 10 pages, 3 figures, accepted for publication in the Journal of Fluid Mechanics Rapid

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