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PLASMA ASTROPHYSICS 121 the Sun and, by implication, that magnetized winds could play an important role in spinning down stars. Later, spurred by observations of accretion disks and jets around a wide variety of objects including protostars, white dwarfs, neutron stars, and black holes, astrophysicists developed models of magnetized winds and jets in disk geometry, included relativistic effects, strong magnetic fields, rapid rotation, and the effects of MHD waves and instabilities on the disks and the outflows. (See Figure 7.1.) Particle Acceleration in Shocks Although our understanding of high-Mach-number shocks is seriously incomplete, studies of particle acceleration in shocks have given us the best theories to date of cosmic-ray acceleration in the interstellar medium. The most notable successes of the theory are that it predicts approximately the correct power-law index of the energy spectrum, cosmic-ray intensity, and cosmic-ray composition (with the exception of the electron-to-ion ratio). Progress has been made on the analytical front through both kinetic and hydrodynamical descriptions of the particles and the shock and on the computational front through Monte Carlo simulations. Magnetized Convection in Stars The subject of stellar convection has a long history, since it was recognized many years ago that the radiative energy flux through a stellar envelope is limited by convective instability. Interest in the interaction of magnetic fields with convection stems from observations of the solar magnetic activity cycle and similar cycles on other stars, which show that magnetic fields are rapidly regenerated and reconfigured in the interiors of convective stars. Until recently, stellar convection was described only by dimensional arguments or mixing length theory. With the development of parallel and massively parallel computer architecture, it has become possible to simulate compressible convection in three dimensions and to include the effects of magnetic fields. Although the smallest relevant length scales are still unresolved by these calculations, the effects of buoyancy, concentration of flux into ropes, and dynamo activityâall processes that are believed to play an important role in the dynamics of stellar magnetic fieldsâare observed and can be studied. Formation of Low-Mass Stars It was recognized long ago that the ratio of magnetic flux to mass is much higher in the interstellar medium than it is in stars. It was proposed that interstellar clouds are supported against their gravitational fields by magnetic forces, that the fields slowly escape from the clouds by ion-neutral relative drift, and that the
PLASMA ASTROPHYSICS 122 FIGURE 7.1 A plasma kinetic-theory model of a relativistic shock wave in the Crab Nebula. Upper left: Contour plot of the surface brightness of x-ray emission at 0.8 Ã . The ''wisp" features are thought to be visible manifestations of the otherwise radiationless outflow of rotational energy from the central pulsar. Upper right: Geometry of the outflow from the pulsar used in the construction of the theoretical model. The pulsar is assumed to lose energy in the form of a magnetohydrodynamic wind, flowing relativistically in an angular sector around the rotational equator of the pulsar. The magnetic field direction is orthogonal to the radial flow. The wind's composition is a mixture of electrons, positrons, and heavy ions, and it is quasi-neutral in the region upstream of the shock wave that terminates the outflow. Estimates indicate that a shock wave forms in the region of the observed wisps. The vector n points toward the observer. Lower panel: Comparison of the surface brightness (solid line) measured in the strip between the dashed lines in the upper panel with that predicted by the model (dashed line). The model represents the electron- positron pairs as a relativistically hot Maxwellian fluid, heated by the collisionless subshock at the leading edge of the shock structure. Heavy ions are modeled as a stream of particles gyrating in the electromagnetic field of the shock, compressing the magnetic field and pair plasma at each turning point of the ions' orbit. Each such compression appears as a surface brightness enhancement. The model successfully predicts the brightness of the faint wisp at -7 arc sec. (Reprinted, by permission, from M. Hoshino, J. Arons, Y.A. Gallant, and A.B. Langdon, Astrophysical Journal 390:454, 1992, and Y.A. Gallant and J. Arons, Astrophysical Journal 435:230, 1994. Copyright Â© 1992, 1994 by the American Astronomical Society.)