Erratum - Interstellar Shock Waves with Magnetic Precursors

Abstract

The structure of steady, radiative, one-dimensional shock waves in partially ionized gas with a transverse magnetic field B 0 is investigated. Under a broad range of conditions applicable to the interstellar medium it is found that such shocks may be preceded by a " magnetic precursor " which heats and compresses the medium ahead of the front where the neutral gas undergoes a discontinuous change of state; indeed, if B 0 is sufficiently large, a shock can exist with no discontinuities in hydrodynamical variables. Within this " magnetic precursor " both ions and electrons stream through the neutral fluid with velocities which may be a significant fraction of the shock speed. The physical processes operative in such shocks are examined, including the effects of charged dust grains in dense molecular clouds. Numerical examples are shown for v s = 10 km s" 1 shocks propagating into diffuse H i or H 2. Shocks with magnetic precursors may have important consequences for the interstellar medium, some of which are briefly considered. Subject headings : hydrodynamics-interstellar : magnetic fields-interstellar : matter-shock waves I. INTRODUCTION Shock waves appear to play a major role in the dynamics and evolution of the interstellar medium. These shock waves-resulting from the expansion of H n regions, cloud-cloud collisions, stellar winds, supernova explosions, etc.-compress, heat, and accelerate interstellar gas. Numerous investigations of the structure of such shocks, including detailed modeling of the hydrodynamics, heating, cooling, chemistry, etc., have been undertaken in recent years (cf. McKee and Hollenbach 1980, and references therein). In nearly all studies of interstellar shock waves the magnetic field has been either assumed to be zero (this is usually considered-incorrectly-to be a valid approximation if pv s 2 > B 0 2 /Sn) or else has been taken to be purely transverse and " frozen " into the gas (e.g., Field et al. 1968) and amplified as the gas is compressed. The magnetic field, however, is coupled only to charged particles, and the " frozen field " assumption is valid only if both (i) the magnetic field is frozen into the ion-electron fluid, and (ii) the ions and electrons are sufficiently well coupled (by collisions) to the neutral particles so that both charged particles and neutral particles have the same bulk velocities. While the first of these requirements is usually satisfied in interstellar shocks, the second is often not. In an important but infrequently cited paper, Mullan (1971) demonstrated that the frozen field assumption breaks down for interstellar shock waves when the fractional ionization is low, as is often the case in H i regions and molecular clouds. Mullan showed that the structure of the shock wave could be significantly changed if the usual frozen field assumption is relaxed and replaced by a hydrodynamic description allowing the neutrals and the ion-electron fluid to have different flow velocities and temperatures. For magnetic field compression to take place, momentum must be transferred from the neutral gas to the ion-electron gas via ion-neutral collisions; if the ion density is low so that the rate/volume of ion-neutral collisions is small, the magnetic field will be compressed only gradually, over a length which can be several orders of magnitude longer than the neutral-neutral mean free path. Mullan demonstrated by model calculations that the extent of this region of ion-electron "slippage" could be quite appreciable. Under certain conditions, the magnetic field can begin to be compressed and accelerated by the shock before the neutral gas-dynamic shock discontinuity (the "jump front ") arrives-in this case the shock will be said to possess a "magnetic precursor." Magnetic precursors occur whenever the ion-electron fluid can propagate compressive (magnetosonic) waves at velocities larger than the shock speed v s. When the fractional ionization is low, a shock will tend to have a magnetic precursor if the magnetic field is at all significant. The intent of the present paper is to discuss the general properties of transverse magnetohydrodynamic (MHD) shock waves with magnetic precursors in media of low fractional ionization, including the effects of radiative cooling. In § II it is seen that MHD shock waves can be divided into three classes : (i) shocks without magnetic precursors (which includes the limit of B 0 0), (ii) "J-type " shocks with magnetic precursors, and (iii) " C-type " shocks ; in "J-type " shocks the neutral fluid undergoes a discontinuous compression "jump," while in " C-type " shocks all of the flow variables are continuous. The remainder of this paper concentrates on shocks with magnetic precursors. The basic MHD equations which determine the variation of the hydrodynamic variables in a time-independent flow are presented in § III. In § IV order-of-magnitude formulae are given which allow a crude estimate to be made of the size of the magnetic precursor and