ON THE HYDRODYNAMIC INTERACTION OF SHOCK-WAVES WITH INTERSTELLAR CLOUDS .1. NONRADIATIVE SHOCKS IN SMALL CLOUDS

The interstellar medium (ISM) is inhomogeneous, with clouds of various temperatures and densities embedded in a tenuous intercloud medium. S hocks propagating through the ISM can ablate or destroy the clouds, at the same time significantly altering the properties of the intercloud medium. This paper presents a comprehensive numerical study of the si mplest case of the interaction between a shock wave and a spherical cl oud, in which the shock far from the cloud is steady and planar, and i n which radiative losses, thermal conduction, magnetic fields, and gra vitational forces are all neglected. As a result, the problem is compl etely specified by two numbers: the Mach number of the shock, M, and t he ratio of the density of the cloud to that of the intercloud medium, chi. For strong shocks we show that the dependence on M scales out, s o the primary independent parameter is chi. Variations from this simpl e case are also considered: the potential effect of radiative losses i s assessed by calculations in which the ratio of specific heats in the cloud is 1.1 instead of 5/3; the effect of the initial shape of the c loud is studied by using a cylindrical cloud instead of a spherical on e; and the role of the initial shock is determined by considering the case of a cloud embedded in a wind. Local adaptive mesh refinement tec hniques with a second-order, two-fluid, two-dimensional Godunov hydrod ynamic scheme are used to address these problems, allowing heretofore unobtainable numerical resolution. Convergence studies to be described in a subsequent paper demonstrate that approximately 100 zones per cl oud radius are needed for accurate results; previous calculations have generally used about a third of this number. The results of the calcu lations are analyzed in terms of global quantities which provide an ov erall description of the shocked cloud: the size and shape of the clou d, the mean density, the mean pressure, the mean velocity, the velocit y dispersion, and the total circulation. The principal result of the c alculations is that small clouds are destroyed in several cloud crushi ng times, where the cloud crushing time t(cc) is the characteristic ti me for the shock to cross through the cloud. (Quantitatively, t(cc) = chi1/2 a0/v(b), where a0 is the initial cloud radius and v, is the vel ocity of the shock in the intercloud medium.) This result, which is co nsistent with that of Nittman, Falle, & Gaskell (1982) based on calcul ations at lower resolution, is contrary to the naive expectation that the destruction of the cloud would occur only after it had swept up a column density of intercloud material comparable to that of the initia l cloud, which requires a time of order chi1/2 t(cc). A model in which the Kelvin-Helmholtz instability fragments the cloud into successivel y smaller pieces is consistent with the numerical results. Contrary to the conclusion of Nittman et al. (1982), cloud material can be accele rated to high velocity by the passage of the shock; a model for the cl oud acceleration is developed. A quantitative model for the generation of vorticity in the shock-cloud interaction shows that vorticity is g enerated at the cloud-intercloud boundary both by the initial passage of the shock and by the subsequent flow of shocked intercloud gas past the cloud. Vorticity is also generated in the intercloud medium when the shock converges on the axis behind the cloud, producing a strong v ortex ring which is carried away by the intercloud shock. Swirling mot ions associated with the vorticity contribute to the destruction of th e cloud and produce an observable velocity dispersion perpendicular to the shock of about 0.1v(b). A model with a radiative cloud shock (gam ma(c) = 1.1) is consistent with the recent observations of a possible shocked cloud in the Cygnus Loop supernova remnant (Fesen, Kwitter, & Downes 1992). It is possible that the observed cloud is elongated alon g the line of sight, however.