We follow the perturbations in the flow of interstellar gas which result from steady forcing by spiral gravitational fields of various strengths. The density response is quite nonlinear even if the amplitude of the spiral field maintained by the disk stars is only a small fraction of the basic axisymmetric field. An analytical study of the properties of slightly nonlinear flows yields certain results which are qualitatively similar to those found numerically for fully nonlinear flows. Galactic shocks arise naturally, indeed necessarily, if the strength of the underlying spiral gravitational field exceeds a certain critical value. The breadth of the zone of high gas compression depends critically on whether the Dopplershifted phase-velocity of the stellar density wave is greater than or less than the "effective acoustic speed" of the gas. In the former case, very narrow compression zones result; in the latter, quite broad zones. This distinction may explain why some galaxies have narrow optical arms while others have broad optical arms. In addition, a certain range of values for the intrinsic frequency of the wave gives rise to ultraharmonic resonances which can introduce secondary compressions of the interstellar gas. This result may relate directly to the origin of the Carina spiral feature in our own Galaxy as well as to the phenomena of branches, spurs, and feathers which are often seen in external spiral galaxies. Subject headings: galactic structure-interstellar matter

Quasi-steady flows of interstellar gas in a spiral gravitational field are followed for the purpose of investigating galactic shocks and the resultant processes of the formation of stars and interstellar clouds. We model the interstellar medium with two stable phases in which thermal balance is maintained through heating by low-energy cosmic rays. The problem, including transitions between the two phases, is given a general formulation but is solved in an approximation which ignores the difference in fluid velocities of the two phases. We also assume that the cosmic-ray flux is uniform in circles about the center of the Galaxy and that the relative abundances of the chemical elements are "normal." For a spiral gravitational field with strength equal to 5 percent that of the axisymmetric field at 10 kpc from the galactic center, the density ratio at maximum and minimum compressions is 9:1 for the intercloud medium while it is 40:1 for the gas in a typical cloud. During the decompression phase of the flow, a small percentage of the mass of the clouds evaporates to become intercloud material, but this small amount is recovered in the shock. As a by-product of phase transitions, the properties of the clouds in the regions between spiral arms are such as to make their detection in 21-cm absorption very difficult. In the absence of the cloud phase, we determine the thickness of the shock layer in the intercloud medium to be typically 50 pc. An interstellar cloud immersed as a test particle in the intercloud medium experiences a dynamic rather than a quasi-static compression as it passes through the shock layer. The critical mass for the gravitational collapse of a cloud is reduced by a large factor because of the compression in the shock. I. INTRODUCTION The problems discussed in this paper are motivated by the desire to understand the detailed mechanisms which trigger the formation of stars in normal spiral galaxies. Central to our discussion are two fundamental ideas: (i) spiral galactic shocks and (ii) the two-phase model of the interstellar medium. Within this context, we concentrate on the roles played by gravitational and thermal mechanisms. We avoid the vexing problem of the magnetic-field geometry by ignoring at the very outset the effects of the interstellar magnetic field. We do this not because we feel these effects to be unimportant, but because we wish to keep the present discussion as simple as possible. a) Basic Concepts On a small scale the main obstacle to star formation is that most of the interstellar clouds would not be even remotely bound by their self-gravitation if the clouds were * Now at the State University of New York at Stony Brook.