The dynamics of self-gravitating gaseous density perturbations in the tightly wound spiral-arm model of the forcing potential (Brown 1969) is investigated. The cloud ensemble of the cold phase of the interstellar medium is regarded as a collisional gas whose 'molecules' are the clouds themselves, and the dynamical evolution of density perturbations is calculated assuming this gas obeys a polytropic pressure-density law. It is suggested that the formation of extreme Population I objects found predominantly along the arms of Sb/Sc systems is regulated by an overall energy balance in the cloud fluid. A single parameter is found which appears to characterize the flow's gravitational response to perturbations; this spiral parameter, Q-sub-sp, differs from the Toomre Q parameter by a factor of the square root of the density enhancement at the shock. It is necessary but not sufficient that Q-sub-sp be less than unity for significant growth to occur.
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Balbus et al. (1985) studied this question.