Does Turbulent Pressure Behave as a Logatrope?

Abstract

We present numerical simulations of an isothermal turbulent gas undergoing gravitational collapse, aimed at testing for ``logatropic'' behavior of the form $P_t\sim \log \rho$, where $P_t$ is the ``turbulent pressure'' and $\rho$ is the density. To this end, we monitor the evolution of the turbulent velocity dispersion $\sigma$ as the density increases during the collapse. A logatropic behavior would require that $\sigma \propto {\rho }^{-1/2}$, a result which, however, is not verified in the simulations. Instead, the velocity dispersion increases with density, implying a polytropic behavior of $P_t$. This behavior is found both in purely hydrodynamic as well as hydromagnetic runs. For purely hydrodynamic and rapidly-collapsing magnetic cases, the velocity dispersion increases roughly as $\sigma \propto {\rho }^{1/2}$, implying $P_t\sim {\rho }^2$, where $P_t$ is the turbulent pressure. For slowly-collapsing magnetic cases the behavior is close to $\sigma \propto {\rho }^{1/4}$, which implies $P_t\sim {\rho }^{3/2}$. We thus suggest that the logatropic ``equation of state'' may represent only the statistically most probable state of an ensemble of clouds in equilibrium between self-gravity and kinetic support, but does not adequately represent the behavior of the ``turbulent pressure'' within a cloud undergoing a dynamic compression due to gravitational collapse. Finally, we discuss the importance of the underlying physical model for the clouds (in equilibrium vs. dynamic) on the results obtained.

Accepted in ApJ. 10 pages, 3 postscript figures

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