DOES TURBULENT PRESSURE BEHAVE AS A LOGATROPE

We present numerical simulations of an isothermal turbulent gas underg oing gravitational collapse, with the aim of testing for ''logatropic' ' behavior of the form P-t similar to log rho, where P-t is the turbul ent pressure and rho is the density. To this end, we monitor the evolu tion of the turbulent velocity dispersion sigma as the density increas es during collapse. A logatropic behavior would require sigma proporti onal to rho(-1/2), a result that is not, however, verified in the simu lations. Instead? the velocity dispersion increases with density, impl ying a polytropic behavior of P-t. This behavior is found both in pure ly hydrodynamic and in hydromagnetic runs. For purely hydrodynamic and rapidly collapsing magnetic cases, the velocity dispersion increases roughly as sigma proportional to rho(1/2), implying P-t similar to rho (2), where P-t is the turbulent pressure. For slowly collapsing magnet ic cases, the behavior is close to sigma proportional to rho(1/4), imp lying P-t similar to rho(3/2). We thus suggest that the logatropic ''e quation 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 th e turbulent pressure within a cloud undergoing a dynamic compression a s a result of gravitational collapse. Finally, we discuss the importan ce of the underlying physical model of the clouds (equilibrium versus dynamic) for the results obtained.