Numerical hydrodynamic simulations are used to determine the evolution of the condensation modes for thermal instabilities in 10 to the 6th to 10 to the 8th K gas. These simulations properly take into account the effects of nonequilibrium cooling below 10 to the 6th K. It is found that only perturbations greater than about 3 kpc develop shocks in the hot environment of cooling flows. These large perturbations evolve through three distinct phases: (1) the formation of a cold core, (2) a supersonic accretion phase onto the cold core which lasts for 10 to the 5th to 10 to the 6th yr with peak shock velocities about 120 km/s, and (3) a subsonic accretion phase. The X-ray emissivity and the optical-ultraviolet line emission associated with thermal instabilities are calculated. These calculations demonstrate that the optical emission from cooling flows probably does not arise from shocked condensations. The calculated optical emission lines are of a higher ionization level and a lower luminosity than the observations. Ultraviolet lines produced in the shocks may be detectable. The core must cool significantly after the shock has dissipated before star formation can commence.
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David et al. (1988) studied this question.