Does ``tau~1'' Terminate the Isothermal Evolution of Collapsing Clouds?

Details Does ``tau~1'' Terminate the Isothermal Evolution of Collapsing Clouds? Does ``tau~1'' Terminate the Isothermal Evolution of Collapsing Clouds?

Jan 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999apj...510..822m&link_type=abstract

The Astrophysical Journal, Volume 510, Issue 2, pp. 822-827.

Astronomy and Astrophysics

Astronomy

45

Hydrodynamics, Ism: Clouds, Radiative Transfer, Stars: Formation

Scientific paper

We examine when gravitationally collapsing clouds terminate their isothermal evolution. According to our previous work, the condition with which isothermality is broken down is classified into three cases, i.e., when (1) the compressional heating rate overtakes the thermal cooling rate, (2) the optical depth for thermal radiation reaches unity, or (3) the compressional heating rate becomes comparable with the energy transport rate because of radiative diffusion. In the present paper this classification is extended to more general values of the initial cloud temperature T_init and opacity kappa, and we determine the critical densities with which these conditions are satisfied. For plausible values of T_init and kappa, we find that the isothermal evolution ceases when case 1 or 3 is satisfied, and case 2 has no significance. We emphasize that the condition of ``tau~1'' never terminates isothermality, but nonisothermal evolutions begin either earlier or later depending on the initial temperature and opacity. This result contrasts with the conventional idea that opaqueness breaks isothermality. On the basis of the critical density discussed above, the minimum Jeans mass for fragmentation, M_F, is reconsidered. In contrast to the results by previous authors that M_F is insensitive to T_init and kappa, we find that M_F can be substantially larger than the typical value of ~10^-2 M_solar depending on T_init and kappa. In particular, M_F increases with decreasing metallicity, M_F~kappa^-1, for low-metal clouds. A cloud with kappa=10^-4 cm^2 g^-1 and T_init=10 K yields M_F=3.7 M_solar. Finally, our critical densities would be helpful for hydrodynamic simulations that are intended to simply handle the hardening of the equation of state.

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