### Isothermal Phase

Below , gas is essentially isothermal . This corresponds to points number 1-3 of Figure 4.16. Since internal energy of gas is transferred to the thermal energy of dusts by collisions, the main coolant in this regime is the dust thermal radiation. The cooling rate per mass is
 (4.107)

where and represent Planck mean absorption coefficient and the Stephan-Boltzman constant. Main heating process for is cosmic-ray heating: (Goldsmith & Langer 1978). Balance between these two majors asks that temperature is constant as
 (4.108)

Heating rate due to dynamical compression,
 (4.109)

increases according to the contraction and it balances with the above cooling at the density (Masunaga, Miyama, & Inutsuka 1998).

The cloud in this phase experiences the dynamical contraction as described in section 4.5. Structure of and is well represented by the Larson-Penston self-similar solution.

Kohji Tomisaka 2012-10-03