Below
, gas is essentially isothermal
.
This corresponds to points number 13 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 StephanBoltzman constant.
Main heating process for
is
cosmicray 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 LarsonPenston selfsimilar
solution.
Kohji Tomisaka
20091210