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First Core
After
, gas is no more isothermal and becomes adiabatic.
Between
,
gas obeys the polytropes.
Above the density
, the optical depth for the thermal radiation
exceeds unity
and radiative cooling can not compensate the
compressional heating.
As long as the temperature is low as
, neither rotation nor vibration
is excited for H molecule.
Even H gas behaves like single-atom molecule.
Thus
.
Between
,
the exponent becomes , which characterizes that the gas consists of
two-atom molecule .
In this phase, relatively large gas pressure supports against the gravity
and the cloud becomes hydrostatic (points number 4-6 of Figure 4.13).
This is called as ``first core'' made by the molecular hydrogen.
The density structure of the first core is well represented by a polytrope sphere with the specific heat
ratio of or the polytropic index
.
From equation (C.11) in Appendix C.1, such a polytrope has a mass-density relation as
|
(4.96) |
where and represent, respectively, the mass of the first core and the central density.
At the beginning, the core mass is equal to
.
As long as the mass increases a factor 3, the central density increases 5 orders of magnitude.
Next: Second Collapse
Up: Evolution to Star
Previous: Isothermal Phase
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Kohji Tomisaka
2007-07-08