Second Core

After the dissociation is completed, the exponent becomes $\gamma =5/3$. This gas forms a second core composed of atomic hydrogen, which is called the second core (points number 7-8 of Figure 4.13). Since the accretion rate [eq.(4.75)] is proportional to $c_s^3$ or $T^{3/2}$, the accretion rates onto the second core $\dot{M}_{\rm 2nd}$ is larger than that of the first core $\dot{M}_{\rm 1st}$ as

$$\frac{\dot{M}_{\rm 2nd}}{\dot{M}_{\rm 1st}} \simeq 5\times ... ...10^{3.5}{\rm K}\right)^{3/2}}{\left(T/10{\rm K}\right)^{3/2}}.$$ (4.97)

Thus, the first core disappears quickly and after that the gas begins to accrete onto the second core, which will be a protostar. However, this is the case of non-rotating, spherical symmetric cloud collapse. As previously seen, the angular momentum plays a crucial role and forms a disk. The evolution must be different completely for such a case.