What physical event causes the initial free-fall collapse to halt and form the first hydrostatic core?

The core becoming optically thick due to high density, trapping internal radiation and increasing temperature

Once a fragment overcomes its Jeans Mass and begins rapid free-fall collapse, the process does not proceed unimpeded to stellar status immediately. As the core shrinks, its density steadily increases. When the density reaches a critical point, estimated around $10^{-13} ext{ g}/ ext{cm}^3$, the material becomes optically thick. This means the core can no longer radiate away the energy generated by the gravitational compression; the heat is trapped inside. This trapping of internal radiation causes a rapid and significant temperature increase, which consequently generates enough thermal pressure to counteract the gravitational infall velocity, thus halting the initial phase of collapse and forming the object termed the first hydrostatic core.