= Solution
A dense cloud core first collapses when <self-gravity> overwhelms its effective support. While radiation escapes readily, compression can remain approximately isothermal and the <Jeans mass> decreases as <density> rises, encouraging <gravitational fragmentation>. Angular <momentum> usually leads to a disk rather than unrestricted spherical infall.
As the central <optical depth> increases, cooling becomes slower than compression and <pressure> produces a <first hydrostatic core>. <molecular hydrogen> dissociation near $2000\ \mathrm K$ absorbs compressional <energy> and lowers the effective adiabatic response, permitting a <second collapse of a protostar>. After dissociation the gas stiffens and a much more compact stellar core forms. An <accretion> shock and surrounding disk then convert infall <energy> into radiation. A small central core forms before most of the envelope arrives, as demonstrated in radiation-hydrodynamic collapse calculations.<Numerical Calculations of the Dynamics of a Collapsing Proto-Star by Richard B. Larson>[Abstract: nonhomologous central core formation, subsequent envelope accretion and infrared reprocessing]{ref}
The isothermal <inside-out collapse of a singular isothermal sphere> model provides one idealized supply law, $\dot M\sim a_T^3/G$, but rotation, <magnetic fields> and an unsteady reservoir modify real <accretion>. Its <luminosity> scale is $L_{\rm acc}\sim GM\dot M/r_*$. Dust can absorb the emerging short-wavelength radiation and re-emit it in the infrared, so an embedded source need not have a directly visible stellar photosphere.
As envelope <accretion> declines, gravitational contraction becomes important on the <Kelvin-Helmholtz cooling time> $t_{\rm KH}\sim GM^2/(r_*L)$. <deuterium-burning energy-generation rate> can temporarily influence the radius; sustained core <hydrogen burning> eventually establishes the <main sequence> if the final <mass> is sufficient. A low-mass convective object approaches along a Hayashi-like track, while more massive objects need not share that track. \b[<accretion>, contraction and nuclear burning are distinct <energy> sources], and a <protostar> is not generally a fixed-mass object.
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