The Isothermal Accretion Rate c_s cubed over G and the Time Needed to Build a Star

This paper addresses a single question: At what rate does an isothermal sphere feed its central protostar in the classic inside-out collapse, and how long does that rate take to assemble stars of one and of ten solar masses at observed core temperatures? Using published molecular-cloud and young-stellar-object measurements as inputs, and carrying the spin-torsion density bound of 9.72 x 10^57 kilograms per cubic metre and its critical shear of 8.56 x 10^32 per second as fixed comparison scales, the calculation finds that the accretion rate at 10 K is about 1.6 x 10^-6 solar masses per year, building a solar-mass star in roughly six hundred thousand years, in line with inferred Class 0 and Class I lifetimes; at 30 K the rate rises by the temperature to the three-halves power and a ten-solar-mass star can be assembled in a comparable interval, which is why warm massive cores are not excluded by the accretion clock alone. The headline values are: mdot 10K = 1.54e-06; t 1Msun yr = 6.47e+05; mdot 30K = 8.03e-06. All values are computed from the stated formulae and inputs; this is a simulated and computed study, not a measurement. Where the comparison scales supplied by the torsion framework turn out to be too remote to influence the process, that outcome is reported as a negative result rather than passed over.