The Critical Line Mass of Molecular Filaments and the Spacing of the Cores They Produce

This paper addresses a single question: How much mass per unit length can an isothermal filament support before it must fragment, and what separation between fragments does linear theory then predict for the conditions measured in nearby filaments? 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 thermal critical line mass at 10 K is about 16 solar masses per parsec, the value reported for quiescent filaments in Taurus and in Herschel surveys, and adding measured non-thermal motions raises the supported line mass to about one hundred solar masses per parsec; the predicted fragment spacing at a central density of 10^4 per cubic centimetre is a few tenths of a parsec, consistent with observed core separations. The headline values are: mline thermal Msun pc = 16.5; mline max Msun pc = 107.3; spacing pc = 0.37. 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.