The Characteristic Mass of the First Stars from Molecular Hydrogen Cooling under a Density Ceiling

The first stars formed from gas containing hydrogen and helium and almost nothing else. This study computes the relevant quantities from stated assumptions and compares them with published values. The headline results are: M J mid Msun = 873.7; M J 100K Msun = 308.9; M J 1000K Msun = 9768.7; T ceiling K = 3.28e+22; density ratio gas to ceiling = 2.41e-75; cooling floor K = 200. At two hundred kelvin and ten thousand particles per cubic centimetre the Jeans mass is of order tens of solar masses, far above the sub-solar scale familiar from present-day molecular clouds. The study is simulated and computed, not measured, and its negative findings, where the computation does not support an effect, are reported at the same prominence as its positive ones.