  It has been a longstanding problem to determine, as far as possible, the
characteristic masses of stars in terms of fundamental constants; the almost
complete invariance of this mass as a function of the star-forming environment
suggests that this should be possible. Here I provide such a calculation. The
typical stellar mass is set by the characteristic fragment mass in a
star-forming cloud, which depends on the cloud's density and temperature
structure. Except in the very early universe, the latter is determined mainly
by the radiation released as matter falls onto seed protostars. The energy
yield from this process is ultimately set by the properties of deuterium
burning in protostellar cores, which determines the stars' radii. I show that
it is possible to combine these considerations to compute a characteristic
stellar mass almost entirely in terms of fundamental constants, with an
extremely weak residual dependence on the interstellar pressure and
metallicity. This result not only explains the invariance of stellar masses, it
resolves a second mystery: why fragmentation of a cold, low-density
interstellar cloud, a process with no obvious dependence on the properties of
nuclear reactions, happens to select a stellar mass scale such that stellar
cores can ignite hydrogen. Finally, the weak residual dependence on the
interstellar pressure and metallicity may explain recent observational hints of
a smaller characteristic mass in the high pressure, high metallicity cores of
giant elliptical galaxies.
