In principle, measurement of the integrated
photon flux in a Balmer line
of a galaxy should provide a direct measurement of the
Lyman continuum luminosity ()
and the corresponding OB SFR in the galaxy.
The idea of this method is quite straightforward. If the galaxy as a whole is Lyman radiation-bounded, i.e. optically thick in the Lyman continuum, it will absorb all the ionizing photons emitted by the OB stars (the so called Case B recombination). Thus the total number of ionizations in the galaxy per unit time is just equal to the total number of ionizing photons emitted, and since the gas is in ionization equilibrium, these ionizations are balanced by the total number of recombinations per unit time.
However, to derive the SFR of a galaxy
from the observed photon flux in a Balmer line
one needs stellar evolution and photoionization models.
The key ingredients in these models are: a) the stellar evolutionary tracks
which describe the luminosity, effective temperature, and mass of a
star as a function on initial mass and age, b) the atmosphere models which
allow the trasformation from effective temperature and surface
gravity to colors and ionizing photon production rates, c) the initial
mass function (IMF) which gives the number of stars
formed in the mass interval (m,m+dm) per total mass of stars that are formed.
The final result is the number of ionizing photons produced in the lifetime of a massive star. With appropriate weighting from the IMF these are summed to give the the ionizing output per mass of star formation, which can be then compared with the observations.