  The average rate of emission of ionizing radiation per unit volume (or
emissivity) in the universe can be calculated as the ratio of the intensity of
the ionizing background to the mean free path of ionizing photons. The
intensity of the background is measured from the mean transmitted flux of the
Lya forest, and the mean free path is measured from the abundance of Lyman
limit systems, which has been observed so far up to z=4. This yields an
emissivity that is not larger than 7 ionizing photons per Hubble time for each
atom in the universe at z=4, which may reasonably arise from QSOs and
star-forming galaxies. In order for the reionization to end by z=6, and
assuming that the clumping factor of ionized gas during the reionization epoch
is close to unity, this ionizing emissivity cannot decline from z=4 up to z ~ 9
by more than a factor 1.5. If the clumping factor were much larger than unity,
then the emissivity would need to rapidly increase with redshift. Unless the
ionizing emissivity increases substantially from z=4 to z ~ 10 - 20, the
Thomson optical depth to the CMB must be in the range 0.045 < tau < 0.09.
