We compute the production rate of photons in the ionizing Lyman continua ( LyC ) of H i ( \lambda \leq 912 Å ) , He i ( \lambda \leq 504 Å ) , and He ii ( \lambda \leq 228 Å ) using recent stellar evolutionary tracks coupled to a grid of non-LTE , line-blanketed WM-basic model atmospheres .
The median LyC production efficiency is Q _ { LyC } = ( 6 \pm 2 ) \times 10 ^ { 60 } LyC photons per M _ { \odot } of star formation ( range [ 3.1 - 9.4 ] \times 10 ^ { 60 } ) corresponding to a revised calibration of 10 ^ { 53.3 \pm 0.2 } photons s ^ { -1 } per M _ { \odot } yr ^ { -1 } .
Efficiencies in the helium continua are Q _ { HeI } \approx 10 ^ { 60 } photons M _ { \odot } ^ { -1 } and Q _ { HeII } \approx 10 ^ { 56 } photons M _ { \odot } ^ { -1 } at solar metallicity and larger at low metallicity .
The critical star formation rate needed to maintain reionization against recombinations at z \approx 7 is \dot { \rho } _ { SFR } = ( 0.012 M _ { \odot } { yr } ^ { -1 } { Mpc } ^ { -3 } ) [ ( 1 + z ) / 8 % ] ^ { 3 } ( C _ { H } / 3 ) ( 0.2 / f _ { esc } ) for fiducial values of IGM clumping factor C _ { H } \approx 3 and LyC escape fraction f _ { esc } \approx 0.2 .
The boost in LyC production efficiency is an important ingredient , together with metallicity , C _ { H } , and f _ { esc } , in assessing whether IGM reionization was complete by z \approx 7 .
Monte-Carlo sampled spectra of coeval starbursts during the first 5 Myr have intrinsic flux ratios of F ( 1500 ) / F ( 900 ) \approx 0.4 - 0.5 and F ( 912 ^ { - } ) / F ( 912 ^ { + } ) \approx 0.4 - 0.7 in the far-UV ( 1500 Å ) , the LyC ( 900 Å ) , and at the Lyman edge ( 912 Å ) .
These ratios can be used to calibrate the LyC escape fractions in starbursts .