The Lyman-Continuum Photon Production Efficiency xi_{ion} of z~4-5
  Galaxies from IRAC-based Halpha Measurements: Implications for the Escape
  Fraction and Cosmic Reionization
  Galaxies represent one of the preferred candidate sources to drive the
reionization of the universe. Even as gains are made in mapping the galaxy UV
luminosity density to z>6, significant uncertainties remain regarding the
conversion to the implied ionizing emissivity. The relevant unknowns are the
Lyman-continuum (LyC) photon production efficiency xi_{ion} and the escape
fraction f_{esc}. As we show here, the first of these unknowns is directly
measureable in z=4-5 galaxies, based on the impact the Halpha line has on the
observed IRAC fluxes. By computing a LyC photon production rate from the
implied Halpha luminosities for a broad selection of z=4-5 galaxies and
comparing this against the dust-corrected UV-continuum luminosities, we provide
the first-ever direct estimates of the LyC photon production efficiency
xi_{ion} for the z>~4 galaxy population. We find log_{10} xi_{ion}/[Hz/ergs] to
have a mean value of 25.27_{-0.03}^{+0.03} and 25.34_{-0.02}^{+0.02} for sub-L*
z=4-5 galaxies adopting Calzetti and SMC dust laws, respectively. Reassuringly,
both values are consistent with standardly assumed xi_{ion}'s in reionization
models, with a slight preference for higher xi_{ion}'s (by ~0.1 dex) adopting
the SMC dust law. A modest ~0.03-dex increase in these estimates would result
if the escape fraction for ionizing photons is non-zero and galaxies dominate
the ionizing emissivity at z~4.4. High values of xi_{ion} (~25.5-25.8 dex) are
derived for the bluest galaxies (beta<-2.3) in our samples, independent of dust
law and consistent with results for a z=7.045 galaxy. Such elevated values of
xi_{ion} would have important consequences, indicating that f_{esc} cannot be
in excess of 13% unless the galaxy UV luminosity function does not extend down
to -13 mag or the clumping factor is greater than 3. A low escape fraction
would fit well with the low rate of LyC leakage observed at z~3.
