Absorption Line Spectroscopy of Gravitationally-Lensed Galaxies: Further   Constraints on the Escape Fraction of Ionizing Photons at High Redshift
  The fraction of ionizing photons escaping from high-redshift star-forming galaxies remains a key obstacle in evaluating whether galaxies were the primary agents of cosmic reionization. We previously proposed using the covering fraction of low-ionization gas, measured via deep absorption line spectroscopy, as a proxy. We now present a significant update, sampling seven gravitationally-lensed sources at $4<z<5$. We show that the absorbing gas in our sources is spatially inhomogeneous with a median covering fraction of 66\%. Correcting for reddening according to a dust-in-cloud model, this implies an estimated absolute escape fraction of $\simeq19\pm6$\%. With possible biases and uncertainties, collectively we find the average escape fraction could be reduced to no less than 11\%, excluding the effect of spatial variations. For one of our lensed sources, we have sufficient signal/noise to demonstrate the presence of such spatial variations and scatter in its dependence on the Ly$\alpha$ equivalent width, consistent with recent simulations. If this source is typical, our lower limit to the escape fraction could be reduced by a further factor $\simeq$2. Across our sample, we find a modest anti-correlation between the inferred escape fraction and the local star formation rate, consistent with a time delay between a burst and leaking Lyman continuum photons. Our analysis demonstrates considerable variations in the escape fraction consistent with being governed by the small-scale behavior of star-forming regions, whose activities fluctuate over short timescales. This supports the suggestion that the escape fraction may increase toward the reionization era when star formation becomes more energetic and burst-like. 
Nicha Leethochawalit, Tucker A. Jones, Richard S. Ellis, Daniel P.   Stark, Adi Zitrin
astro-ph.GA