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Empirical Constraints on the Star Formation & Redshift Dependence of the Lyman Alpha `Effective' Escape Fraction

We derive empirical constraints on the volume averaged `effective' escape fraction of Lyman Alpha (Lya) photons from star forming galaxies as a function of redshift, by comparing star formation functions inferred directly from observations, to observed Lya luminosity functions. Our analysis shows that the effective escape fraction increases from f_esc^eff ~ 1-5 % at z=0, to f_esc^eff ~ 10 % at z=3-4, and to f_esc^eff=30-50 % at z=6. Our constraint at z=6 lies above predictions by models that do not include winds, and therefore hints at the importance of winds in the Lya transfer process (even) at this redshift. We can reproduce Lya luminosity functions with an f_esc^eff that does not depend on the galaxies star formation rates (SFR) over up to ~2 orders of magnitude in Lya luminosity. It is possible to reproduce the luminosity functions with an f_esc^eff that decreases with SFR - which appears favored by observations of drop-out galaxies - in models which include a large scatter (~ 1.0 dex) in f_esc^eff, and/or in which star forming galaxies only have a non-zero f_esc^eff for a fraction of their life-time or a fraction of sightlines. We provide a fitting formula that summarizes our findings.