Constraining the Lyman Alpha Escape Fraction with Far-Infrared
  Observations of Lyman Alpha Emitters
  We study the far-infrared properties of 498 Lyman Alpha Emitters (LAEs) at
z=2.8, 3.1 and 4.5 in the Extended Chandra Deep Field-South, using 250, 350 and
500 micron data from the Herschel Multi-tiered Extragalactic Survey (HerMES)
and 870 micron data from the LABOCA ECDFS Submillimeter Survey (LESS). None of
the 126, 280 or 92 LAEs at z=2.8, 3.1 and 4.5, respectively, are individually
detected in the far-infrared data. We use stacking to probe the average
emission to deeper flux limits, reaching $1\sigma$ depths of ~0.1 to 0.4 mJy.
The LAEs are also undetected at $\ge3\sigma$ in the stacks, although a
$2.5\sigma$ signal is observed at 870 micron for the z=2.8 sources. We consider
a wide range of far-infrared spectral energy distributions (SEDs), including a
M82 and an Sd galaxy template, to determine upper limits on the far-infrared
luminosities and far-infrared-derived star-formation rates of the LAEs. These
star-formation rates are then combined with those inferred from the Ly$\alpha$
and UV emission to determine lower limits on the LAEs Ly$\alpha$ escape
fraction ($f_{\rm esc}($Ly$\alpha$)). For the Sd SED template, the inferred
LAEs $f_{\rm esc}($Ly$\alpha$) are $\gtrsim30%$ ($1\sigma$) at z=2.8, 3.1 and
4.5, which are all significantly higher than the global $f_{\rm
esc}($Ly$\alpha$) at these redshifts. Thus, if the LAEs $f_{\rm
esc}($Ly$\alpha$) follows the global evolution then they have warmer
far-infrared SEDs than the Sd galaxy template. The average and M82 SEDs produce
lower limits on the LAE $f_{\rm esc}($Ly$\alpha$) of ~10 to 20% ($1\sigma$),
all of which are slightly higher than the global evolution of $f_{\rm
esc}($Ly$\alpha$) but consistent with it at the 2 to 3$\sigma$ level.
