X-ray Constraints on the Lyman-Alpha Escape Fraction
  We have coadded X-ray flux of all known Lyman Alpha Emitters (LAEs) in the 4
Msec Chandra Deep Field South (CDF-S) region, to place sensitive upper limits
on the average unobscured star-formation rate (SFR_X) in these galaxies. A very
small fraction of Lyman-Alpha galaxies in the field are individually detected
in the X-rays, implying a low fraction of AGN activity. After excluding the few
X-ray detected LAEs, we stack the undetected LAEs located in the 4 Ms CDF-S
data and 250 ks Extended CDF-S (ECDFS) data, and compute a 1-\sigma upper limit
on SFR_X < 14, 28, 28, 140, 440, 880 M$_{\sun}$ yr$^{-1}$ for LAEs located at z
= 2.1, 3.1, 3.2, 4.5, 5.7 and 6.5, respectively. The upper limit of SFR_X in
LAEs can be then be compared to SFR$_{Ly\alpha}$ derived from Lyman-Alpha line
and thus can constrain on the Lyman-Alpha escape fraction
($f^{Esc}_{Ly\alpha}$). We derive a lower limit on f(Lyman-Alpha Escape) > 14%
(84 % confidence level, 1-\sigma lower limit) for LAEs at redshift z ~ 2.1 and
z ~ 3.1-3.2. At z > 4, the current LAE samples are not of sufficient size to
constrain SFR_X well. By averaging all the LAEs at z> 2, the X-ray
non-detection constrains f(Lyman-Alpha Escape) > 17% (84 % confidence level,
1-\sigma lower limit), and rejects f(Lyman-Alpha Escape) < 5.7% at the 99.87%
confidence level from 2.1 < z < 6.5.
