Ly{\alpha} Equivalent Width Distribution of Ly{\alpha} Emitting Galaxies at Redshift z $\sim$ 4.5

Ly{\alpha} line EWs provide important clues to the physical nature of high redshift LAEs. However, measuring the Ly{\alpha} EW distribution of high-z narrowband selected LAEs can be hard because many sources do not have broadband photometry. We investigate the possible biases in measuring the intrinsic Ly{\alpha} EW distribution for a LAE sample at z $\sim$ 4.5 in the Extended CDFS. Only weak Malmquist-type bias in both the intrinsic Ly{\alpha} luminosity function and the Ly{\alpha} EW distribution were found. However, the observed EW distribution is severely biased if one only considers LAEs with detections in the continuum. Taking the broadband non-detections into account requires fitting the distribution of the broadband-to-narrowband ratio, which then gives a larger EW distribution scale length. Assuming an exponential form of the intrinsic Ly{\alpha} EW distribution dN/dEW = N exp(-EW/W$_0$), we obtain W$_0$ = 167+/-44{\AA} (uncorrected for IGM absorption of Ly{\alpha}). We discuss the likely range of IGM absorption effects in light of recent measurements of Ly{\alpha} line profiles and velocity offsets. Our data are consistent with Ly{\alpha} EW being independent of UV luminosity (i.e., we do not see evidence for the "Ando" effect). Our simulations also imply that broad-band images should be 0.5-1 magnitude deeper than narrowband images for an effective and reasonably complete LAE survey. Comparing with consistent measurements at other redshifts, we see a strong evolution in Ly{\alpha} EW distribution with redshift which goes as a power-law form of W$_0$ $\prop$(1+z)^{\xi}, with {\xi} = 1.1$\pm$0.1 (0.6$\pm$0.1) if no IGM corrections are applied to the Ly{\alpha} line; or {\xi} = 1.7$\pm$0.1 (1.2$\pm$0.1) after applying a maximal IGM-absorption correction to Ly{\alpha} line) for an exponential (a gaussian) EW distribution from z = 0.3 to 6.5.