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Lyα Equivalent Width Distribution of Lyα Emitting Galaxies at Redshift z $\sim$ 4.5

Lyα line EWs provide important clues to the physical nature of high redshift LAEs. However, measuring the Lyα 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 Lyα EW distribution for a LAE sample at z $\sim$ 4.5 in the Extended CDFS. Only weak Malmquist-type bias in both the intrinsic Lyα luminosity function and the Lyα 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 Lyα EW distribution dN/dEW = N exp(-EW/W$_0$), we obtain W$_0$ = 167+/-44Å (uncorrected for IGM absorption of Lyα). We discuss the likely range of IGM absorption effects in light of recent measurements of Lyα line profiles and velocity offsets. Our data are consistent with Lyα 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 Lyα EW distribution with redshift which goes as a power-law form of W$_0$ $\prop$(1+z)$^$ξ, with ξ = 1.1$\pm$0.1 (0.6$\pm$0.1) if no IGM corrections are applied to the Lyα line; or ξ = 1.7$\pm$0.1 (1.2$\pm$0.1) after applying a maximal IGM-absorption correction to Lyα line) for an exponential (a gaussian) EW distribution from z = 0.3 to 6.5.