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The fraction of galaxies with strong Ly$\alpha$ emission has been observed todecrease rapidly with redshift at $z \ge 6$, after a gradual increase at $z<6$. This has been interpreted as a hint of the reionization of theintergalactic medium (IGM): the emitted Ly$\alpha$ photons would be scatteredby an increasingly neutral IGM at $z>6$. We study this effect by modeling theionization and Ly$\alpha$ radiative transfer in the infall region and the IGMaround a Ly$\alpha$ emitting galaxy (LAE), for a spherical halo model with themean density and radial velocity profiles in the standard $\Lambda$CDMcosmological scenario. We find that the expected fast increase of the ionizingbackground intensity toward the end of the reionization epoch implies a rapidevolution of halo infall regions from being self-shielded against the externalionizing background to being mostly ionized. Whereas self-shielded infallregions can scatter the Ly$\alpha$ photons over a much larger area than thecommonly used apertures for observing LAEs, the same infalling gas is no longeroptically thick to the Ly$\alpha$ emission line after it is ionized by theexternal background, making the Ly$\alpha$ emission more compact and brighterwithin the observed apertures. Based on this simple model, we show that theobserved drop in the abundance of LAEs at $z>6$ does not imply a rapid increasewith redshift of the fraction of the whole IGM volume that is atomic, but isaccounted for by a rapid increase of the neutral fraction in the infall regionsaround galaxy host halos.

On the decreasing fraction of Strong Ly$\alpha$ Emitters around $z$ $\sim$ $6$-$7$