Connecting Faint End Slopes of the Lyman-$\alpha$ emitter and Lyman-break Galaxy Luminosity Functions

TL;DR

This paper models the Ly$ ext{α}$ luminosity functions of high-redshift galaxies, revealing a steeper faint-end slope than UV-LFs and predicting a potential turn-over that informs the understanding of the Epoch of Reionization.

Contribution

It introduces a phenomenological model linking Ly$ ext{α}$ and UV luminosity functions, predicting their shapes and faint-end behaviors at $z=3-6$, and discusses implications for reionization.

Findings

Ly$ ext{α}$ LFs are well-described by Schechter functions over certain luminosities.

The faint-end slope of Ly$ ext{α}$ LFs is steeper than UV-LFs, especially at $z ightarrow 4$.

A turn-over in Ly$ ext{α}$ LF may indicate flattening of UV-LF at specific magnitudes.

Abstract

We predict Lyman-$\alpha$ (Ly$\alpha$) luminosity functions (LFs) of Ly$\alpha$-selected galaxies (Ly$\alpha$ emitters, or LAEs) at $z=3-6$ using the phenomenological model of Dijkstra & Wyithe (2012). This model combines observed UV-LFs of Lyman-break galaxies (LBGs, or drop out galaxies), with constraints on their distribution of Ly$\alpha$ line strengths as a function of UV-luminosity and redshift. Our analysis shows that while Ly$\alpha$ LFs of LAEs are generally not Schechter functions, these provide a good description over the luminosity range of $\log_{10}( L_{\alpha}/{\rm erg}\,{\rm s}^{-1})=41-44$. Motivated by this result, we predict Schechter function parameters at $z=3-6$. Our analysis further shows that (i) the faint end slope of the Ly$\alpha$ LF is steeper than that of the UV-LF of Lyman-break galaxies, (with a median $\alpha_{Ly\alpha} < -2.0$ at $z\gtrsim 4$), and (ii) a turn-over in the Ly$\alpha$ LF of LAEs at Ly$\alpha$ luminosities $10^{40}$ erg s$^{-1}<L_{\alpha}\lesssim 10^{41}$ erg s$^{-1}$ may signal a flattening of UV-LF of Lyman-break galaxies at $-12>M_{\rm UV}>-14$. We discuss the implications of these results - which can be tested directly with upcoming surveys - for the Epoch of Reionization.