The MUSE-Wide Survey: A determination of the Lyman $\alpha$ emitter luminosity function at $3<z<6$

Abstract

(Abridged) We investigate the Lyman $\alpha$ emitter luminosity function (LAE LF) within the redshift range $2.9\le z\le 6$ from the first instalment of the blind integral field spectroscopic survey MUSE-Wide. This initial part of the survey probes a region of 22.2 arcmin${}^2$ in the CANDELS/GOODS-S field. The dataset provided us with 237 LAEs from which we construct the LAE LF in the luminosity range $42.2\le \log L_{\mathrm{Ly}\alpha }[{\mathrm{erg}\mathrm{s}}^{-1}]\le 43.5$ within a volume of $2.3\times 10^5$ Mpc${}^3$. For the LF construction we utilise three different non-parametric estimators: The classical $1/V_{\max }$ method, the $C^{-}$ method, and an improved binned estimator for the differential LF. All three methods deliver consistent results, with the cumulative LAE LF being $\Phi (\log L_{\mathrm{Ly}\alpha }[{\mathrm{erg}\mathrm{s}}^{-1}]=43.5)\simeq 3\times 10^{-6}$ Mpc${}^{-3}$ and $\Phi (\log L_{\mathrm{Ly}\alpha }[{\mathrm{erg}\mathrm{s}}^{-1}]=42.2)\simeq 2\times 10^{-3}$ Mpc${}^{-3}$ towards the bright- and faint-end of our survey, respectively. By employing a non-parametric statistical test, as well as by comparing the full sample to sub-samples in redshift bins, we find no supporting evidence for an evolving LAE LF over the probed redshift and luminosity range. We determine the best-fitting Schechter function parameters $\alpha =-1.84_{-0.41}^{+0.42}$ and $\log L^{\ast }[{\mathrm{erg}\mathrm{s}}^{-1}]=42.2_{-0.16}^{+0.22}$ with the corresponding normalisation $\log {\varphi }^{\ast }[{\mathrm{Mpc}}^{-3}]=-2.71$. When correcting for completeness in the LAE LF determinations, we take into account that LAEs exhibit diffuse extended low surface-brightness haloes. We compare the resulting LF to one obtained where we apply a correction assuming compact point-like emission. We find that the standard correction underestimates the LAE LF at the faint end of our survey by a factor of 2.5.

23 pages, 18 figures. A&A in press