The MUSE &ITHubble&IT Ultra Deep Field Survey VI. The faint-end of the Lyα luminosity function at 2.91 < &ITz&IT < 6.64and implications for reionisation

We present the deepest study to date of the Ly alpha luminosity function in a blank field using blind integral field spectroscopy from MUSE. We constructed a sample of 604 Ly alpha emitters (LAEs) across the redshift range 2.91 < z < 6.64 using automatic detection software in the Hubble Ultra Deep Lield. The deep data cubes allowed us to calculate accurate total Ly alpha fluxes capturing low surface-brightness extended Ly alpha emission now known to be a generic property of high-redshift star-forming galaxies. We simulated realistic extended LAEs to fully characterise the selection function of our samples, and performed flux-recovery experiments to test and correct for bias in our determination of total Ly alpha fluxes. We find that an accurate completeness correction accounting for extended emission reveals a very steep faint-end slope of the luminosity function, alpha, down to luminosities of log(10) L erg s(-1) < 41.5, applying both the 1/V-max and maximum likelihood estimators. Splitting the sample into three broad redshift bins, we see the faint-end slope increasing from -2.03(-0.07)(+1.42) at z approximate to 3.44 to -2.86(-infinity)(+0.76) Z approximate to 76 at z approximate to 5.48, however no strong evolution is seen between the 68% confidence regions in L*-alpha parameter space. Using the Ly alpha line flux as a proxy for star formation activity, and integrating the observed luminosity functions, we find that LAEs' contribution to the cosmic star formation rate density rises with redshift until it is comparable to that from continuum-selected samples by z approximate to 6. This implies that LAEs may contribute more to the star-formation activity of the early Universe than previously thought, as any additional intergalactic medium (IGM) correction would act to further boost the Ly alpha luminosities. Linally, assuming fiducial values for the escape of Ly alpha and LyC radiation, and the dumpiness of the IGM, we integrated the maximum likelihood luminosity function at 5.00 < z < 6.64 and find we require only a small extrapolation beyond the data (<1 dex in luminosity) for LAEs alone to maintain an ionised IGM at z approximate to 6.