MUSE deep-fields: The Ly α luminosity function in the Hubble Deep Field-South at 2.91 < z < 6.64

We present the first estimate of the Ly α luminosity function using blind spectroscopy from the Multi Unit Spectroscopic Explorer, MUSE, in the Hubble Deep Field-South. Using automatic source-detection software, we assemble a homogeneously detected sample of 59 Ly α emitters covering a flux range of -18.0 &lt; log10 (F) &lt; -16.3 (erg s-1 cm-2), corresponding to luminosities of 41.4 &lt; log10 (L) &lt; 42.8 (erg s-1). As recent studies have shown, Ly α fluxes can be underestimated by a factor of 2 or more via traditional methods, and so we undertake a careful assessment of each object's Ly α flux using a curve-of-growth analysis to account for extended emission. We describe our self-consistent method for determining the completeness of the sample, and present an estimate of the global Ly α luminosity function between redshifts 2.91 &lt; z &lt; 6.64 using the 1/Vmax estimator. We find that the luminosity function is higher than many number densities reported in the literature by a factor of 2-3, although our result is consistent at the 1σ level with most of these studies. Our observed luminosity function is also in good agreement with predictions from semi-analytic models, and shows no evidence for strong evolution between the high- and low-redshift halves of the data. We demonstrate that one's approach to Ly α flux estimation does alter the observed luminosity function, and caution that accurate flux assessments will be crucial in measurements of the faint-end slope. This is a pilot study for the Ly αLy α luminosity function in the MUSE deep-fields, to be built on with data from the Hubble Ultra Deep Field that will increase the size of our sample by almost a factor of 10.