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 alpha 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 alpha emitters covering a flux range of -18.0 < log(10) (F) < -16.3 (erg s(-1) cm(-2)), corresponding to luminosities of 41.4 < log(10) (L) < 42.8 (erg s(-1)). As recent studies have shown, Ly alpha 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 alpha 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 alpha luminosity function between redshifts 2.91 < z < 6.64 using the 1/V-max 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 1 sigma 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 alpha 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 alpha 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.