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 < log10 (F) < -16.3 (erg s^-1 cm^-2), corresponding to luminosities of 41.4 < log10 (L) < 42.8 (erg s^-1). As recent studies have shown, Ly{\alpha} fluxes can be underestimated by a factor of two 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/Vmax estimator. We find 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 which will increase the size of our sample by almost a factor of 10.