MUSE Deep-Fields: The Lya 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.
