Abstract
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.
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