Heavily reddened type 1 quasars at z > 2 I: Evidence for significant
  obscured black-hole growth at the highest quasar luminosities
  We present a new population of z>2 dust-reddened, Type 1 quasars with
0.5<E(B-V)<1.5, selected using near infra-red (NIR) imaging data from the
UKIDSS-LAS, ESO-VHS and WISE surveys. NIR spectra obtained using the Very Large
Telescope (VLT) for 24 new objects bring our total sample of spectroscopically
confirmed hyperluminous (>10^{13}L_0), high-redshift dusty quasars to 38. There
is no evidence for reddened quasars having significantly different H$\alpha$
equivalent widths relative to unobscured quasars. The average black-hole masses
(~10^9-10^10 M_0) and bolometric luminosities (~10^{47} erg/s) are comparable
to the most luminous unobscured quasars at the same redshift, but with a tail
extending to very high luminosities of ~10^{48} erg/s. Sixty-six per cent of
the reddened quasars are detected at $>3\sigma$ at 22um by WISE. The average
6um rest-frame luminosity is log10(L6um/erg/s)=47.1+/-0.4, making the objects
among the mid-infrared brightest AGN currently known. The extinction-corrected
space-density estimate now extends over three magnitudes (-30 < M_i < -27) and
demonstrates that the reddened quasar luminosity function is significantly
flatter than that of the unobscured quasar population at z=2-3. At the
brightest magnitudes, M_i < -29, the space density of our dust-reddened
population exceeds that of unobscured quasars. A model where the probability
that a quasar becomes dust-reddened increases at high luminosity is consistent
with the observations and such a dependence could be explained by an increase
in luminosity and extinction during AGN-fuelling phases. The properties of our
obscured Type 1 quasars are distinct from the heavily obscured, Compton-thick
AGN that have been identified at much fainter luminosities and we conclude that
they likely correspond to a brief evolutionary phase in massive galaxy
formation.
