AGNs at the cosmic dawn: predictions for future surveys from a
  $\Lambda$CDM cosmological model
  Telescopes to be launched over the next decade-and-a-half, such as JWST,
EUCLID, ATHENA and Lynx, promise to revolutionise the study of the high
redshift Universe and greatly advance our understanding of the early stages of
galaxy formation. We use a model that follows the evolution of the masses and
spins of supermassive black holes (SMBHs) within a semi-analytic model of
galaxy formation to make predictions for the Active Galactic Nucleus (AGN)
luminosity function at $z\geq7$ in the broadband filters of JWST and EUCLID at
near-infrared wavelengths, and ATHENA and Lynx at X-ray energies. The
predictions of our model are relatively insensitive to the choice of seed black
hole mass, except at the lowest luminosities
($L_{\mathrm{bol}}<10^{43}\mathrm{ergs^{-1}}$) and the highest redshifts
($z>10$). We predict that surveys with these different telescopes will select
somewhat different samples of SMBHs, with EUCLID unveiling the most massive,
highest accretion rate SMBHs, Lynx the least massive, lowest accretion rate
SMBHs, and JWST and ATHENA covering objects inbetween. At $z=7$, we predict
that typical detectable SMBHs will have masses,
$M_{\mathrm{BH}}\sim10^{5-8}M_{\odot}$, and Eddington normalised mass accretion
rates, $\dot{M}/\dot{M}_{\mathrm{Edd}}\sim0.6-2$. The SMBHs will be hosted by
galaxies of stellar mass $M_{\star}\sim10^{8-10}M_{\odot}$, and dark matter
haloes of mass $M_{\mathrm{halo}}\sim10^{11-12}M_{\odot}$. We predict that the
detectable SMBHs at $z=10$ will have slightly smaller black holes, accreting at
slightly higher Eddington normalised mass accretion rates, in slightly lower
mass host galaxies compared to those at $z=7$, and reside in haloes of mass
$M_{\mathrm{halo}}\sim10^{10-11}M_{\odot}$.
