On the co-evolution of supermassive black holes and their host galaxies
  since z = 3
  [Abridged] To investigate the evolution in the relation between galaxy
stellar and central black hole mass we construct a volume limited complete
sample of 85 AGN with host galaxy stellar masses M_{*} > 10^{10.5} M_{sol}, and
specific X-ray luminosities L_{X} > 2.35 x 10^{43} erg s^{-1} at 0.4 < z < 3.
We calculate the Eddington limiting masses of the supermassive black holes
residing at the centre of these galaxies, and observe an increase in the
average Eddington limiting black hole mass with redshift. By assuming that
there is no evolution in the Eddington ratio (\mu) and then that there is
maximum possible evolution to the Eddington limit, we quantify the maximum
possible evolution in the M_{*} / M_{BH} ratio as lying in the range 700 <
M_{*}/M_{BH} < 10000, compared with the local value of M_{*}/M_{BH} ~ 1000. We
furthermore find that the fraction of galaxies which are AGN (with L_{X} > 2.35
x 10^{43} erg s^{-1}) rises with redshift from 1.2 +/- 0.2 % at z = 0.7 to 7.4
+/- 2.0 % at z = 2.5. We use our results to calculate the maximum timescales
for which our sample of AGN can continue to accrete at their observed rates
before surpassing the local galaxy-black hole mass relation. We use these
timescales to calculate the total fraction of massive galaxies which will be
active (with L_{X} > 2.35 x 10^{43} erg s^{-1}) since z = 3, finding that at
least ~ 40% of all massive galaxies will be Seyfert luminosity AGN or brighter
during this epoch. Further, we calculate the energy density due to AGN activity
in the Universe as 1.0 (+/- 0.3) x 10^{57} erg Mpc^{-3} Gyr^{-1}, potentially
providing a significant source of energy for AGN feedback on star formation. We
also use this method to compute the evolution in the X-ray luminosity density
of AGN with redshift, finding that massive galaxy Seyfert luminosity AGN are
the dominant source of X-ray emission in the Universe at z < 3.
