To investigate the evolution in the relation between galaxy stellar and central black hole mass we identify a population of 508 X-ray selected AGN ( Active Galactic Nuclei ) at 0.4 < z < 6 residing within host galaxies with stellar masses in the range 10 ^ { 10 } M _ { \odot } < M _ { * } < 10 ^ { 12 } M _ { \odot } .
From this sample we construct a volume limited complete sample of 85 AGN with host galaxy stellar masses M _ { * } > 10 ^ { 10.5 } M _ { \odot } , and specific X-ray luminosities L _ { X } > 2.35 \times 10 ^ { 43 } erg s ^ { -1 } at 0.4 < z < 3 .
We calculate the Eddington limiting masses of the supermassive black holes ( SMBHs ) residing at the centre of these galaxies , and observe an increase in the average Eddington limiting black hole mass with redshift .
While the black hole mass and Eddington ratio , \mu , are degenerate , if we assume that the local M _ { BH } - M _ { * } relation holds at all redshifts we find that the mean Eddington ratio \mu rises from 0.056 +/- 0.010 at z = 0.7 to 0.087 +/- 0.011 at z = 1.25 , with no significant evolution thereafter to z = 3 .
Alternatively , by assuming that there is no evolution in \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 } \sim 1000 .
We furthermore find that the fraction of galaxies which are AGN ( with L _ { X } > 2.35 \times 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 \times 10 ^ { 43 } erg s ^ { -1 } ) since z = 3 , finding that at least \sim 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 ) \times 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 .