Limits on the high redshift growth of massive black holes

We place firm upper limits on the global accretion history of massive black holes at z ≳ 5 from the recently measured unresolved fraction of the cosmic X-ray background. The maximum allowed unresolved intensity observed at 1.5 keV implies a maximum accreted-mass density onto massive black holes of ρacc ≲ 1.4 × 104 M⊙ Mpc-3 for z ≳ 5. Considering the contribution of lower-z AGNs, the value reduces to ρacc ≲ 0.66 × 104 M⊙ Mpc-3. The tension between the need for the efficient and rapid accretion required by the observation of massive black holes already in place at z ≳ 7 and the strict upper limit on the accreted mass derived from the X-ray background may indicate that black holes are rare in high redshift galaxies or that accretion is only efficient for the black holes hosted by rare galaxies.