Using an X-ray stacking procedure , we provide a robust upper limit to the X-ray luminosity per object of a set of 54 z \approx 5.8 galaxy candidates in the Hubble Ultra Deep Field ( HUDF ) , which is within the 1 Ms-exposure Chandra Deep Field-South ( CDF-S ) .
With an effective total exposure of 44 Ms for the stack , the 3 \sigma flux-density limit of 2.1 \times 10 ^ { -17 } { erg } { cm } ^ { -2 } { s } ^ { -1 } ( soft-band ) gives a 3 \sigma upper-limit luminosity of L _ { X } = 8 \times 10 ^ { 42 } erg s ^ { -1 } per object at a rest-frame hard energy range of \sim 3 – 14 keV at z \approx 5.8 for a photon index of \Gamma = 2 .
For an active accreting black hole ( or “ mini-quasar ” ) emitting at the Eddington luminosity ( \eta _ { Edd } = 1 ) , and the Sazonov et al .
average-QSO spectral energy distribution , we calculate an upper limit on the black hole mass , M _ { bh } < 3 \times 10 ^ { 6 } \eta _ { Edd } ^ { -1 } M _ { \odot } 
( 3 \sigma ) .
The X-ray limit further implies an upper limit on the rate density of UV ionizing photons from accreting black holes at that redshift , \dot { n } _ { ioniz } < 2 \times 10 ^ { 51 } { s } ^ { -1 } { Mpc } ^ { -3 } ( 3 \sigma ) , which is less than 1/10 of the number needed to ionize the universe .
Because the constraint is anchored in the rest-frame hard X-ray regime , a steeper spectrum for “ mini-quasars ” would imply relatively fewer ionizing UV photons .
Unless there are large populations of active black holes around this mass that are unassociated with luminous galaxies , mini-quasars do not appear to contribute significantly to the budget of ionizing photons at z \approx 6 .