  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~5.8 galaxy candidates in the
Hubble Ultra Deep Field, 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 2.1E-17 erg/cm^2/s (soft-band) gives a
3-sigma upper-limit luminosity of L_X = 8E42 erg/s per object at a rest-frame
hard energy range of 3-14 keV at z~5.8 for a photon index of Gamma=2. For an
active accreting black hole (or "mini-quasar") emitting at the Eddington
luminosity, and the Sazonov et al. average-QSO spectral energy distribution, we
calculate an upper limit on the black hole mass, M_bh < 3E6 Msun (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, n-dot (ioniz) < 2E51
/s/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~6.
