  We investigate the stability of black hole accretion disks in a primordial
environment (POP III disks for short), by solving the vertical structure of
optically thick disks, including convective energy transport, and by employing
a one-zone model for optically thin isothermal disks. Because of the absence of
metals in POP III disks, we find significant differences in stability
associated with ionization between POP III disks and the disks of solar
metallicity. An unstable branch in S-shaped equilibrium curves on the
Mdot-Sigma (mass accretion rate - surface density) plane extends to a larger
surface density compared with the case of disks of solar metallicity. The
resulting equilibrium loci indicate that quasi-periodic oscillations in
luminosity can also be driven in POP III disks, and their maximal luminosity is
typically by an order of magnitude larger than that of the disks of solar
metallicity. Such a strong outburst of POP III disks can be observed by future
huge telescopes, in case that the mass is supplied onto the disks at the Bondi
accretion rates in typical virialized small dark halos.
