  We report a sensitive X-ray search for the proposed intermediate mass black
hole (IMBH) in the massive Galactic cluster, Omega Centauri (NGC 5139).
Combining Chandra X-ray Observatory data from Cycles 1 and 13, we obtain a deep
(~291 ks) exposure of the central regions of the cluster. We find no evidence
for an X-ray point source near any of the cluster's proposed dynamical centers,
and place an upper limit on the X-ray flux from a central source of f_X(0.5-7.0
keV) <= 5.0x10^-16 erg cm^-2 s^-1, after correcting for absorption. This
corresponds to an unabsorbed X-ray luminosity of L_X(0.5-7.0 keV) <= 1.6x10^30
erg s^-1, for a cluster distance of 5.2 kpc, Galactic column density N_H =
1.2x10^21 cm^-2, and powerlaw spectrum with Gamma = 2.3. If a ~10^4 M_sun IMBH
resides in the cluster's core, as suggested by some stellar dynamical studies,
its Eddington luminosity would be L_Edd ~10^42 erg s^-1. The new X-ray limit
would then establish an Eddington ratio of L_X/L_Edd <~ 10^-12, a factor of ~10
lower than even the quiescent state of our Galaxy's notoriously inefficient
supermassive black hole Sgr A*, and imply accretion efficiencies as low as eta
<~ 10^-6 - 10^-8. This study leaves open three possibilities: either Omega Cen
does not harbor an IMBH or, if an IMBH does exist, it must experience very
little or very inefficient accretion.
