Powering the 10^62 erg nuclear outburst in the MS0735.6+7421 cluster central galaxy by accretion implies that its supermassive black hole (SMBH) grew by ~6x10^8 solar masses over the past 100 Myr. We place upper limits on the amount of cold gas and star formation near the nucleus of <10^9 solar masses and <2 solar masses per year, respectively. These limits imply that an implausibly large fraction of the preexisting cold gas in the bulge must have been consumed by its SMBH at the rate of ~3-5 solar masses per year while leaving no trace of star formation. Such a high accretion rate would be difficult to maintain by stellar accretion or the Bondi mechanism, unless the black hole mass approaches 10^11 solar masses. Its feeble nuclear luminosities in the UV, I, and X-ray bands compared to its enormous mechanical power are inconsistent with rapid accretion onto a ~5x10^9 solar mass black hole. We suggest instead that the AGN outburst is powered by a rapidly-spinning black hole. A maximally-spinning, 10^9 solar mass black hole contains enough rotational energy, ~10^62 erg, to quench a cooling flow over its lifetime and to contribute significantly to the excess entropy found in the hot atmospheres of groups and clusters. Two modes of AGN feedback may be quenching star formation in elliptical galaxies centered in cooling halos at late times. An accretion mode that operates in gas-rich systems, and a spin mode operating at modest accretion rates. The spin conjecture may be avoided in MS0735 by appealing to Bondi accretion onto a central black hole whose mass greatly exceeds 10^10 solar mass. The host galaxys unusually large, 3.8 kpc stellar core radius (light deficit) may witness the presence of an ultramassive black hole.
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