Recently , Allen et al .
measured a tight correlation between the Bondi accretion rates and jet powers of the nuclei of nearby X-ray luminous elliptical galaxies .
We employ two models of jet powering to understand the above correlation and derive constraints on the spin and accretion rate of the central black holes .
The first is the Blandford-Znajek model , in which the spin energy of the hole is extracted as jet power ; the second model is an hybrid version of the Blandford-Payne and Blandford-Znajek processes , in which the outflow is generated in the inner parts of the accretion disk .
We assume advection-dominated accretion flows ( ADAF ) and account for general relativistic effects .
Our modelling implies that for typical values of the disk viscosity parameter \alpha \sim 0.01 - 1 the tight correlation implies the narrow range of spins j \approx 0.7 - 1 and accretion rates \dot { M } ( R _ { ms } ) \approx ( 0.01 - 1 ) \dot { M } _ { Bondi } .
Our results provide support for the “ spin paradigm ” scenario and suggest that the central black holes in the cores of clusters of galaxies must be rapidly rotating in order to drive radio jets powerful enough to quench the cooling flows .