Black Hole Spin and the Radio Loud/Quiet Dichotomy of Active Galactic
  Nuclei
  Radio loud active galactic nuclei (AGN) are on average 1000 times brighter in
the radio band compared to radio quiet AGN. We investigate whether this radio
loud/quiet dichotomy can be due to differences in the spin of the central black
holes that power the radio-emitting jets. Using general relativistic
magnetohydrodynamic simulations, we construct steady state axisymmetric
numerical models for a wide range of black hole spins (dimensionless spin
parameter 0.1 <= a <= 0.9999 and a variety of jet geometries. We assume that
the total magnetic flux through the black hole horizon at radius r_H(a) is held
constant. If the black hole is surrounded by a thin accretion disk, we find
that the total black hole power output depends approximately quadratically on
the angular frequency of the hole, P \propto \Omega_H^2 \propto (a/r_H)^2. We
conclude that, in this scenario, differences in the black hole spin can produce
power variations of only a few tens at most. However, if the disk is thick such
that the jet subtends a narrow solid angle around the polar axis, then the
power dependence becomes much steeper, P \propto \Omega_H^4 or even \propto
\Omega_H^6. Power variations of 1000 are then possible for realistic black hole
spin distributions. We derive an analytic solution that accurately reproduces
the steeper scaling of jet power with \Omega_H, and we provide a numerical
fitting formula that reproduces all our simulation results. We discuss other
physical effects that might contribute to the observed radio loud/quiet
dichotomy of AGN.
