Constraints on jet formation mechanisms with the most energetic giant
  outbursts in MS 0735+7421
  Giant X-ray cavities lie in some active galactic nuclei (AGNs) locating in
central galaxies of clusters, most of these cavities are thought to be inflated
by jets of AGNs. The jets can be either powered by rotating black holes or the
accretion disks surrounding black holes, or both. In this work, we choose the
most energetic cavity, MS 0735+7421, with stored energy ~ 10^62 erg, to
constrain the jet formation mechanisms and the evolution of the central massive
black hole in this source. The bolometric luminosity of the AGN in this cavity
is ~ 10^(-5) L_Edd, however, the mean power of the jet required to inflate the
cavity is estimated as ~ 0.02 L_Edd, which implies that the source has
experienced strong outbursts previously. During outbursts, the jet power and
the mass accretion rate should be significantly higher than its present values.
We construct an accretion disk model, in which the angular momentum and energy
carried away by jets is properly included, to calculate the spin and mass
evolution of the massive black hole. In our calculations, different jet
formation mechanisms are employed, and we find that the jets generated with the
Blandford-Znajek (BZ) mechanism are unable to produce the giant cavity with ~
10^62 erg in this source. Only the jets accelerated with the combination of the
Blandford-Payne (BP) and BZ mechanisms can successfully inflate such a giant
cavity, if the magnetic pressure is close to equipartition with the total
(radiation+gas) pressure of the accretion disk. For dynamo generated magnetic
field in the disk, such an energetic giant cavity can be inflated by the
magnetically driven jets only if the initial black hole spin parameter a_0 >
0.95. Our calculations show that the final spin parameter a of the black hole
is always ~ 0:9 - 0.998 for all the computational examples which can provide
sufficient energy for the cavity of MS 0735+7421.
