The Lifetime and Powers of FR IIs in Galaxy Clusters
  We have identified and studied a sample of 151 FR IIs found in brightest
cluster galaxies (BCGs) in the MaxBCG cluster catalog with data from FIRST and
NVSS. We have compared the radio luminosities and projected lengths of these FR
IIs to the projected length distribution of a range of mock catalogs generated
by an FR II model and estimate the FR II lifetime to be 1.9 x 10^8 yr. The
uncertainty in the lifetime calculation is a factor of two, due primarily to
uncertainties in the ICM density and the FR II axial ratio. We furthermore
measure the jet power distribution of FR IIs in BCGs and find that it is well
described by a log-normal distribution with a median power of 1.1 x 10^37 W and
a coefficient of variation of 2.2. These jet powers are nearly linearly related
to the observed luminosities, and this relation is steeper than many other
estimates, although it is dependent on the jet model. We investigate
correlations between FR II and cluster properties and find that galaxy
luminosity is correlated with jet power. This implies that jet power is also
correlated with black hole mass, as the stellar luminosity of a BCG should be a
good proxy for its spheroid mass and therefore the black hole mass. Jet power,
however, is not correlated with cluster richness, nor is FR II lifetime
strongly correlated with any cluster properties. We calculate the enthalpy of
the lobes to examine the impact of the FR IIs on the ICM and find that heating
due to adiabatic expansion is too small to offset radiative cooling by a factor
of at least six. In contrast, the jet power is approximately an order of
magnitude larger than required to counteract cooling. We conclude that if
feedback from FR IIs offsets cooling of the ICM, then heating must be primarily
due to another mechanism associated with FR II expansion.
