  Jets launched by the supermassive black holes in the centers of cool-core
clusters are the most likely heat source to solve the cooling flow problem. One
way for this heating to occur is through generation of a turbulent cascade by
jet-inflated bubbles. Measurements of the X-ray intensity power spectra show
evidence of this cascade in different regions of the cluster, constraining the
role of driving mechanisms. We analyze feedback simulations of the Perseus
cluster to constrain the effect of the jet activity on the intensity
fluctuations and kinematics of the cluster atmosphere. We find that, within the
inner 60 kiloparsecs, the power spectra of the predicted surface brightness
fluctuations are broadly consistent with those measured by Chandra and that
even a single episode of jet activity can generate a long-lasting imprint on
the intensity fluctuations in the innermost region of the cluster. AGN-driven
motions within the same region approach the values reported by Hitomi during
and right after the AGN episode. However, the line-of-sight velocity dispersion
excited by the jet in simulations underpredicts the Hitomi measurement. This
indicates that driving a volume-filling sustained level of turbulence requires
several episodes of jet activity, and/or additional processes drive turbulence
outside the 60-kpc sphere. This also suggests that sharp edges of the bubbles
in the innermost region of the cluster contribute substantially to the
intensity of fluctuations, consistent with the Perseus observations in the
inner 30-kpc region. We discuss new diagnostics to decompose annular power
spectra to constrain past episodes of jet activity.
