  Recent observations of giant ellipticals and brightest cluster galaxies
(BCGs) provide tentative evidence for a correlation between the luminosity of
the H$\alpha$ emitting gas filaments and the strength of feedback associated
with the active galactic nucleus (AGN). Motivated by this, we use 3D
radiation-hydrodynamic simulations with the code Enzo to examine and quantify
the relationship between the observable properties of the H$\alpha$ filaments
and the kinetic and radiative feedback from supermassive black holes in BCGs.
We find that the spatial extent and total mass of the filaments show positive
correlations with AGN feedback power and can therefore be used as probes of the
AGN activity. We also examine the relationship between the AGN feedback power
and velocity dispersion of the H$\alpha$ filaments and find that the kinetic
luminosity shows statistically significant correlation with the component of
the velocity dispersion along the jet axis but not the components perpendicular
to it.
