Recent analysis shows that it is important to explicitly include the gravitational potential of the central brightest central galaxy ( BCG ) to infer the acceleration due to gravity ( g ) and the free-fall time ( t _ { ff } \equiv [ 2 r / g ] ^ { 1 / 2 } ) in cool cluster cores .
Accurately measuring t _ { ff } is crucial because according to numerical simulations cold gas condensation and strong feedback occur in cluster cores with min ( t _ { cool } / t _ { ff } ) below a threshold value close to 10 .
Recent observations which include the BCG gravity show that the observed threshold in min ( t _ { cool } / t _ { ff } ) lies at a somewhat higher value , close to 10-30 ; there are only a few clusters in which this ratio falls much below 10 .
In this paper we compare numerical simulations of feedback AGN ( Active Galactic Nuclei ) jets interacting with the intracluster medium ( ICM ) , with and without a BCG potential .
We find that , for a fixed feedback efficiency , the presence of a BCG does not significantly affect the temperature but increases ( decreases ) the core density ( entropy ) on average .
Most importantly , min ( t _ { cool } / t _ { ff } ) is only affected slightly by the inclusion of the BCG gravity .
Also notable is that the lowest value of min ( t _ { cool } / t _ { ff } ) in the NFW+BCG runs are about twice larger than in the NFW runs because of a shorter time for feedback heating ( which scales with the free-fall time ) in the former .
We also look at the role of depletion of cold gas due to star formation and show that it only affects the rotationally dominant component ( torus ) , while the radially dominant component ( which regulates the feedback cycle ) remains largely unaffected .
Stellar gas depletion also increases the duty cycle of AGN jets .
The distribution of metals due to AGN jets in our simulations is predominantly along the jet direction and the radial spread of metals is less compared to the observations .
We also show that the turbulence in cool core clusters is weak , consistent with recent Hitomi results on Perseus cluster .