Feedback heating from active galactic nuclei ( AGNs ) has been commonly invoked to suppress cooling flows predicted in hot gas in elliptical galaxies , galaxy groups and clusters .
Previous studies have focused on if and how AGN feedback heats the gas , but little paid attention to its triggering mechanism .
Using spherically symmetric simulations , we investigate how large-scale cooling flows are accreted by central supermassive black holes ( SMBHs ) in eight well-observed systems and find an interesting dichotomy .
In massive clusters , the gas develops a central cooling catastrophe within about the cooling time ( typically \sim 100 - 300 Myr ) , resulting in a cold-mode accretion onto SMBHs .
However , in our four simulated systems on group and galaxy scales at a low metallicity Z = 0.3 Z _ { \sun } , the gas quickly settles into a long-term state which has a cuspy central temperature profile extending to several tens to about 100 pc .
At the more realistic solar metallicity , two groups ( with R _ { e } \sim 4 kpc ) still host the long-term hot-mode accretion .
Both accretion modes naturally appear in our idealized calculations where only cooling , gas inflow , and compressional heating are considered .
The long-term hot-mode accretion is maintained by the quickly-established closeness between the timescales of these processes , preferably in systems with low gas densities , low gas metallicities , and importantly , compact central galaxies , which result in strong gravitational acceleration and compressional heating at the intermediate radii .
Our calculations predict that central cuspy temperature profiles appear more often in smaller systems than galaxy clusters , which instead often host significant cold gas and star formation .