We use hydrodynamic simulations with adaptive grid refinement to study the
dependence of hot gas flows in X-ray luminous giant elliptical galaxies on
the efficiency of heat supply to the gas. We consider a number of potential
heating mechanisms including Type Ia supernovae and sporadic nuclear activ
ity of a central supermassive black hole. As a starting point for this rese
arch we use an equilibrium hydrostatic recycling model. We show that a comp
act cooling inflow develops, if the heating is slightly insufficient to cou
nterbalance radiative cooling of the hot gas in the central few kiloparsecs
. An excessive heating in the centre, instead, drives a convectively unstab
le outflow. We model the onset of the instability and a quasi-steady convec
tive regime in the core of the galaxy in two dimensions assuming axial symm
etry.
Provided the power of net energy supply in the core is not too high, the co
nvection remains subsonic. The convective pattern is dominated by buoyancy
driven large-scale mushroom-like structures. Unlike in the case of a coolin
g inflow, the X-ray surface brightness of an (on average) isentropic convec
tive core does not display a sharp maximum at the centre. A hybrid model, w
hich combines a subsonic peripheral cooling inflow with an inner convective
core, appears to be stable. We also discuss observational implications of
these results.