Growth and evolution of thermal instabilities in idealized galaxy cluster cores

Heat input roughly balances radiative cooling in the gaseous cores of galaxy clusters even when the central cooling time is short, implying that cooling triggers a feedback loop that maintains thermal balance. Furthermore, cores with short cooling times tend to have multiphase structure, suggesting that the intracluster medium (ICM) becomes locally thermally unstable for cooling times $\lesssim 1$ Gyr. Both observations and theoretical models have linked the condensation of cold gas with heating by an active galactic nucleus (AGN) through a cycle in which cooling gas fuels the AGN and drives energetic outbursts that reheat the ICM and maintain a state of approximate thermal balance. In this work, we use 2D and 3D hydrodynamic simulations to study the onset of condensation in idealized galaxy-cluster cores. In particular, we look at how the condensation process depends on the ratio of cooling time to freefall time and on the geometry of the gravitational potential. We conclude that the ICM can always evolve to a state in which condensation occurs if given enough time, but that an initial timescale ratio $t_{cool}/t_{ff}\lesssim 10$ is needed for thermal instability to grow quickly enough to affect realistic cluster cores within a timescale that is relevant for cosmological structure formation. We find that instability leads to convection and that perturbations continue to grow while the gas convects. Condensation occurs when the timescale ratio in the low-entropy tail of the perturbation distribution drops below $t_{cool}/t_{ff}\lesssim 3$, even if the volume-averaged timescale ratio is substantially greater. In our simulations, the geometry of the gravitational potential does not have a strong effect on thermal stability. Finally, we find that if condensation is powering feedback, a conversion efficiency of around ${10}^{-3}$ for converting the condensed mass into thermal energy is sufficient to maintain thermal balance in the ICM.