Cold gas in cluster cores: Global stability analysis and non-linear simulations of thermal instability

Abstract

We perform global linear stability analysis and idealized numerical simulations in globalthermal balance to understand the condensation of cold gas from hot/virial atmospheres(coronae), in particular the intraclustermedium (ICM).We pay particular attention to geometry(e.g. spherical versus plane-parallel) and the nature of the gravitational potential. Global linearanalysis gives a similar value for the fastest growing thermal instability modes in spherical andCartesian geometries. Simulations and observations suggest that cooling in haloes criticallydepends on the ratio of the cooling time to the free-fall time (tcool/tff). Extended cold gascondenses out of the ICM only if this ratio is smaller than a threshold value close to 10.Previous works highlighted the difference between the nature of cold gas condensation inspherical and plane-parallel atmospheres; namely, cold gas condensation appeared easier inspherical atmospheres. This apparent difference due to geometry arises because the previousplane-parallel simulations focused on in situ condensation of multiphase gas but sphericalsimulations studied condensation anywhere in the box. Unlike previous claims, our non-linearsimulations show that there are only minor differences in cold gas condensation, either in situor anywhere, for different geometries. The amount of cold gas depends on the shape of tcool/tff;gas has more time to condense if gravitational acceleration decreases towards the centre. Inour idealized plane-parallel simulations with heating balancing cooling in each layer, therecan be significant mass/energy/momentum transfer across layers that can trigger condensationand drive tcool/tff far beyond the critical value close to 10.