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We perform global linear stability analysis and idealized numericalsimulations in global thermal balance to understand the condensation of coldgas from hot/virial atmospheres (coronae), in particular the intraclustermedium (ICM). We pay particular attention to geometry (e.g., spherical versusplane-parallel) and the nature of the gravitational potential. Global linearanalysis gives a similar value for the fastest growing thermal instabilitymodes in spherical and Cartesian geometries. Simulations and observationssuggest that cooling in halos critically depends on the ratio of the coolingtime to the free-fall time ($t_{cool}/t_{ff}$). Extended cold gas condenses outof 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 gascondensation in spherical and plane-parallel atmospheres; namely, cold gascondensation appeared easier in spherical atmospheres. This apparent differencedue to geometry arises because the previous plane-parallel simulations focussedon {\em in situ} condensation of multiphase gas but spherical simulationsstudied condensation {\em anywhere} in the box. Unlike previous claims, ournonlinear simulations show that there are only minor differences in cold gascondensation, either in situ or anywhere, for different geometries. The amountof cold gas condensing depends on the shape of the gravitational potentialwell; gas has more time to condense if gravitational acceleration decreasestoward the center. In our idealized simulations with heating balancing coolingin each layer, there can be significant mass/energy/momentum transfer acrosslayers that can trigger condensation and drive $t_{cool}/t_{ff}$ far beyond thecritical value close to 10. Triggered condensation is very prominent inplane-parallel simulations, in which a large amount of cold gas condenses out.

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