= Solution
If gas cannot radiate enough energy to fall below the <virial temperature>, infall converts gravitational energy into heat through shocks and compression. Thermal pressure can support an extended atmosphere in the <dark-matter halo>. It need not have the same density profile as the collisionless <dark matter>, because its entropy and pressure matter.
A useful quantitative comparison is the <radiative gas cooling time> $t_{\rm cool}\sim(3/2)nk_BT/(n_en_i\Lambda)$ against the halo dynamical time $t_{\rm dyn}\sim r_{\rm vir}/V_{\rm vir}$. If cooling remains slow or a heating source balances it, the gas stays predominantly hot and diffuse, rather than forming a compact, cold, self-gravitating stellar system. \b[Without sufficient cooling, most baryons remain pressure-supported halo gas.] Very slow cooling can still feed gradual central condensation; the condition is about energy loss relative to the evolution time, not an absolute prohibition on any inward motion.
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