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Thermal Instability & the Feedback Regulation of Hot Halos in Clusters, Groups, and Galaxies

Observations of clusters and groups imply that such halos are roughly in global thermal equilibrium, with heating balancing cooling when averaged over sufficiently long time- and length-scales; the ICM is, however, very likely to be locally thermally unstable. Using simple observationally-motivated heating prescriptions, we show that local thermal instability (TI) can produce a multi-phase medium---with ~ 10000 K cold filaments condensing out of the hot ICM---only when the ratio of the TI timescale in the hot plasma (t_{TI}) to the free-fall timescale (t_{ff}) satisfies t_{TI}/t_{ff} <~ 10. This criterion quantitatively explains why cold gas and star formation are preferentially observed in low-entropy clusters and groups. In addition, the interplay among heating, cooling, and TI reduces the net cooling rate and the mass accretion rate at small radii by factors of ~ 100 relative to cooling-flow models. This dramatic reduction is in line with observations. The feedback efficiency required to prevent a cooling-flow is ~ 0.001 for clusters and decreases for lower mass halos; supernova heating may be energetically sufficient to balance cooling in galactic halos. We further argue that the ICM self-adjusts so that t_{TI}/t_{ff} >~ 10 at all radii. When this criterion is not satisfied, cold filaments condense out of the hot phase and reduce the density of the ICM. These cold filaments can power the black hole and/or stellar feedback required for global thermal balance, which drives t_{TI}/t_{ff} >~ 10. In comparison to clusters, groups have central cores with lower densities and larger radii. This can account for the deviations from self-similarity in the X-ray luminosity-temperature (L_X-T_X) relation. The high-velocity clouds observed in the Galactic halo can also be due to local TI producing multi-phase gas close to the virial radius.