The centers of relaxed galaxy clusters radiate X-rays so fiercely that their gas should collapse into cold catastrophe, and it stubbornly does not. Core cooling times are far shorter than cluster ages, classical theory predicted cooling flows depositing hundreds to a thousand solar masses of cold gas per year onto central galaxies, and XMM-Newton's grating spectroscopy delivered the verdict that named the problem: the spectral lines of gas cooling through intermediate temperatures are missing, and observed star formation and cold gas in cluster cores amount to only a few percent of the predicted deposition. Something reheats the cores almost exactly as fast as they cool.
The standard thermostat is AGN feedback: the central black hole accretes, inflates cavities mapped beautifully by Chandra, and the cavity enthalpy roughly matches the cooling luminosity across samples, a genuine success of energetics. The fine print is the problem's persistence: the balance must hold within tens of percent, continuously, for many gigayears, in every cool-core cluster, across three decades of cooling luminosity, via a duty cycle and coupling efficiency that simulations achieve only with tuned subgrid recipes; the heating must be distributed through the core without driving the strong turbulence that Hitomi and XRISM now show is absent (kinetic pressure below 10 percent of thermal in Perseus and its siblings); and the cycle must self-regulate from kiloparsec accretion physics to megaparsec thermodynamics. A thermostat that gentle, that reliable, and that quiet remains unbuilt from first principles.
The standing is a solved-in-energetics, unsolved-in-mechanism classic: the budget balances, the physics of distributing heat without stirring, everywhere and always, does not, and the quiescent-core measurements have sharpened the paradox the cavity census once seemed to settle.