Entropy Floors

The gas in galaxy groups remembers a heating event the standard model never threw. Self-similar gravitational collapse makes a clean prediction: X-ray luminosity should scale as temperature squared across the mass ladder. Observed groups and clusters break it, with L_X scaling as T to the power 2.6 to 3, the deficit concentrated in low-mass systems, and the cause was isolated decades ago: an entropy floor of 100 to 300 keV cm^2 in group cores, excess entropy that gravity cannot generate, requiring 1 to 3 keV per particle of non-gravitational heating deposited in the gas (Ponman et al. 1999; Voit 2005). The floor is strikingly universal, present across systems spanning factors of thirty in virial temperature, in centrally active and quiet systems alike.

The standard account assembles the floor from feedback history: supernova winds fall short by an order of magnitude on the energetics, leaving AGN preheating, every group's gas processed by sufficient black-hole heating episodes before or during assembly, with simulations achieving the observed relations only through tuned duty cycles, coupling efficiencies, and ejection radii. The universality is the assumption's burden: stochastic AGN histories must converge on the same entropy pedestal everywhere, including systems whose current nuclei are silent, and the preheating epoch must inject without overcooking cluster cores or violating the quiescence the kinematic measurements now enforce. The floor functions, in practice, as an initial condition the model must manufacture dynamically in every halo's past.

The standing is a thirty-year-old thermodynamic anomaly wearing a feedback costume: the scaling relations are precision data, the energetics are settled, the mechanism's universality remains assumed rather than derived, and the redshift evolution of the floor, the discriminating measurement, awaits high-z group X-ray spectroscopy.

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