Dissolution Heating and the Cooling-Flow Budget of a Galaxy Cluster: Right Total, Wrong Profile

Cool-core galaxy clusters radiate up to 1e45 erg per second from their inner hundred kiloparsecs, yet spectroscopy shows the gas does not cool and deposit mass at anything like the classical rate — the longstanding cooling-flow problem, whose standard resolution is feedback from the central black hole. This paper tests the exotic alternative that a uniform heating term fed by the surviving vacuum density, Q = f u_L / t_H with u_L = 5.25e-09 erg per cubic centimetre, supplies the missing heat. For a Perseus-like core (central electron density 4.6e-02 per cubic centimetre, temperature 5e7 K), the integrated cooling luminosity inside 100 kpc is 7.41e44 erg per second, implying a classical deposition rate of 695 solar masses per year. Matching that luminosity with the uniform term requires f = 0.52 — energetically possible on paper, but the term's radial profile is wrong in a way no value of f can repair: at the matching coupling, heating supplies only 0.203 of the cooling at 10 kpc, where the need is greatest, while supplying 2.62 times the cooling at 100 kpc, with the crossover at 68 kpc. The core would still cool catastrophically while the outskirts are driven to heat — an inverted version of the observed entropy structure, in which entropy rises monotonically outward. In addition, f = 0.52 exceeds the Lyman-alpha forest bound on a uniform term (5.6e-11) by ten orders of magnitude. Dissolution heating fails the cooling-flow problem twice: in magnitude, and in shape. Computed from stated assumptions; not a measurement.