Halo Gas Condensation Rates with a Cooling-Time Floor: The Fuel Supply of a Milky-Way-Like Galaxy

A galaxy's star formation is fed, over cosmic time, by the condensation of its hot halo gas. The standard estimate of that supply — the gas mass inside the radius where the cooling time equals the halo's age, divided by the age — gives 11.1 solar masses per year for the Milky-Way-mass halo modelled here (hot-gas mass 1.57e11 solar masses inside the virial radius, cooling radius 188 kpc), comfortably above the galaxy's observed star formation rate of one to two solar masses per year and so consistent with a picture in which feedback disposes of most of the supply. This paper computes how a uniform dissolution heating term Q = f u_L / t_H, fed by the surviving vacuum density u_L = 5.25e-09 erg per cubic centimetre, erodes that supply. Because the term is density-independent, it imposes a minimum density for net cooling, n_min = sqrt(Q/Lambda): gas more dilute than n_min cannot cool at all, whatever its cooling time formally says. The condensation rate is untouched at the forest-permitted coupling and at f = 1e-08; it falls to 9.74 solar masses per year at f = 1e-06 (cooling radius 167 kpc), to 3.65 at f = 1e-04 (75 kpc), and to 0.27 at f = 1e-02 (18 kpc) — below the galaxy's star formation rate, at which point the model galaxy would starve. Sustained star formation in Milky-Way-like galaxies therefore independently requires f below roughly 1e-03, and the mechanism of the erosion — an outer halo sterilised first, the supply shrinking from the outside in — is a distinctive, falsifiable pattern. Computed from stated assumptions; not a measurement.