The Field Length in Halo Gas with a Heating Floor, and the Smallest Clouds That Can Survive

Cold clouds embedded in a hot halo live or die by thermal conduction. The Field length, lambda_F = sqrt(kappa T / (net cooling per unit volume)), sets the scale below which conduction overwhelms radiative cooling and a cloud cannot maintain itself; it is the halo's minimum cloud size. This paper computes the Field length across circumgalactic conditions with Spitzer conductivity and with the net cooling reduced by a uniform dissolution heating term Q = f u_L / t_H, where u_L = 5.25e-09 erg per cubic centimetre is the surviving vacuum density. At n = 1e-03 per cubic centimetre and T = 1e6 K, lambda_F is 1,795 pc with no heating term, essentially unchanged (1,800 pc) at f = 1e-05, and 2,749 pc at f = 1e-03; it diverges where the heating term reaches the full cooling rate, at f = 1.74e-03. At the lower density n = 1e-04, lambda_F is 17,947 pc already at f = 0, grows to 27,488 pc at f = 1e-05, and diverges at f = 1.74e-05. Classical evaporation times for cold clouds (density 0.1 per cubic centimetre) in the hot phase run from 0.57 million years at 10 pc to 57 million years at 100 pc and 5,660 million years at 1 kpc, lengthening tenfold if conductivity is suppressed by a factor of ten. The observed existence of cold circumgalactic structure therefore requires no vacuum assistance and permits none of consequence: at the forest-bounded coupling (f below 5.6e-11) every Field length in the table is the standard one. Computed from stated assumptions; not a measurement.