Circumgalactic Electron Densities from Fast Radio Burst Dispersion Measures and the Heating They Require

Fast radio bursts measure the free-electron column along their sightlines with no dependence on the gas temperature or ionisation corrections that burden absorption studies. This paper converts the published range of halo dispersion measures for Milky-Way-mass galaxies, DM_halo = 30-80 pc per cubic centimetre, into mean circumgalactic electron densities over a 200 kpc path — 1.50e-04 to 4.00e-04 per cubic centimetre — and computes what those densities imply thermally. At a halo temperature of 1e6 K the corresponding cooling times are 4.90, 2.94 and 1.84 billion years for DM_halo of 30, 50 and 80 respectively: all shorter than the age of the haloes the gas inhabits. Dispersion-inferred halo gas therefore cannot simply have been left hot; it must be reheated, continuously or cyclically, at a volumetric rate equal to its cooling rate. Expressing that required rate in units of the dissolution parametrisation Q = f u_L / t_H, with u_L = 5.25e-09 erg per cubic centimetre the surviving vacuum density, the required coupling is f = 3.38e-05 to 2.40e-04 — roughly a million times the largest uniform coupling the Lyman-alpha forest temperature allows (f below 5.6e-11). Whatever keeps circumgalactic gas hot, it is not a uniform term fed by the vacuum sector; the dispersion data make that conclusion independent of any absorption-line modelling. Computed from stated assumptions; not a measurement.