A Bound on Dissolution-Driven Ionisation from the Neutral Fraction of Low-Redshift Intergalactic Gas

Energy deposited by a vacuum sector into intergalactic gas need not arrive as heat: it could arrive as ionisation. This paper bounds that channel separately. A dissolution ionisation term is parametrised by an energy input Q_ion = g u_L / t_H per unit volume, with u_L = 5.25e-09 erg per cubic centimetre the surviving vacuum density; costing each ionisation at 34 eV (13.6 eV of threshold plus secondary losses) converts it to an ionisation rate per hydrogen atom, Gamma_vac, which adds to the metagalactic ultraviolet background in the photoionisation equilibrium x_HI = n_e alpha_B/(Gamma_UVB + Gamma_vac). At overdensity 10 and z = 0.2, the ultraviolet background alone (Gamma_UVB = 5e-14 per second) gives a neutral fraction of 1.98e-05; at g = 1 the dissolution rate would be Gamma_vac = 6.42e-11 per second, over a thousand times the background, and the forest would be drastically more transparent than observed. Requiring predicted H I columns at overdensities 3 to 100 to shift by no more than thirty percent bounds g at 7.01e-05 (overdensity 3), 2.34e-04 (overdensity 10) and 7.01e-04 (overdensity 30). The ionisation channel is bounded far more weakly than the heating channel (f below 5.6e-11), because ionisation is an expensive way to spend energy — each event costs 34 eV and changes one atom — while heating is cheap and cumulative; the two bounds together nevertheless close the energy budget of any dissolution coupling to baryons, in both of the forms such a coupling could take. Computed from stated assumptions; not a measurement.