Broad Lyman-Alpha Absorbers: Temperature Ceilings from Line Widths and the Baryon Share of the Broad-Line Population

Broad Lyman-alpha absorbers — hydrogen absorption lines wider than thermal broadening at photoionised temperatures — are the ultraviolet signature of warm intergalactic gas, plausibly the cooler part of the warm-hot phase. This paper works the basic inference chain for a stated system: line width b = 50 kilometres per second, neutral column 3.00e+13 per square centimetre. Pure thermal broadening at that width implies a temperature ceiling of 1.51e+05 kelvin; the thermal width at 1e5 kelvin is 41.0 kilometres per second and at 3e5 kelvin, 70.0. With an adopted neutral fraction of 1.00e-05, the total hydrogen column is 3.00e+18 per square centimetre. Combining that column with an adopted incidence of 30 systems per unit redshift gives a baryon share of 0.028 for the broad-line population — rising to 0.0933 if the neutral fraction is 3e-06 and falling to 0.00933 at 3e-05. The neutral fraction, not the line statistics, is the controlling uncertainty, and its temperature sensitivity is the reason broad absorbers complement rather than duplicate the X-ray census.