Dispersion-Measure Scatter as a Probe of Halo Phase Structure: Cloud Sizes and Filling Factors

Absorption spectroscopy established that galactic haloes are multiphase; dispersion measures of fast radio bursts can now weigh that phase structure statistically, because a sightline's dispersion depends on how the halo's electrons are arranged, not only on how many there are. This paper builds a two-phase halo model — a hot 1e6 K volume-filling phase plus cold 1e4 K clouds in pressure balance at density contrast 100, with volume filling factor phi and cloud radius r_c — constrained to a fixed mean halo dispersion of 50 pc per cubic centimetre over a 200 kpc path, and computes the sightline-to-sightline scatter the clouds imprint. Kiloparsec clouds produce large scatter even when rare: at phi = 0.001, with a mean of only 0.15 cloud crossings per sightline, the scatter is 17.6 pc per cubic centimetre; at phi = 0.01 (1.5 crossings) it is 30.8. Shrinking the clouds to 0.1 kpc at the same filling factor raises the crossing count to 15 and reduces the scatter to 9.7. The cold mass fraction is the binding constraint in the other direction: phi = 0.01 already places 50 percent of the halo's gas mass in cold clouds, and phi = 0.05 places 84 percent, against the minority cold fractions absorption surveys infer. Cold clouds at these densities cool in 10.6 to 57.4 million years and so require continuous regeneration or confinement. The joint message of mean, scatter and mass fraction is that halo gas can be strongly clumped only in small clouds: the dispersion data and the absorption data, read together, are beginning to fix both axes of the phase diagram. Computed from stated assumptions; not a measurement.