Filling factors and scale heights of the diffuse ionized gas in the Milky Way

The combination of dispersion measures of pulsars, distances from the model of Cordes & Lazio (2002) and emission measures from the WHAM survey enabled a statistical study of electron densities and filling factors of the diffuse ionized gas (DIG) in the Milky Way. The emission measures were corrected for absorption and contributions from beyond the pulsar distance. For a sample of 157 pulsars at |b | > 5. and 60° < ℓ < 360°, located in mainly interarm regions within about 3 kpc from the Sun, we find that: (1) The average volume filling factor along the line of sight $ \bar f _{\rm v} $ and the mean density in ionized clouds $ \bar n _{\rm c} $ are inversely correlated: $ \bar f _{\rm v} $($ \bar n _{\rm c} $) = (0.0184 ± 0.0011)$ \bar n _{\rm c} $–1.07 ± 0.03 for the ranges 0.03 < $ \bar n _{\rm c} $ < 2 cm–3 and 0.8 > $ \bar f _{\rm v} $ > 0.01. This relationship is very tight. The inverse correlation of $ \bar f _{\rm v} $ and $ \bar n _{\rm c} $ causes the well‐known constancy of the average electron density along the line of sight. As $ \bar f _{\rm v} $(z ) increases with distance from the Galactic plane |z |, the average size of the ionized clouds increases with |z |. (2) For |z| < 0.9 kpc the local density in clouds n c(z ) and local filling factor f (z ) are inversely correlated because the local electron density n e(z ) = f (z )n c(z ) is constant. We suggest that f (z ) reaches a maximum value of >0.3 near |z | = 0.9 kpc, whereas n c(z ) continues to decrease to higher |z |, thus causing the observed flattening in the distribution of dispersion measures perpendicular to the Galactic plane above this height. (3) For |z | < 0.9 kpc the local distributions n c(z ), f (z ) and $ n _{\rm e}^{2} $(z ) have the same scale height which is in the range 250 < h ≲ 500 pc. (4) The average degree of ionization of the warm atomic gas $ \bar I _{\rm w} $(z ) increases towards higher |z | similarly to $ \bar f _{\rm v} $(z ). Towards |z | = 1 kpc, $ \bar f _{\rm v} $(z ) = 0.24 ± 0.05 and $ \bar I _{\rm w} $(z ) = 0.24 ± 0.02. Near |z | = 1 kpc most of the warm, atomic hydrogen is ionized. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)