2008A&A...490..179B

We analyse electron densities and filling factors of the diffuse ionized gas (DIG) in the Solar neighbourhood. We have combined dispersion measures and emission measures towards 38 pulsars at distances known to better than 50%, from which we derived the mean density in clouds, N_c, and their volume filling factor, F_v, averaged along the line of sight. The emission measures were corrected for absorption by dust and contributions from beyond the pulsar distance. The scale height of the electron layer for our sample is 0.93±0.13kpc and the midplane electron density is 0.023±0.004/cm3, in agreement with earlier results. The average density along the line of sight is <n_e≥0.018±0.002cm^–3 and is nearly constant. Since <n_e≥F_vN_c, an inverse relationship between F_v and N_c is expected. We find F_v(N_c)=(0.011±0.003)N_c^{–1.20±0.13}, which holds for the ranges N_c=0.05-1cm^–3 and F_v=0.4-0.01. Near the Galactic plane the dependence of F_v on N_c is significantly stronger than away from the plane. F_v does not systematically change along or perpendicular to the Galactic plane, but the spread about the mean value of 0.08±0.02 is considerable. The total pathlength through the ionized regions increases linearly to about 80pc towards |z|=1kpc. Our study of F_v and N_c of the DIG is the first one based on a sample of pulsars with known distances. We confirm the existence of a tight, nearly inverse correlation between F_v and N_c in the DIG. The exact form of this relation depends on the regions in the Galaxy probed by the pulsar sample. The inverse F_v-N_c relation is consistent with a hierarchical, fractal density distribution in the DIG caused by turbulence. The observed near constancy of <n_e> then is a signature of fractal structure in the ionized medium, which is most pronounced outside the thin disk.