A Relation Between the Warm Neutral and Ionized Media Observed in the Canadian Galactic Plane Survey

We report on a comparison between 21 cm rotation measure (RM) and the optically-thin atomic hydrogen column density (N_HI) measured towards unresolved extragalactic sources in the Galactic plane of the northern sky. HI column densities integrated to the Galactic edge are measured immediately surrounding each of nearly 2000 sources in 1-arcminute 21 cm line data, and are compared to RMs observed from polarized emission of each source. RM data are binned in column-density bins 4x10^20 cm^-2 wide, and one observes a strong relationship between the number of hydrogen atoms in a 1 cm^2 column through the plane and the mean RM along the same line-of-sight and path length. The relationship is linear over one order of magnitude (from 0.8-14x10^21 atoms cm^-2) of column densities, with a constant RM/N_HI -23.2+/-2.3 rad m^-2/10^21 atoms cm^-2, and a positive RM of 45.0+/-13.8 rad m^-2 in the presence of no atomic hydrogen. This slope is used to calculate a mean volume-averaged magnetic field in the 2nd quadrant of <B_||>~1.0+/-0.1 micro-Gauss directed away from the Sun, assuming an ionization fraction of 8% (consistent with the WNM). The remarkable consistency between this field and <B>=1.2 micro-Gauss found with the same RM sources and a Galactic model of dispersion measures suggests that electrons in the partially ionized WNM are mainly responsible for pulsar dispersion measures, and thus the partially-ionized WNM is the dominant form of the magneto-ionic interstellar medium.