Joint Analysis of HI Absorption Zeeman Measurements and the Morphology of Filamentary HI Emission

We present a joint analysis of HI absorption Zeeman measurements and the morphology of filamentary HI emission to investigate the three-dimensional structure of the magnetic field in the diffuse neutral interstellar medium (ISM). Our analysis is based on the Arecibo Millennium Survey and new data from the Five-hundred-meter Aperture Spherical radio Telescope (FAST) toward radio sources 3C 75, 3C 207, and 3C 409. Toward 3C 409, we make a 4$σ$ Zeeman detection and infer $B_{LOS}$ = 9.1 +/- 1.9$μ$G, in agreement with Arecibo results. We quantify the dispersion of HI filaments at the locations and velocities of Zeeman components using GALFA-HI narrow-channel emission maps. Focusing on a subsample of 42 spectrally distinct components, we find a weak but statistically significant positive correlation (Spearman r = 0.3, $p = 0.01$) between $|B_{LOS}|$ and the circular variance of HI filament orientation angles. To examine its origin, we characterize the environments probed by HI absorption using dust emission, 3D dust maps, OH absorption, and CO emission. We find evidence that existing HI absorption Zeeman measurements trace magnetic fields that are coherent on parsec scales, probe primarily local gas ($100$-$500$ pc, often at distances consistent with the Local Bubble wall), and exhibit systematic differences in the magnitude of $B_{LOS}$. We attribute the correlation between Zeeman measurements and filamentary HI morphology to large-scale variations in magnetic field strength and/or inclination angle across different Galactic environments, which could arise due to the Local Bubble geometry or enhanced total field strength in denser regions.