An Observational Geometric Diagnostic Framework for Torus–Jet–Bar–Disk Orientation in Disk Galaxies

We present an observational geometric diagnostic framework for examining the relative orientation of torus-like central structures, jet-like axial features, bar-like projections, and spiral disks in disk galaxies. Although these components are commonly described as separate morphological elements, their repeated spatial association suggests a coherent galactic-scale configuration rather than incidental alignment. We compare three structurally distinct systems with complementary observational roles. NGC 1068 shows a nuclear torus-axis configuration, including an elongated torus-like central structure and jet-like features. NGC 4258 shows jet-like features extending across the spiral-disk region on galactic scales. NGC 1097 displays, within a single observational frame, a central bar, crossing jet-like features, and a developed spiral disk. Using these galaxies as comparative geometric cases, we construct a visual-geometric reconstruction of the relative orientation among the torus-like structure, jet-related axis, bar-like projection, and spiral disk. The comparison identifies a recurring structural pattern linking the bulge region, central axis, projected bar-like structure, and large-scale disk. This pattern supports the interpretation that these components are mutually organized elements of a common galactic framework. We further discuss whether electromagnetic fields associated with the central black hole and its surrounding partially ionized plasma torus may contribute to disk-galaxy organization and maintenance—a possibility whose physical significance is underscored by the rarity of face-on systems in which torus-like, jet-like, and disk structures are simultaneously resolvable, making the consistency of this geometric pattern across available cases particularly significant.