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. In NGC 1068, the relative orientation of the central structure, jet axis, and spiral disk is examined. 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 two-armed spiral-disk structure. 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. Because face-on systems in which torus-like, jet-like, and disk structures are simultaneously resolvable are rare, the consistency of the geometric relationships identified across the available cases warrants further investigation.