Morphology of the Planetary Nebula Abell 21 from Deep Narrowband Imaging. Structural Analysis, Geometrical Model, and Interaction with the Interstellar Medium

We present a morphological study of the planetary nebula Abell 21 (Sh2-274, the Medusa Nebula), based on our own images obtained in the Hα, [O III], and [S II] emission lines. The aim is to explore the geometric and structural information that can be extracted from quantitative analysis of astronomical images, and to assess its potential and limitations for interpreting the three-dimensional morphology of an evolved planetary nebula. The study includes the delineation of nebular boundaries, elliptical fitting, intensity-profile analysis, and spatial comparison of filamentary structures across the three emission bands. Regions with differing emission characteristics, bright condensations, and possible signatures of interaction with the interstellar medium are also examined. The filament distribution suggests the presence of two partially overlapping ring-like structures whose projected geometry is compatible with a barrel-shaped bipolar morphology. Assuming that both rings represent originally circular cross-sections, a combined geometric inclination of approximately 62.7° relative to the plane of the sky is obtained, broadly consistent with the spectroscopic estimate reported by Lozinskaya (1973). The displacement of the central star relative to the proposed geometric centre, the structure of the eastern interaction front, the extensive northwestern nebulosity, and an outer [O III]-emitting envelope are also investigated. The barrel-shaped hypothesis provides a coherent interpretation of several observed features, although it does not constitute a demonstrated three-dimensional reconstruction. The study highlights the value of image-based morphological analysis for developing testable hypotheses, as well as the need for spectroscopic and kinematic observations to verify them.