Hoag-type Galaxies: A Photometric Study of the Cores and Rings of Thirty Systems from the DESI Legacy Survey

Hoag-type galaxies contain a smooth central core surrounded by a detached outer ring, but their rarity has limited previous studies mainly to individual systems. We identify thirty galaxies with apparent Hoag-type morphology in DESI imaging by visually inspecting two machine-learning ring-galaxy catalogues and analyse their core and ring properties using DESI Legacy Imaging Surveys $g$, $r$, and $z$ images. We measure the rings after subtracting two-dimensional core models and compare the cores with matched SDSS galaxies. The cores lie predominantly on the red sequence, whereas the rings span a broader colour range extending toward the blue cloud. The cores broadly follow early-type mass scaling relations, but their mass-matched distributions tend towards slightly bluer colours, smaller sizes, higher stellar-mass surface densities, and lower concentrations and Sérsic indices. Of the 16 systems with SDSS group information, 14 (87.5 per cent) are centrals, compared with $\sim64\%$ in the mass-matched early-type control sample. The halo-mass and large-scale overdensity distributions become much more similar after central--satellite status is also matched. Ring stellar-mass surface density and normalized width decrease with increasing core-plus-inner-halo to ring mass ratio. Most core $R_{90}$ values lie inside the outermost stable circular orbit of a simplified core-plus-ring model, while the rings frequently extend across its unstable interval. The slightly bluer core colours, lower concentrations, and lower Sérsic indices suggest a possible secular contribution, but the compact, dense cores imply more complex structural assembly than a simple diffuse-pseudobulge origin. The high central fraction may favour gas retention and ring survival by reducing satellite-specific environmental processing. The diversity of ring properties nevertheless leaves room for multiple formation pathways.