RadialPaths: Radial profiles in multi-centred astronomical structures

Abstract

Radial profiles are routinely used to locate structural changes within resolved astronomical systems, but they generally define radial position relative to a single centre. In interacting, clumpy, or otherwise multi-centred structures, the radial location assigned to a feature can depend on the adopted centre. We introduce a centre-conditioned radial representation for connected structures with multiple centres. Distances are measured through the observed source footprint rather than across excluded background, and can be viewed as arrival times of fronts propagating from the centres. Each location is associated with the centre reached first and described by two complementary coordinates: relative centre--boundary depth and normalized progression away from that centre. For an ideal centred circular source, both reduce exactly to the familiar normalized radius $r/R$; in folded, elongated, or tailed geometries they separate because proximity to a lateral boundary and progression through the structure represent different notions of ``outward''. Synthetic examples show that single-centre and equivalent-area radial descriptions do not retain the association between localized features and individual centres, whereas centre-conditioned profiles do. In two JADES DR2 systems, the resulting F277W profiles remain stable under modest changes in the adopted source footprint and one-pixel centre shifts. The construction assumes neither a light-profile law nor an overlapping flux decomposition, and the same radial geometry can be applied to registered maps of continuum light, colour, emission lines, stellar-population properties, and line-of-sight kinematics. An accompanying Python package, \textsf{RadialPaths}, provides the reference implementation together with documentation and online tutorials at \href{https://rafaelsdesouza.com.br/radialpaths} {GitHub}.