Physical meaning and interpretive limits of correlations among cometary secular light-curve parameters

Abstract The physical meaning and interpretive limits of correlations among cometary secular light-curve (SLC) parameters are examined using two published SLC datasets. A distinction is made between relations that arise structurally from the adopted formalism and those that more plausibly reflect the persistence, extent and evolution of cometary activity. In the first dataset, brighter comets tend to show both larger secular amplitudes and broader active arcs, indicating a close connection between coma brightness, activity strength and heliocentric activity extent. In the second framework, nucleus diameter is strongly anti-correlated with modelled active area, consistent with lower effective fractional activity in larger short-period comet nuclei, although this result remains model-dependent. Both datasets also support the general picture that photometrically younger comets are more active and remain active over wider orbital intervals, but age-related trends require caution because the corresponding proxies are partly embedded in the SLC formalism. Two compact empirical descriptors are introduced within the empirical SLC framework, the coma–nucleus flux contrast $C_{\rm CN}\equiv 10^{0.4A_{\rm SEC}(1,1)}$ and the Activity Range; the former is proposed as a stable observational flag for assessing the likely reliability of nucleus-brightness and nucleus-size estimates in the presence of coma contamination. Independent reconstructions of additional comets from published Magnitudes Graph solutions, including C/2014 UN271, C/2023 A3, 12P/Pons–Brooks and 2I/Borisov, recover distant activation, branch changes and activity asymmetries beyond the original tabulated samples. Overall, SLC parameters contain physically useful information, but their interpretation requires a clear separation between structural, model-dependent and genuinely empirical trends.