A probabilistic approach to separate mergers and jellyfish galaxies: Application of morphological non-parametric indexes to the DESI Legacy Survey
Galaxy morphology traces the physical processes that shape galaxy evolution, but non-parametric diagnostic boundaries depend on image quality and preprocessing. We investigate the classification of regular spirals, regular ellipticals, mergers, and jellyfish (ram-pressure-stripping candidate) galaxies in the DESI Legacy Imaging Surveys. Using galmex measurements of ten non-parametric morphological indices, we evaluate two-dimensional diagnostic planes with a cross-validated Bayesian kernel-density classifier and combine all indices using probability-calibrated LightGBM models. For separating regular spirals, regular ellipticals, and perturbed systems, the most informative planes combine Shannon entropy with $M_{20}$ or asymmetry indices, reaching balanced accuracies of 0.76-0.77. We provide survey-specific probabilistic boundaries in the entropy-$M_{20}$ and entropy-shape-asymmetry planes. Separating mergers from jellyfish candidates is more challenging; the best two-dimensional combinations, all involving concentration, reach balanced accuracies of approximately 0.73. The calibrated three-class LightGBM model achieves a balanced accuracy and macro-F1 score of 0.89, while the four-class model achieves 0.75 and 0.76, respectively. We provide class probabilities and preferred classifications for 1,744,454 galaxies. Our results show that non-parametric morphology identifies broad structural disturbance reliably, but distinguishing its physical origin is harder: jellyfish candidates occupy a relatively coherent region of parameter space, whereas mergers span diverse and overlapping morphologies.