Hessian-based photometric substructure as an evolutionary tracer of OB cluster candidates in M31

Abstract Using Hubble Space Telescope images from the PHAT and PHAST surveys, we construct an updated catalogue of 747 OB cluster (OBC) candidates. We introduce a dimensionless structural metric, the trace coefficient of variation (CVtr), derived from the Hessian matrix in four HST bands, to quantify the internal photometric substructure of partially resolved OBC candidates. Cross-matching with the subset of M31 clusters that have independent colour–magnitude diagram (CMD) age estimates yields 254 objects in common. We find statistically significant anti-correlations between CVtr and age in the UV and blue bands, suggesting a progressive smoothing of the light distribution as clusters evolve. Given the substantial intrinsic scatter, CVtr should not be interpreted as a precise age indicator for individual clusters, but rather as a statistical structural proxy for ensemble cluster populations. Bootstrap resampling confirms the robustness of these trends. Forward modelling of synthetic clusters analysed with the same pipeline reproduces an overall decline of CVtr with age, while also revealing wavelength-dependent departures from a simple monotonic relation at young ages. These results show that second-order photometric structure contains measurable evolutionary information within the CMD-calibrated regime (~10–300 Myr).