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

Abstract

Using \textit{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 ($CV_{\rm tr}$), derived from the Hessian matrix in four \textit{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 247 objects in common. We find statistically significant anti-correlations between $CV_{\rm tr}$ and age in the UV and blue bands, suggesting a progressive smoothing of the light distribution as clusters evolve. Bootstrap resampling confirms the robustness of these trends. Forward modelling of synthetic clusters analysed with the same pipeline recovers a monotonic $CV_{\rm tr}$--age relation under simplified but physically motivated assumptions. These results show that second-order photometric structure contains measurable evolutionary information within the CMD-calibrated regime ($\sim10$--300~Myr).