Spectral Hardness as the Primary Discriminator: Unveiling the Collapsar--Merger Boundary with a Gold-Standard Gamma-Ray Burst Sample

Abstract

In this Letter, we establish a robust, physically motivated classification method using a Support Vector Machine (SVM) trained on a "gold-standard" sample of 24 GRBs with spectroscopically confirmed progenitors (associated SNe or KNe). By isolating the prompt main spike to excise contamination from extended emission, we derive a quantitative classification index, I_SVM = 5.01 log_10 E_p,i - 1.25 log_10 E_iso - 0.34 log_10 T_90,z - 12.90 (units: keV, 10^52 erg, s). Events with I_SVM > 0 are classified as mergers. Analysis of the standardized classification weights reveals that the discriminative power of E_p,i is approximately 5 times that of T_90,z, while E_iso contributes a weight comparable to E_p,i. This quantitatively demonstrates that spectral hardness and energetics, rather than duration, are the primary physical signatures distinguishing mergers from collapsars. The derived boundary implies a stringent hardness ceiling for collapsars, while mergers are identified as outliers with excessive hardness relative to their energy budget. The classifier successfully identifies the nature of historic test cases, including the ultra-long GRB 111209A (collapsar) and the short GRB 050709 (merger), independent of instrumental eras. This tool paves the way for cleaning archival and future high-redshift GRB samples for precision cosmology.