Shortening the Baseline: Characterising Type Ia Supernovae Using Δ m 10( X )

Abstract An explorative study of Type Ia Supernovae (SNe Ia) light curves is presented. Δmt(X) decline-rate metrics are used to evaluate alternative characterisations of light curve diversity and the Luminosity-Width Relation (LWR). Using a sample of 362 SNe Ia from the Carnegie Supernova Project (CSP-I and CSP-II), Gaussian Process regression is used to fit B- and g-band light curves and measure decline-rates across multiple post-maximum timescales. The LWR is calibrated using a clean subsample of SNe Ia with host-independent distance moduli and Fitzpatrick (1999) reddening corrections. Decline-rates Δm10(B) and Δm10(g) are found to capture the LWR effectively, while mitigating the severe degeneracy that affects longer timescales for fast-declining (Δm15(B) ≥ 1.6 mag) events. Continuous, piecewise linear models are presented that seamlessly anchor the transition between normal and fast-declining regimes. The decline-rate Δm10(X) closely approximates the results of the more complex colour-stretch parameters, requiring less post-maximum temporal coverage than Δm15(B) or sBV, and offers an even greater sensitivity for slow decliners. Δm10(B) provides a precise and practical tool for large-scale photometric surveys and real-time observer classification.