Shortening the Baseline: Characterising Type Ia Supernovae Using $Δm_{10}(X)$

Abstract

An explorative study of Type Ia Supernovae (SNe Ia) light curves is presented. $Δm_{t}(X)$ 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 $Δm_{10}(B)$ and $Δm_{10}(g)$ are found to capture the LWR effectively, while mitigating the severe degeneracy that affects longer timescales for fast-declining ($Δm_{15}(B) \geq 1.6$ mag) events. Continuous, piecewise linear models are presented that seamlessly anchor the transition between normal and fast-declining regimes. The decline-rate $Δm_{10}(X)$ closely approximates the results of the more complex colour-stretch parameters, requiring less post-maximum temporal coverage than $Δm_{15}(B)$ or $s_{BV}$, and offers an even greater sensitivity for slow decliners. $Δm_{10}(B)$ provides a precise and practical tool for large-scale photometric surveys and real-time observer classification.photometric surveys and real-time observer classification.