Decoding the Early-Time Light Curves of Type Ia Supernovae. II. Population Parameters of One Thousand ZTF Supernovae

Early-time light curves of Type Ia Supernovae (SNe Ia) encode critical information about their progenitor systems. We characterize the rise of normal SNe Ia using a volume-complete sample of 972 events from the Zwicky Transient Facility Data Release 2, an order of magnitude larger than any previous dataset for similar analyses. Fitting light curves up to 30% of peak flux with a power-law model under a hierarchical Bayesian framework, we provide robust population-level constraints on the rise time (t rise; mu=18.55 plus or minus0.08 days, sigma=1.42 plus or minus0.07 days), rise index (alpha; mu=2.10 plus or minus0.04, sigma=0.48 plus or minus0.03 in ZTF r), and g-r color evolution (alpha g - alpha r; mu=0.20 plus or minus0.02, sigma=0.17 plus or minus0.02). These power-law fits are sensitive to the chosen truncation epoch if data beyond about 40% of peak flux are included, but generally converge when restricted to earlier epochs. The relation between rise morphology and light-curve width (SALT2 x 1 stretch) bifurcates into two distinct regimes: high-stretch SNe Ia show clear trends where a higher x 1 correlates with shallower rises and more persistent blue colors, whereas low-stretch SNe Ia lack such trends. While rise times correlate positively with x 1 overall, this relation flattens significantly within the high-stretch population. Searching for anomalies, we identify several normal SNe Ia with unusually long rise times, which potentially exhibit short-duration (2 days) flux excesses over a smooth rise. Long-duration (about 5 days) flux excesses appear common within the high-stretch population and are tied to the shallow rises and early blue colors, pointing to widespread outward 56 Ni mixing. Multi-dimensional explosion models with more realistic progenitor setups are needed to fully reproduce the observed dichotomy in rise morphology and stretch.