Decoding the Early-Time Light Curves of Type Ia Supernovae. I. A Hierarchical Bayesian Framework for Demographic Inference

Light curves of Type Ia Supernovae (SNe Ia) in the days following explosion encode the diversity of progenitor systems and explosion physics. We present a hierarchical Bayesian framework to robustly constrain the population-level light-curve morphology of SNe Ia by fitting a large light-curve dataset simultaneously to power-law rises. Using a multivariate Gaussian population prior, this framework automatically down-weights sparsely sampled SNe and noisy measurements in the inference, obviating the need for restrictive quality cuts that introduce selection biases. Validation on simulated power-law light curves demonstrates that the population prior effectively suppresses the volume-projection bias from the asymmetric likelihood: compared to the classic two-step approach of fitting individual SNe and then aggregating the results, the hierarchical approach dramatically reduces the bias on the population-level parameters (mean, scatter, and correlation). When fitting the power-law model to light curves with more realistic morphologies, while the rise time can be mildly underestimated due to model misspecification, the recovered population scatter remains reliable. Furthermore, SNe with early flux excesses can emerge as outliers in the inferred parameter space, offering a potential diagnostic for identifying such events. Finally, we show that the inferred population distribution can also improve individual-event inference. Restricting the population prior to nuisance amplitudes, while preserving the complete correlation structure, regularizes fits to individual SNe without shrinking the physically meaningful rise time and rise index toward their population means.