With growing data from ongoing and future supernova surveys it is possible to empirically quantify the shapes of SNIa light curves in more detail, and to quantitatively relate the shape parameters with the intrinsic properties of SNIa. Building such relationship is critical in controlling systematic errors associated with supernova cosmology. Based on a collection of well-observed SNIa samples accumulated in the past years, we construct an empirical SNIa light curve model using a statistical method called the functional principal component analysis (FPCA) for sparse and irregularly sampled functional data. Using this method, the entire light curve of an SNIa is represented by a linear combination of principal component functions, and the SNIa is represented by a few numbers called principal component scores. These scores are used to establish relations between light curve shapes and physical quantities such as intrinsic color, interstellar dust reddening, spectral line strength, and spectral classes. These relations allow for descriptions of some critical physical quantities based purely on light curve shape parameters. Our study shows that some important spectral feature information is being encoded in the broad band light curves, for instance, we find that the light curve shapes are correlated with the velocity and velocity gradient of the Si II $lambda$6355 line. This is important for supernova surveys, e.g., LSST and WFIRST. Moreover, the FPCA light curve model is used to construct the entire light curve shape, which in turn is used in a functional linear form to adjust intrinsic luminosity when fitting distance models.
Download