Functional Light Curve Models for Type Ia Supernovae and Mira Variables, with Their Application of Distance Determination

Abstract

Both type Ia supernovae and variable stars are important distance indicators in astronomy. The peak luminosity of type Ia supernovae and the period-luminosity relation of Miras can be employed for relative distance determination. For both SNIa and Mira, we develop light curve models with noisy, sparse and irregularly-sampled data.

We develop a functional principal component method for SNIa light curves. Each SNIa light curve is expressed as a linear combination of a mean function and several principal component functions. The coefficients of the principal component functions are called scores. The proposed method takes into account peak registration, shape constraints and is equipped with a fast training algorithm. The resulting model provides high quality fit to each light curve. In addition, the scores present powerful characterization of SNIa. They demonstrate connection with interstellar dusting, spectral classes and other physical properties. Moreover, the method provides a functional linear form in place of the commonly used ΔM15 parameter for distance predictions.

We also develop a semi-parametric model for Mira period estimation. The proposed method has a close relation with a Gaussian process model, and is solved in an empirical Bayesian framework. The empirical Bayesian is solved by a fast quasi-Newton algorithm with warm start, and combined with a grid search in the frequency parameter due to the related high multimodality. The proposed method is compared with the traditional Lomb-Scargle method in a large-scale simulation and shows considerable improvement.