A novel optimal transport-based approach for interpolating spectral time series. Paving the way for photometric classification of supernovae

The Vera C. Rubin Observatory is set to discover 1 million supernovae (SNe) within its first operational year. Given the impracticality of spectroscopic classification at such scales, it is mandatory to develop a reliable photometric classification framework. This paper introduces a novel method for creating spectral time series that can be used not only to generate synthetic light curves for photometric classification, but also in applications such as K-corrections and bolometric corrections. This approach is particularly valuable in the era of large astronomical surveys, where it can significantly enhance the analysis and understanding of an increasing number of SNe, even in the absence of extensive spectroscopic data By employing interpolations based on optimal transport theory, starting from a spectroscopic sequence, we derive weighted average spectra with high cadence. The weights incorporate an uncertainty factor for penalizing interpolations between spectra that show significant epoch differences and lead to a poor match between the synthetic and observed photometry. Our analysis reveals that even with a phase difference of up to 40 days between pairs of spectra, optical transport can generate interpolated spectral time series that closely resemble the original ones. Synthetic photometry extracted from these spectral time series aligns well with observed photometry. The best results are achieved in the V band, with relative residuals of less than 10 for 87 and 84 of the data for type Ia and II, respectively. For the B g R and r bands, the relative residuals are between 65 and 87 within the previously mentioned 10 threshold for both classes. The worse results correspond to the i and I bands, where, in the case of SN Ia, the values drop to 53 and 42, respectively. We introduce a new method for constructing spectral time series for individual SNe starting from a sparse spectroscopic sequence, and demonstrate its capability to produce reliable light curves that can be used for photometric classification.