A Novel Optimal Transport-Based Approach for Interpolating Spectral Time Series: Paving the Way for Photometric Classification of Supernovae

This paper introduces a novel method for creating spectral time series, which can be used for generating synthetic light curves for photometric classification but also for applications like 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. methods: 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 with significant epoch differences and with poor match between the synthetic and observed photometry. results: Our analysis reveals that even with 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 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. conclusions: We introduce a new method to construct spectral time series for individual SN starting from a sparse spectroscopic sequence, demonstrating its capability to produce reliable light curves that can be used for photometric classification.