HOLISMOKES: V. Microlensing of type II supernovae and time-delay inference through spectroscopic phase retrieval.

We investigate strongly gravitationally lensed type II supernovae (LSNe II) for time-delay cosmography, incorporating microlensing effects; this expands on previous microlensing studies of type Ia supernovae (SNe Ia). We use the radiative-transfer code TARDIS to recreate five spectra of the prototypical SN 1999em at different times within the plateau phase of the light curve. The microlensing-induced deformations of the spectra and light curves are calculated by placing the SN into magnification maps generated with the code GERLUMPH. We study the impact of microlensing on the color curves and find that there is no strong influence on them during the investigated time interval of the plateau phase. The color curves are only weakly affected by microlensing due to the almost achromatic behavior of the intensity profiles. However, the lack of nonlinear structure in the color curves during the plateau phase of type II-plateau supernovae makes time-delay measurements more challenging compared to SN Ia color curves, given the possible presence of differential dust extinction. Therefore, we further investigate SN phase inference through spectral absorption lines under the influence of microlensing and Gaussian noise. As the spectral features shift to longer wavelengths with progressing time after explosion, the measured wavelength of a specific absorption line provides information on the epoch of the SN. The comparison between retrieved epochs of two observed lensing images then gives the time delay of the images. We find that the phase retrieval method that uses spectral features yields accurate delays with uncertainties of ≲2 days, making it a promising approach. [ABSTRACT FROM AUTHOR]