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, which expands on
previous microlensing studies of type Ia supernovae (SNe Ia). We use the
radiative-transfer code ${\rm \small TARDIS}$ 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 ${\rm \small GERLUMPH}$. 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 non-linear structure in the color
curves makes time-delay measurements difficult 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 using spectral
features yields accurate delays with uncertainties $\small {\lesssim}$2 days,
making it a promising approach.
