Precise Time Delays from Strongly Gravitationally Lensed Type Ia
  Supernovae with Chromatically Microlensed Images
  Time delays between the multiple images of strongly lensed Type Ia supernovae
(gl\sneia) have the potential to deliver precise cosmological constraints, but
the effects of microlensing on the measurement have not been studied in detail.
Here we quantify the effect of microlensing on the gl\snia\ yield of the Large
Synoptic Survey Telescope (LSST) and the effect of microlensing on the
precision and accuracy of time delays that can be extracted from LSST gl\sneia.
Microlensing has a negligible effect on the LSST gl\snia\ yield, but it can be
increased by a factor of $\sim$2 to 930 systems using a novel photometric
identification technique based on spectral template fitting. Crucially, the
microlensing of gl\sneia\ is achromatic until 3 rest-frame weeks after the
explosion, making the early-time color curves microlensing-insensitive time
delay indicators. By fitting simulated flux and color observations of
microlensed gl\sneia\ with their underlying, unlensed spectral templates, we
forecast the distribution of absolute time delay error due to microlensing for
LSST, which is unbiased at the sub-percent level and peaked at 1\% for color
curve observations in the achromatic phase, while for light curve observations
it is comparable to state-of-the-art mass modeling uncertainties (4\%). About
70\% of LSST gl\snia\ images should be discovered during the achromatic phase,
indicating that microlensing time delay uncertainties can be minimized if
prompt multicolor follow-up observations are obtained. Accounting for
microlensing, the 1--2 day time delay on the recently discovered gl\snia\
iPTF16geu can be measured to 40\% precision, limiting its cosmological utility.
