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.