Measuring accretion disk sizes of lensed quasars with microlensing time
  delay in multi-band light curves
  Time-delay cosmography in strongly lensed quasars offer an independent way of
measuring the Hubble constant, $H_0$. However, it has been proposed that the
combination of microlensing and source-size effects, also known as microlensing
time delay can potentially increase the uncertainty in time-delay measurements
as well as lead to a biased time delay. In this work, we first investigate how
microlensing time delay changes with assumptions on the initial mass function
(IMF) and find that the more massive microlenses produce the sharper
distributions of microlensing time delays. We also find that the IMF has modest
effect on the the magnification probability distributions. Second, we present a
new method to measure the color-dependent source size in lensed quasars using
the microlensing time delays inferred from multi-band light curves. In practice
the relevant observable is the differential microlensing time delays between
different bands. We show from simulation using the facility as Vera C. Rubin
Observatory that if this differential time delay between bands can be measured
with a precision of $0.1$ days in any given lensed image, the disk size can be
recovered to within a factor of $2$. If four lensed images are used, our method
is able to achieve an unbiased source measurement within error of the order of
$20\%$, which is comparable with other techniques.
