Constraining the microlensing effect on time delays with new time-delay prediction model in $H_{0}$ measurements

Time-delay strong lensing provides a unique way to directly measure the Hubble constant ($H_{0}$). The precision of the $H_{0}$ measurement depends on the uncertainties in the time-delay measurements, the mass distribution of the main deflector(s), and the mass distribution along the line of sight. Tie and Kochanek (2018) have proposed a new microlensing effect on time delays based on differential magnification of the coherent accretion disc variability of the lensed quasar. If real, this effect could significantly broaden the uncertainty on the time delay measurements by up to $30\%$ for lens systems such as PG1115+080, which have relatively short time delays and monitoring over several different epochs. In this paper we develop a new technique that uses the time-delay ratios and simulated microlensing maps within a Bayesian framework in order to limit the allowed combinations of microlensing delays and thus to lessen the uncertainties due to the proposed effect. We show that, under the assumption of Tie and Kochanek (2018), the uncertainty on the time-delay distance ($D_{\Delta t}$, which is proportional to 1/$H_{0}$) of short time-delay ($\sim18$ days) lens, PG1115+080, increases from $\sim7\%$ to $\sim10\%$ by simultaneously fitting the three time-delay measurements from the three different datasets across twenty years, while in the case of long time-delay ($\sim90$ days) lens, the microlensing effect on time delays is negligible as the uncertainty on $D_{\Delta t}$ of RXJ1131-1231 only increases from $\sim2.5\%$ to $\sim2.6\%$.