Constraining the microlensing effect on time delays with a new time-delay prediction model in H0 measurements

Time- delaystrong 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- delaymeasurements, the mass distributionof the main deflector(s), and the mass distributionalong the line of sight. Tie & Kochanek have proposed a new microlensing effect on time delaysbased on differential magnification of the coherent accretion discvariability of the lensed quasar. If real, this effect could significantly broaden the uncertainty on the time- delaymeasurements by up to 30 per cent for lens systems such as PG 1115+080, which have relatively short time delaysand monitoring over several different epochs. In this paper we develop a new technique that uses the cosmological time- delayratios and simulated microlensing maps within a Bayesian framework in order to limit the allowed combinations of microlensing delaysand thus to lessen the uncertainties due to the proposed effect. We show that, under the assumption of Tie & Kochanek, the uncertainty on the time- delaydistance (D-Delta t, which is proportional to 1/H-0) of the short time- delay(similar to 18 d) lens, PG 1115+080, increases from similar to 7 per cent to similar to 10 per cent by simultaneously fitting the three time- delaymeasurements from the three different data sets across 20 yr, while in the case of the long time- delay(similar to 90 d) lens, the microlensing effect on time delaysis negligible as the uncertainty on D-Delta t of RXJ 1131-1231 only increases from similar to 2.5 per cent to similar to 2.6 per cent.