Hubble Constant from LSST Strong lens time delays with microlensing
  systematics
  Strong lens time delays have been widely used in cosmological studies,
especially to infer $H_0$. The upcoming LSST will provide several hundred well
measured time delays from the light curves of lensed quasars. However, due to
the inclination of the finite AGN accretion disc and the differential
magnification of the coherent temperature fluctuations, the microlensing by the
stars can lead to changes in the actual time delay on the light-crossing time
scale of the emission region $\sim days$. We first study how this would change
the uncertainty of $H_0$ in the LSST era, assuming the microlensing time delays
can be well estimated. We adopt 1/3, 1 and 3 days respectively as the typical
microlensing time delay uncertainties. The relative uncertainty of $H_0$ will
be enlarged to $0.47\%$, $0.51\%$, $0.76\%$, respectively from the one without
microlensing impact $0.45\%$. Then, due to the lack of understandings on the
quasar models and microlensing patterns, we also test the reliability of the
results if one neglects this effect in the analysis. The biases of $H_0$ will
be $0.12\%$, $0.22\%$ and $0.70\%$, respectively, suggesting that 1 day is the
cut-off for a robust $H_0$ estimate.
