Finding gravitational-wave black holes with parallax microlensing

The LIGO-Virgo gravitational-wave (GW) observation unveiled the new population of black holes (BHs) that appears to have an extended mass spectrum up to around $70M_\odot$, much heavier than the previously-believed mass range ($\sim 8M_\odot$). In this paper, we study the capability of a microlensing observation of stars in the Milky Way (MW) bulge region to identify BHs of GW mass scales, taking into account the microlensing parallax characterized by the parameter $\pi_{\rm E}\propto M^{-1/2}$ ($M$ is the mass of a lens), which is a dimension-less quantity defined by the ratio of the astronomical unit to the projected Einstein radius. First, assuming that BHs follow the same spatial and velocity distributions of stars as predicted by the standard MW model, we show that microlensing events with long light curve timescales, $t_{\rm E}\gtrsim 100~{\rm days}$, and small parallax effects, $\pi_{\rm E}\sim 10^{-2}$, are dominated by BH lenses compared to stellar-mass lenses. Second, using a Markov chain Monte Carlo analysis of the simulated light curve, we show that BH lens candidates are securely identified on individual basis, if the parallax effect is detected or well constrained to the precision of a percent level in $\pi_{\rm E}$. We also discuss that a microlensing event of an intermediate-mass BH of $\sim 1000M_\odot$, if it occurs, can be identified in a distinguishable way from stellar-mass BHs.