Spectral Microlensing of Extragalactic H II Regions by Stellar-Mass Black Holes

Most of the Milky Way's predicted stellar-mass black holes remain hidden, especially at high Galactic latitudes or in the Galactic halo, where traditional dense-field stellar microlensing is ineffective. We propose an alternative method to map this isolated population via the spectral microlensing of compact, extragalactic H II regions. Projected onto the source plane, the physical Einstein radius of a Galactic black hole can match the typical core sizes of H II regions in distant galaxies. Microlensing triggers an achromatic magnification, producing distinct narrow emission-line excesses in integrated galaxy spectra. Because gravitational lensing is wavelength-independent, intrinsic line ratios are preserved, offering a robust discriminant against false-positive astrophysical transients. Notably, the efficiency of this method depends critically on the size of the H II regions: while extended regions suffer from low optical depth, compact regions with a physical size 10 pc offer significantly higher magnifications. These compact cores, however, are heavily dust-obscured at optical wavelengths, making infrared and radio observations the primary windows for this method. Even so, the spatial sparseness of background H II regions and the stringent alignment requirement for high magnification limit the expected event rate to about 10-6 per year. Nevertheless, this method offers a unique opportunity to detect stellar-mass black holes and constrain their abundance in such low-density environments.