Detecting Galactic MACHOs with VERA through Astrometric Microlensing of Distant Radio Sources

In this paper we investigate the properties of astrometric microlensing ofdistant radio sources (QSOs and radio galaxies) due to MACHOs, and discusstheir implications for VERA (VLBI Exploration of Radio Astrometry). First weshow that in case of astrometric microlensing of distant sources, the eventduration is only a function of the lens mass and tangential velocity, butindependent of the lens distance, in contrast to the well-known three-folddegeneracy for photometric microlensing. Moreover, the lens mass $M$ is scaledby the tangential velocity $v_\perp$ as $M\propto v_\perp$, rather than$M\propto v_\perp^2$ which is the case for photometric microlensing. Thus, inastrometric microlensing the dependence of the lens mass on the unknownparameter $v_\perp$ is weaker, indicating that the duration of astrometricmicrolensing event is a better quantity to study the mass of lensing objectsthan that of photometric microlensing. We also calculate the optical depth andevent rate, and show that within 20$^\circ$ of the galactic center a typicalevent rate for 10 $\mu$as-level shift is larger than $2.5 \times 10^{-4}$ eventper year, assuming that a quarter of the halo is made up with MACHOs. Thisindicates that if one monitors a few hundred sources for $\sim$20 years, suchan astrometric microlensing event is detectable. Since a typical event durationis found to be fairly long (5 to 15 years), the frequency of the monitoringobservation can be relatively low, i.e., once per six months, which is ratherreasonable for practical observations. We discuss practical strategy forobserving astrometric microlensing with VERA, and argue that an astrometricmicrolensing event due to MACHOs can be detected by VERA within a few decades.Comment: 10 pages, 6 figures included, accepted for publication in PAS