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We develop a method for identifying a compact object in binary systems withastrometric measurements and apply it to some binaries. Compact objects in somehigh-mass X-ray binaries and gamma-ray binaries are unknown, which isresponsible for the fact that emission mechanisms in such systems have not yetconfirmed. The accurate estimate of the mass of the compact object allows us toidentify the compact object in such systems. Astrometric measurements areexpected to enable us to estimate the masses of the compact objects in thebinary systems via a determination of a binary orbit. We aim to evaluate thepossibility of the identification of the compact objects for some binarysystems. We then calculate probabilities that the compact object is correctlyidentified with astrometric observation (= confidence level) by taking intoaccount a dependence of the orbital shape on orbital parameters anddistributions of masses of white dwarfs, neutron stars, and black holes. Wefind that the astrometric measurements with the precision of 70 $\mu$as for$\gamma$~Cas allows us to identify the compact object at 99% confidence levelif the compact object is a white dwarf with 0.6 M$_{\odot}$. In addition, wecan identify the compact object with the precision of 10 $\mu$as at 97% orlarger confidence level for LS~I~+61$^{\circ}$~303 and 99% or larger forHESS~J0632+057. These results imply that the astrometric measurements with the10-$\mu$as precision level can realize the identification of compact objectsfor $\gamma$~Cas, LS~I~+61$^{\circ}$~303, and HESS~J0632+057.

Uncovering the identities of compact objects in high-mass X-ray binaries and gamma-ray binaries by astrometric measurements