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The merger of two galaxies, each hosting a supermassive black hole (SMBH) ofmass $10^6$\,M$_{\odot}$ or more, could yield a bound SMBH binary. For theearly-type galaxy NGC\,4472, we study how astrometry with a next-generationVery Large Array (ngVLA) could be used to monitor the reflex motion of theprimary SMBH of mass $M_{\rm pri}$, as it is tugged on by the secondary SMBH ofmass $M_{\rm sec}$. Casting the orbit of the putative SMBH binary in terms ofits period $P$, semimajor axis $a_{\rm bin}$, and mass ratio $q = M_{\rm sec} /M_{\rm pri} \le 1$, we find the following: (1) Orbits with fiducial periods of$P = 4$\,yr and 40\,yr could be spatially resolved and monitored. (2) For a95\% accuracy of $2\,\mu$as per monitoring epoch, sub-parsec values of $a_{\rmbin}$ could be accessed over a range of mass ratios notionally encompassingmajor ($q > \frac{1}{4}$) and minor ($q < \frac{1}{4}$) galaxy mergers. (3) Ifno reflex motion is detected for $M_{\rm pri}$ after 1(10)\,yr of monitoring, aSMBH binary with period $P = 4(40)$\,yr and mass ratio $q > 0.01(0.003)$ couldbe excluded. This would suggest no present-day evidence for a past major mergerlike that recently simulated, where scouring by a $q \sim 1$ SMBH binary formeda stellar core with kinematic traits like those of NGC\,4472. (4) Astrometricmonitoring could independently check the upper limits on $q$ from searches forcontinuous gravitational waves from NGC\,4472.

Toward Astrometric Constraints on a Supermassive Black Hole Binary in the Early-Type Galaxy NGC\,4472