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

The merger of two galaxies, each hosting a supermassive black hole (SMBH) of mass 10(6) M-circle dot or more, could yield a bound SMBH binary. For the early-type galaxy NGC 4472, we study how astrometry with a next-generation Very Large Array could be used to monitor the reflex motion of the primary SMBH of mass M-pri, as it is tugged on by the secondary SMBH of mass M-sec. Casting the orbit of the putative SMBH binary in terms of its period P, semimajor axis a(bin), and mass ratio q = M-sec/M-pri <= 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 a 95% accuracy of 2 mu as per monitoring epoch, subparsec values of a(bin) could be accessed over a range of mass ratios notionally encompassing major (q > 1/4) and minor (q < 1/4) galaxy mergers. (3) If no reflex motion is detected for M-pri after 1 (10) yr of monitoring, an SMBH binary with period P = 4 (40) yr and mass ratio q > 0.01 (0.003) could be excluded. This would suggest no present-day evidence for a past major merger like that recently simulated, where scouring by a q similar to 1 SMBH binary formed a stellar core with kinematic traits like those of NGC 4472. (4) Astrometric monitoring could independently check the upper limits on q from searches for continuous gravitational waves from NGC 4472.