Constraining the Binarity of Massive Black Holes in the Galactic Center and Some Nearby Galaxies via Pulsar Timing Array Observations of Gravitational Waves

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Massive black holes (MBHs) exist in the Galactic center (GC) and other nearby galactic nuclei. As a natural outcome of galaxy mergers, some MBHs may have a black hole (BH) companion. In this paper, assuming that the MBHs in the GC and some nearby galaxies are in binaries with orbital periods ranging from months to years (gravitational-wave frequency ∼1–100 nHz), we investigate the detectability of gravitational waves from these binary MBHs (BBHs) and constraints on the parameter space for the existence of BBHs in the GC, Large Magellanic Cloud (LMC), M31, M32, and M87 that may be obtained by current/future pulsar timing array (PTA) observations. We find that a BBH in the GC, if any, can be revealed by the Square Kilometre Array PTA (SKA-PTA) if it has mass ratio q ≳ 10−4–10−3 and semimajor axis a ∼ 20–103 au. The existence of a BH companion of the MBH can be revealed by SKA-PTA with ∼20 yr observations in M31 if q ≳ 10−4 and a ∼ 102–104 au or in M87 if q ≳ 10−5 and a ∼ 103–2 × 104 au, but not in the LMC and M32 if q ≪ 1. If a number of millisecond stable pulsars with distances ≲0.1–1 pc away from the central MBH in the GC, the LMC, M32, or M31 can be detected in future and applied to PTAs, a BH companion with mass even down to ∼100 M ⊙, close to stellar masses, can be revealed by such PTAs. Future PTAs are expected to provide an independent way to reveal BBHs and low-mass MBH companions in the GC and nearby galaxies, improving our understandings of the formation and evolution of MBHs and galaxies.