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Constraints on Individual Supermassive Black Hole Binaries from Pulsar Timing Array Limits on Continuous Gravitational Waves

Pulsar timing arrays (PTAs) are placing increasingly stringent constraints on the strain amplitude of continuous gravitational waves emitted by supermassive black hole binaries on subparsec scales. In this paper, we incorporate independent information about the dynamical masses $M_{bh}$ of supermassive black holes in specific galaxies at known distances and use this additional information to further constrain whether or not those galaxies could host a detectable supermassive black hole binary. We estimate the strain amplitudes from individual binaries as a function of binary mass ratio for two samples of nearby galaxies: (1) those with direct dynamical measurements of $M_{bh}$ in the literature, and (2) the 116 most massive early-type galaxies (and thus likely hosts of the most massive black holes) within 108 Mpc from the MASSIVE Survey. Our exploratory analysis shows that the current PTA upper limits on continuous waves (as a function of angular position in the sky) can already constrain the mass ratios of hypothetical black hole binaries in many galaxies in our samples. The constraints are stronger for galaxies with larger $M_{bh}$ and at smaller distances. For the black holes with $M_{bh} \gtrsim 5\times 10^9 M_\odot$ at the centers of NGC 1600, NGC 4889, NGC 4486 (M87) and NGC 4649 (M60), any binary companion in orbit within the PTA frequency bands would have to have a mass ratio of a few percent or less.