Constraints on Supermassive Black Hole Binaries from the Lack of Resolvable Sources in the NANOGrav 15-yr Dataset

Pulsar timing arrays (PTAs) have found evidence of a gravitational wave background (GWB) consistent with a population of supermassive black hole binaries (SMBHBs), but have not yet resolved a continuous wave (CW) from an individual binary. We present the first SMBHB population constraints incorporating PTA upper limits on CWs, based on the NANOGrav 15-year (NG15) data. Using semi-analytic models to generate simulated populations, we calculate each sample's GWB likelihood by free spectral comparison and CW nondetection (nCW) likelihoods by (1) mapping each realization's highest CW signal-to-noise ratio (S/N) to a detection probability and (2) counting the fraction of realizations without a binary close enough that NG15 would have detected it. CW nondetection favors populations in which many lower-mass sources, rather than a few ultramassive ones, dominate the GWB. This information is complementary to that provided by the GWB amplitude, breaking the degeneracy between the masses and number of binaries required to reproduce the observed spectrum. Relative to GWB-only constraints, the joint posteriors favor higher galaxy merger rates, lower M BH - M bulge scatter, shorter binary lifetimes, and steeper small-separation hardening. The most detectable sources in the S/N-weighted joint posterior have chirp masses about 10 9.6 M, luminosity distances about 1300 Mpc, and frequencies about 6 nHz, while the nCW-only constraints favor lower frequencies, coinciding with the NG15 4 nHz candidate. These constraints will tighten if CW nondetection continues.