Testing the Binary Hypothesis: Pulsar Timing Constraints on Supermassive Black Hole Binary Candidates

The advent of time domain astronomy is revolutionising our understanding of the Universe. Programs such as the Catalina Real-time Transient Survey (CRTS) or the Palomar Transient Factory (PTF) surveyed millions of objects for several years, allowing variability studies on large statistical samples. The inspection of $\approx$ 250k quasars in CRTS resulted in a catalogue of 111 potentially periodic sources, put forward as supermassive black hole binary (SMBHB) candidates. A similar investigation on PTF data yielded 33 candidates from a sample of 33k objects. Working under the SMBHB hypothesis, we compute the implied SMBHB merger rate and we use it to construct the expected gravitational wave background (GWB) at nano-Hz frequencies, probed by pulsar timing arrays (PTAs). After correcting for incompleteness, we find that the implied GWB exceeds the current most stringent PTA upper limits by almost an order of magnitude for the CRTS sample, and by at least a factor of 2-3 for the PTF sample. Eccentricity and/or coupling with the environment can only suppress the signal by a factor of $\approx 2$ in the relevant frequency range and cannot account for the inconsistency. The inferred GWB can be reconciled with the PTA upper limits only if nearly all 111 candidates are false positives and AGN hosting a single SMBH exhibit prominent variability without the need of an SMBH companion. Alternatively, alleviating this severe tension would require that the typical black hole mass has been overestimated by a factor of $\gtrsim 4$, very low typical mass ratios $q=M_2/M_1<0.01$, or else that the loudest gravitational wave sources are preferentially false positives.