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We estimate the merger timescale of spectroscopically-selected, subparsecsupermassive black hole binary (SMBHB) candidates by comparing their expectedcontribution to the gravitational wave background (GWB) with the sensitivity ofcurrent pulsar timing array (PTA) experiments and in particular, with thelatest upper limit placed by the North American Nanohertz Observatory forGravitational Waves (NANOGrav). We find that the average timescale tocoalescence of such SMBHBs is $\langle t_{\rm evol} \rangle > 6\times10^4\,$yr, assuming that their orbital evolution in the PTA frequency band isdriven by emission of gravitational waves. If some fraction of SMBHBs do notreside in spectroscopically detected active galaxies, and their incidence inactive and inactive galaxies is similar, then the merger timescale could be$\sim 10$ times longer, $\langle t_{\rm evol} \rangle > 6\times 10^5\,$yr.These limits are consistent with the range of timescales predicted bytheoretical models and imply that all the SMBHB candidates in our spectroscopicsample could be binaries without violating the observational constraints on theGWB. This result illustrates the power of the multi-messenger approach,facilitated by the PTAs, in providing an independent statistical test of thenature of SMBHB candidates discovered in electromagnetic searches.

Pulsar Timing Array Constraints on the Merger Timescale of Subparsec Supermassive Black Hole Binary Candidates