Pulsar Timing Array Constraints on the Merger Timescale of Subparsec
  Supermassive Black Hole Binary Candidates
  We estimate the merger timescale of spectroscopically-selected, subparsec
supermassive black hole binary (SMBHB) candidates by comparing their expected
contribution to the gravitational wave background (GWB) with the sensitivity of
current pulsar timing array (PTA) experiments and in particular, with the
latest upper limit placed by the North American Nanohertz Observatory for
Gravitational Waves (NANOGrav). We find that the average timescale to
coalescence of such SMBHBs is $\langle t_{\rm evol} \rangle > 6\times
10^4\,$yr, assuming that their orbital evolution in the PTA frequency band is
driven by emission of gravitational waves. If some fraction of SMBHBs do not
reside in spectroscopically detected active galaxies, and their incidence in
active 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 by
theoretical models and imply that all the SMBHB candidates in our spectroscopic
sample could be binaries without violating the observational constraints on the
GWB. This result illustrates the power of the multi-messenger approach,
facilitated by the PTAs, in providing an independent statistical test of the
nature of SMBHB candidates discovered in electromagnetic searches.
