Gravitational waves coming from Super Massive Black Hole Binaries (SMBHBs) are targeted by both Pulsar Timing Array (PTA) and Space Laser Interferometry (SLI).
The possibility of a single SMBHB being tracked first by PTA, through inspiral, and later by SLI, up to merger and ring down, has been previously suggested. Although the bounding parameters are drawn by the current PTA or the upcoming Square Kilometer Array (SKA), and by the New Gravitational Observatory (NGO), derived from the Laser Interferometer Space Antenna (LISA), this paper also addresses sequential detection beyond specific project constraints. We consider PTA-SKA, which is sensitive from 10^(-9) to p x 10^(-7) Hz (p=4, 8), and SLI, which operates from s x 10^(-5) up to 1 Hz (s = 1, 3). A SMBHB in the range 2x 10^(8) - 2 x 10^(9) solar masses (the masses are normalised to a (1+z) factor, the red shift lying between z = 0.2 and z=1.5) moves from the PTA-SKA to the SLI band over a period ranging from two months to fifty years. By combining three Super Massive Black Hole (SMBH)-host relations with three accretion prescriptions, nine astrophysical scenarios are formed. They are then related to three levels of pulsar timing residuals (50, 5, 1 ns), generating twenty-seven cases. For residuals of 1 ns, sequential detection probability will never be better than 4.7 x 10^(-4) y^(-2) or 3.3 x 10^(-6) y^(-2) (per year to merger and per year of survey), according to the best and worst astrophysical scenarios, respectively; put differently this means one sequential detection every 46 or 550 years for an equivalent maximum time to merger and duration of the survey. The chances of sequential detection are further reduced by increasing values of the s parameter (they vanish for s = 10) and of the SLI noise, and by decreasing values of the remnant spin.