On the complementarity of pulsar timing and space laser interferometry
  for the individual detection of supermassive black hole binaries
  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. REST OF
THE ABSTRACT IN THE PDF FILE.
