Determining gravitational wave radiation from close galaxy pairs using a
  binary population synthesis approach
  Context. The early phase of the coalescence of supermassive black hole (SMBH)
binaries from their host galaxies provides a guaranteed source of low-frequency
(nHz-$\mu$Hz) gravitational wave (GW) radiation by pulsar timing observations.
These types of GW sources would survive the coalescing and be potentially
identifiable. Aims. We aim to provide an outline of a new method for detecting
GW radiation from individual SMBH systems based on the Sloan Digital Sky Survey
(SDSS) observational results, which can be verified by future observations.
Methods. Combining the sensitivity of the international Pulsar Timing Array
(PTA) and the Square Kilometer Array (SKA) detectors, we used a binary
population synthesis (BPS) approach to determine GW radiation from close galaxy
pairs under the assumption that SMBHs formed at the core of merged galaxies. We
also performed second post-Newtonian approximation methods to estimate the
variation of the strain amplitude with time. Results. We find that the value of
the strain amplitude \emph{h} varies from about $10^{-14}$ to $10^{-17}$ using
the observations of 20 years, and we estimate that about 100 SMBH sources can
be detected with the SKA detector.
