  This paper presents a technique to search for supermassive black hole
binaries (MBHBs) in the Sloan Digital Sky Survey (SDSS). The search is based on
the peculiar properties of merging galaxies that are found in a mock galaxy
catalog from the Millennium Simulation. MBHBs are expected to be the main
gravitational wave (GW) sources for pulsar timing arrays (PTAs); however, it is
still unclear if the observed GW signal will be produced by a few single MBHBs,
or if it will have the properties of a stochastic background. The goal of this
work is to produce a map of the sky in which each galaxy is assigned a
probability of having suffered a recent merger, and of hosting a MBHB that
could be detected by PTAs. This constitutes a step forward in the understanding
of the expected PTA signal: the skymap can be used to investigate the
clustering properties of PTA sources and the spatial distribution of the
observable GW signal power; moreover, galaxies with the highest probabilities
could be used as inputs in targeted searches for individual GW sources. We also
investigate the distribution of neighboring galaxies around galaxies hosting
MBHBs, finding that the most likely detectable PTA sources are located in dense
galaxy environments. Different techniques are used in the search, including
Bayesian and Machine Learning algorithms, with consistent outputs. Our method
generates a list of galaxies classified as MBHB hosts, that can be combined
with other searches to effectively reduce the number of misclassifications. The
spectral coverage of the SDSS reaches less than a fifth of the sky, and the
catalog becomes severely incomplete at large redshifts; however, this technique
can be applied in the future to larger catalogs to obtain complete,
observationally-based information of the expected GW signal detectable by PTAs.
