  Supermassive black holes are expected to pair as a result of galaxy mergers,
and form a bound binary at parsec or sub-parsec scales. These scales are
unresolved even in nearby galaxies, and thus detection of non-active black hole
binaries must rely on stellar dynamics. Here we show that these systems could
be indirectly detected through the trail that the black holes leave as they
spiral inwards. We analyze two numerical simulations of inspiralling black
holes (equal masses and 10:1 mass ratio) in the stellar environment of a
galactic centre. We studied the effect of the binary on the structure of the
stellar population, with particular emphasis on projected kinematics and
directly measurable moments of the velocity distribution. We present those
moments as high-resolution 2D maps. As shown in past scattering experiments, a
torus of stars counter-rotating with respect to the black holes exists in
scales ~ 5 to 10 times larger than the binary separation. While this is seen in
the average velocity map in the unequal mass case, it is obscured by a more
strongly co-rotating outer region in the equal mass case; however, the inner
counter-rotation could still be detected by studying the higher moments of the
velocity distribution. Additionally, the maps reveal a dip in velocity
dispersion in the inner region, as well as more pronounced signatures in the
higher distribution moments. These maps could serve as templates for integral
field spectroscopy observations of nearby galactic centres. The discovery of
such signatures may help census the population of supermassive black hole
binaries and refine signal rate predictions for future space-based low
frequency gravitational wave detectors.
