The kinematic signature of the inspiral phase of massive binary black holes

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 analyse 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 similar to 5-10 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 corotating 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.