  In the Milky Way the central massive black hole, SgrA*, coexists with a
compact nuclear star cluster that contains a sub-parsec concentration of
fast-moving young stars called S-stars. Their location and age are not easily
explained by current star formation models, and in several scenarios the
presence of an intermediate-mass black hole (IMBH) has been invoked. We use
GRAVITY astrometric and SINFONI, KECK, and GNIRS spectroscopic data of S2 to
investigate whether a second massive object could be present deep in the
Galactic Centre (GC) in the form of an IMBH binary companion to SgrA*. To solve
the three-body problem, we used a post-Newtonian framework and consider two
types of settings: (i) a hierarchical set-up where the star S2 orbits the SgrA*
- IMBH binary and (ii) a non-hierarchical set-up where the IMBH trajectory lies
outside the S2 orbit. In both cases we explore the full 20-dimensional
parameter space by employing a Bayesian dynamic nested sampling method. For the
hierarchical case we find: IMBH masses > 2000 Msun on orbits with smaller
semi-major axes than S2 are largely excluded. For the non-hierarchical case the
parameter space contains several pockets of valid IMBH solutions. However, a
closer analysis of their impact on the resident stars reveals that IMBHs on
semi-major axes larger than S2 tend to disrupt the S-star cluster in less than
a million years. This makes the existence of an IMBH among the S-stars highly
unlikely. The current S2 data do not formally require the presence of an IMBH.
If an IMBH hides in the GC, it has to be either a low-mass IMBH inside the S2
orbit that moves on a short and significantly inclined trajectory or an IMBH
with a semi-major axis >1". We provide the parameter maps of valid IMBH
solutions in the GC and discuss the general structure of our results.
(abridged)
