Are we observing a NSC in course of formation in the NGC 4654 galaxy?
  We use direct $N$-body simulations to explore some possible scenarios for the
future evolution of two massive clusters observed toward the center of
NGC\,4654, a spiral galaxy with mass similar to that of the Milky Way. Using
archival HST data, we obtain the photometric masses of the two clusters,
$M=3\times 10^5$ M$_\odot$ and $M=1.7\times 10^6$ M$_\odot$, their half-light
radii, $R_{\rm eff}\sim4$ pc and $R_{\rm eff} \sim 6$ pc, and their projected
distances from the photometric center of the galaxy (both $<22$ pc). The
knowledge of the structure and separation of these two clusters ($\sim 24$ pc)
provides a unique view for studying the dynamics of a galactic central zone
hosting massive clusters. Varying some of the unknown clusters orbital
parameters, we carry out several $N$-body simulations showing that the future
evolution of these clusters will inevitably result in their merger. We find
that, mainly depending on the shape of their relative orbit, they will merge
into the galactic center in less than 82 Myr. In addition to the tidal
interaction, a proper consideration of the dynamical friction braking would
shorten the merging times up to few Myr. We also investigate the possibility to
form a massive NSC in the center of the galaxy by this process. Our analysis
suggests that for low eccentricity orbits, and relatively long merger times,
the final merged cluster is spherical in shape, with an effective radius of few
parsecs and a mass within the effective radius of the order of
$10^5\,\mathrm{M_{\odot}}$. Because the central density of such a cluster is
higher than that of the host galaxy, it is likely that this merger remnant
could be the likely embryo of a future NSC.
