Dynamics of Intermediate-Mass Black Holes Wandering in the Milky Way
  Galaxy Using the Illustris TNG50 Simulation
  The detection of Intermediate-Mass Black Holes (IMBHs) in dwarf galaxies is
crucial to closing the gap in the wide mass distribution of black holes ($\sim
3 \, \rm M_{\odot}$ to $\sim 5 \times 10^{10} \, \rm M_{\odot}$). IMBHs
originally located at the center of dwarfs that later collide with the Milky
Way (MW) could be wandering, undetected, in our Galaxy. We used TNG50, the
highest-resolution run of the IllustrisTNG project, to study the kinematics and
dynamics of star clusters, in the appropriate mass range, acting as IMBH
proxies in a MW analog galaxy. We showed that $\sim 87\%$ of our studied IMBHs
drift inward. The radial velocity of these sinking IMBHs has a median magnitude
of $\sim 0.44 \, \rm ckpc \, h^{-1} \, Gyr^{-1}$ and no dependence on the black
hole mass. The central $1 \, \rm ckpc \, h^{-1}$ has the highest number density
of IMBHs in the galaxy. A physical toy model with linear drag forces was
developed to explain the orbital circularization with time. These findings
constrain the spatial distribution of IMBHs, suggesting that future searches
should focus on the central regions of the Galaxy. Additionally, we found that
the 3D velocity distribution of IMBHs with respect to the galactic center has a
mean of $\sim 180 \, \rm km \, s^{-1}$ and larger variance with decreasing
radius. Remarkably, the velocity distribution relative to the local gas shows
significantly lower values, with a mean of $\sim 88 \, \rm km \, s^{-1}$. These
results are instrumental for predicting the accretion and radiation properties
of IMBHs, facilitating their detection with future surveys.
