Wandering off the centre: a characterization of the random motion of
  intermediate-mass black holes in star clusters
  Despite recent observational efforts, unequivocal signs for the presence of
intermediate-mass black holes (IMBHs) in globular clusters (GCs) have not been
found yet. Especially when the presence of IMBHs is constrained through
dynamical modeling of stellar kinematics, it is fundamental to account for the
displacement that the IMBH might have with respect to the GC centre. In this
paper we analyse the IMBH wandering around the stellar density centre using a
set of realistic direct N-body simulations of star cluster evolution. Guided by
the simulation results, we develop a basic yet accurate model that can be used
to estimate the average IMBH radial displacement ($\left<r_\mathrm{bh}\right>$)
in terms of structural quantities as the core radius ($r_\mathrm{c}$), mass
($M_\mathrm{c}$), and velocity dispersion ($\sigma_\mathrm{c}$), in addition to
the average stellar mass ($m_\mathrm{c}$) and the IMBH mass ($M_\mathrm{bh}$).
The model can be expressed by the equation
$\left<r_\mathrm{bh}\right>/r_\mathrm{c}=A(m_\mathrm{c}/M_\mathrm{bh})^\alpha[\sigma_\mathrm{c}^2r_\mathrm{c}/(GM_\mathrm{c})]^\beta$,
in which the free parameters $A,\alpha,\beta$ are calculated through comparison
with the numerical results on the IMBH displacement. The model is then applied
to Galactic GCs, finding that for an IMBH mass equal to 0.1% of the GC mass,
the typical expected displacement of a putative IMBH is around $1''$ for most
Galactic GCs, but IMBHs can wander to larger angular distances in some objects,
including a prediction of a $2.5''$ displacement for NGC 5139 ($\omega$ Cen),
and $>10''$ for NGC 5053, NGC 6366 and ARP2.
