SIMBAD references

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 modelling 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 (<r_bh> ) in terms of structural quantities as the core radius (r_c), mass (M_c), and velocity dispersion (σ_c), in addition to the average stellar mass (m_c) and the IMBH mass (M_bh). The model can be expressed by the equation [?\left?]<r_ bh_{[?\right?]>/r} c_=A(m c_/M bh₎α^[σ_ c2r_ c_/(GM c_)]^β, in which the free parameters A, α, and β 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 per cent of the GC mass, the typical expected displacement of a putative IMBH is around 1 arcsec for most Galactic GCs, but IMBHs can wander to larger angular distances in some objects, including a prediction of a 2.5 arcsec displacement for NGC 5139 (ω Cen), and >10 arcsec for NGC5053, NGC6366, and ARP2.