The presence of intermediate-mass black holes in globular clusters and their connection with extreme horizontal branch stars

ABSTRACT

By means of a multimass isotropic and spherical model that includes the self-consistent treatment of a central intermediate-mass black hole (IMBH), the influence of this black hole on the morphological and physical properties of globular clusters is investigated. In agreement with recent numerical studies, it is found that a cluster (with mass M) hosting an IMBH (with mass M_•) shows, outside the region of gravitational influence of the black hole, a core-like profile resembling a King profile with concentration c < 2, although with a slightly steeper behaviour in the core region. In particular, the core logarithmic slope is s≲ 0.25 for reasonably low IMBH masses (M_•≲ 10⁻²M), and c decreases monotonically with M_•. Completely power-law density profiles (similar to, for example, those of collapsed clusters) are admitted only in the presence of a black hole with an unrealistic M_• > M. The mass range estimate 12s− 4.8 < log (M_•/M) < −1.1c− 0.69, depending on the morphological parameters, is deduced by considering a wide range of models. Applying this estimate to a set of 39 globular clusters, it is found that NGC 2808, NGC 6388, M80, M13, M62, M54 and G1 (in M31) probably host an IMBH. For them, the scaling laws M_•∼ 0.09(M/M_⊙)^0.7 M_⊙ and M_•∼ 50(σ_obs/km s⁻¹)^1.2 M_⊙ are identified from weighted least-squares fits. An important result of this ‘collective’ study is that a strong correlation exists between the presence of an extreme blue horizontal branch and the presence of an IMBH. In particular, the presence of a central IMBH in M13 and NGC 6388 could explain why these clusters possess extreme horizontal-branch stars, in contrast to their ‘second parameter’ counterparts M3 and 47 Tuc.