Black Hole Dynamics in Stellar Clusters

Sammanfattning: Star clusters can harbour many exotic objects, including black holes (BHs), X-ray binaries and blue straggler stars. In dense stellar environments like globular clusters (GCs), two-body relaxation drives their dynamical evolution, where gravitational interactions between stars strive to equalize their kinetic energy in the cluster. Theoretical studies have indicated that some of these clusters can retain a substantial number of stellar-mass black holes. As these black holes are more massive than typical stars, they segregate to the cluster centre due to dynamical friction and can form a black hole subsystem (BHS). In the last decade, several BH candidates have been observed in GCs. In crowded cores of GCs, frequent gravitational encounters between stars and binary systems can occur. The exchange of energy in these interactions help sustain the cluster's core from collapsing. Abundant interactions among BHs can lead to their coalescence under the emission of gravitational waves to create intermediate-mass BHs (IMBHs) with masses of a few hundred to thousands of times the mass of our Sun. This project sheds light on how the presence of a BHS or an IMBH can influence the evolution and present-day observable properties of GCs. We utilize results from over 1500 GC models that were simulated using the MOCCA code for evolving realistic star clusters. We correlate the clusters' dynamical state to the distributions and observable signatures of various stellar populations. Using the simulation output, we investigate cluster morphologies, retention rates of BHs and the distributions of observable stellar populations in the absence or presence of BHs or IMBHs. We quantify the segregation between stellar populations using the Dr50 and A+ parameters, which measure their relative distributions from the centre of the cluster. These parameters are used to quantify the difference in cumulative radial distributions between populations of main-sequence stars, blue stragglers and giants. We find that segregation is more enhanced in clusters with short relaxation times that are likely to be hosting an IMBH. Formation rates of blue stragglers are equally related to the cluster's relaxation time. An increased number of blue stragglers are found in heavily segregated (A+ > 0.05) clusters with relaxation times (~1 Gyr) having significant central surface brightness. Longer relaxation times and large half-mass radii are associated with clusters forming a BHS, with central surface brightness < 10^{4} L⊙ pc^{-2}. Clusters hosting IMBHs with large initial binary fractions (95%) have a retained median binary fraction of ≈ 12% in the innermost 0.05 parsecs that decreases in a power-law ~(r/rhl)^{-0.132} outwards, while BHS models have a slightly increased binary fraction in their cores of ≈ 14% with a shallower slope of ~(r/rhl)^{-0.013}. For clusters with initial binary fractions of 10%, core binary fractions are still higher for BHS models, but have a faster depletion outwards compared to models hosting an IMBH. We conclude that clusters with initially short relaxation times are typically heavily segregated and contain IMBHs with fewer, but harder, binaries in their cores, contrary to systems with many BHs. Since clusters neither hosting a BHS nor an IMBH might also have short relaxation times and strong segregation, low binary fractions and large central surface brightness values can become a further indication for the presence of an IMBH. Using segregation values for 50 known GCs in the Milky way, we predict numbers of BHs and masses of IMBHs by correlating the simulated numbers and masses of BHs with observed segregation. Comparable estimates with recently published works are produced, in particular, for NGC 3201, where we find an estimate of 64^{+158}_{-45} BHs retained in the cluster. We also note that 47 Tuc is best explained hosting an IMBH in our parameter space. We stress that the dynamics of BHs affect segregation on a more substantial grade than initial concentration and that short relaxation times and extensive segregation can be sufficient enough for ruling out the presence of a BHS, but further information about core binary fractions and central surface brightness is needed to identify clusters harbouring an IMBH.