N-body modeling of globular clusters: detecting intermediate-mass black holes by non-equipartition in HST proper motions

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Intermediate Mass Black Holes {IMBHs} are objects of considerable astrophysical significance. They have been invoked as possible remnants of Population III stars, precursors of supermassive black holes, sources of ultra-luminous X-ray emission, and emitters of gravitational waves. The centers of globular clusters, where they may have formed through runaway collapse of massive stars, may be our best chance of detecting them. HST studies of velocity dispersions have provided tentative evidence, but the measurements are difficult and the results have been disputed. It is thus important to explore and develop additional indicators of the presence of an IMBH in these systems. In a Cycle 16 theory project we focused on the fingerprints of an IMBH derived from HST photometry. We showed that an IMBH leads to a detectable quenching of mass segregation. Analysis of HST-ACS data for NGC 2298 validated the method, and ruled out an IMBH of more than 300 solar masses. We propose here to extend the search for IMBH signatures from photometry to kinematics. The velocity dispersion of stars in collisionally relaxed stellar systems such as globular clusters scales with main sequence mass as sigma m^alpha. A value alpha = -0.5 corresponds to equipartition. Mass-dependent kinematics can now be measured from HST proper motion studies {e.g., alpha = -0.21 for Omega Cen}. Preliminary analysis shows that the value of alpha can be used as indicator of the presence of an IMBH. In fact, the quenching of mass segregation is a result of the degree of equipartition that the system attains. However, detailed numerical simulations are required to quantify this. Therefore we propose {a} to carry out a new, larger set of realistic N-body simulations of star clusters with IMBHs, primordial binaries and stellar evolution to predict in detail the expected kinematic signatures and {b} to compare these predictions to datasets that are {becoming} available. Considerable HST resources have been invested in proper motions studies of some dozen clusters, but theoretical simulations are generally not performed as part of such programs. Our methods are complementary to other efforts to detect IMBHs in globulars, and will allow new constraints to be derived from HST data that are already being obtained.;

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