The Kapteyn moving group has been postulated as tidal debris from $omega$ Centauri. If true, members of the group should show some of the chemical abundance patterns known for stars in the cluster. We present an optical and near-infrared high-resolut
ion, high-S/N spectroscopic study of 14 stars of the Kapteyn group, plus 10 additional stars (the $omega$ Cen-group) that, while not listed as members of the Kapteyn group as originally defined, have been nevertheless associated dynamically with $omega$ Centauri. Abundances for Na, O, Mg, Al, Ca and Ba were derived from the optical spectra, while the strength of the chromospheric He I 10830 {AA} line is studied as a possible helium abundance indicator. The resulting Na-O and Mg-Al patterns for stars of the combined Kapteyn and $omega$ Cen-group samples do not resemble those of $omega$ Centauri, and are not different from those of field stars of the Galactic halo. The distribution of equivalent widths of the He I 10830 {AA} line is consistent with that found among non-active field stars. Therefore, no evidence is found for second-generation stars within our samples, which most likely rules out a globular-cluster origin. Moreover, no hint of the unique Ba-overabundance at the metal-rich end, well-established for $omega$ Centauri stars, is seen among stars of the combined samples. Because this specific Ba pattern is present in $omega$ Centauri irrespective of stellar generation, this would rule out the possibility that our entire sample might be composed of only first generation stars from the cluster. Finally, for the stars of the Kapteyn group, the possibility of an origin in the hypothetical $omega$ Centauris parent galaxy is disfavored by the different run of $alpha$-elements with metallicity between our targets and stars from present-day dwarf galaxies.
Establishing or ruling out, either through solid mass measurements or upper limits, the presence of intermediate-mass black holes (IMBHs) at the centers of star clusters would profoundly impact our understanding of problems ranging from the formation
and long-term dynamical evolution of stellar systems, to the nature of the seeds and the growth mechanisms of supermassive black holes. While there are sound theoretical arguments both for and against their presence in todays clusters, observational studies have so far not yielded truly conclusive IMBH detections nor upper limits. We argue that the most promising approach to solving this issue is provided by the combination of measurements of the proper motions of stars at the centers of Galactic globular clusters and dynamical models able to take full advantage of this type of data set. We present a program based on HST observations and recently developed tools for dynamical analysis designed to do just that.
