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Black holes have been found over a wide range of masses, from stellar remnants with masses of 5-150 solar masses (Msun), to those found at the centers of galaxies with $M>10^5$ Msun. However, only a few debated candidate black holes exist between 150 and $10^5$ Msun. Determining the population of these intermediate-mass black holes is an important step towards understanding supermassive black hole formation in the early universe. Several studies have claimed the detection of a central black hole in $\omega$ Centauri, the Milky Way's most massive globular cluster. However, these studies have been questioned due to the possible mass contribution of stellar mass black holes, their sensitivity to the cluster center, and the lack of fast-moving stars above the escape velocity. Here we report observations of seven fast-moving stars in the central 3 arcseconds (0.08 pc) of $\omega$ Centauri. The velocities of the fast-moving stars are significantly higher than the expected central escape velocity of the star cluster, so their presence can only be explained by being bound to a massive black hole. From the velocities alone, we can infer a firm lower limit of the black hole mass of $\sim$8,200 Msun, making this a compelling candidate for an intermediate-mass black hole in the local universe., Comment: 33 pages, 11 figures, and 2 tables. Published in Nature. This is the accepted author's version. The version of record is available from the Journal (open access)

Omega Centauri ($\omega$ Cen) is the most massive globular cluster of the Milky Way. It is thought to be the nucleus of an accreted dwarf galaxy because of its high mass and its complex stellar populations. To decipher its formation history and study its dynamics, we created the most comprehensive kinematic catalog for its inner region, by analyzing both archival and new Hubble Space Telescope (HST) data. Our catalog contains 1 395 781 proper-motion measurements out to the half-light radius of the cluster ($\sim$5.0') and down to $m_{F625W}\approx$25. The typical baseline for our proper-motion measurements is 20 years, leading to a median 1D proper motion precision of $\sim$11 $\mu$as yr$^{-1}$ for stars with $m_{F625W}\approx$18 mag, with even better precision ($\sim$6.6 $\mu$as yr$^{-1}$) achieved in the extensively observed centermost (r$<$1.5') region. In addition to our astrometric measurements, we also obtained precise HST photometry in seven filters spanning from the ultraviolet to the near-infrared. This allows detailed color-magnitude-diagram studies and to separate the multiple stellar populations of the cluster. In this work, we describe the data reduction used to obtain both the photometric and the proper-motion measurements. We also illustrate the creation and the content of our catalog, which is made publicly available. Finally, we present measurements of the plane-of-sky rotation of $\omega$ Cen in the previously unprobed inner few arcminutes and a precise measurement of the inclination $i = (43.9\pm1.3)^\circ$., Comment: 43 pages, 25 figures, 9 tables. Published by ApJ. The full catalog is publicly available under: https://doi.org/10.5281/zenodo.11104046