Context: By studying the optical brightness surface density of the globular cluster NGC 6388, it has been recently proposed that it harbors a central intermediate-mass black hole with mass ≃ 5.7×103 Msun. Aims: We expect that the compact object in the center of NGC 6388 emits radiation in the X-ray band as a consequence of the accretion from the surrounding matter. We searched for XMM-Newton and Chandra observations towards NGC 6388 to test this hypothesis. Methods: We determine both the hardness ratios and luminosity with a minimum set of assumptions for each of the identified field sources. Results: The Chandra satellite disentangles several point-like X-ray sources, probably low mass X-ray binaries, well within the core radius of the globular cluster. However, three of them, coinciding with the cluster center of gravity, remain unresolved. Their total luminosity is L_X^Obs ≃ 2.7×1033 erg s-1. If one of these sources is the X-ray counterpart of the intermediate-mass black hole in NGC 6388, the corresponding upper limit on the accretion efficiency, with respect to the Eddington luminosity, is 3×10-9. This measurement could be tightened if moderately deep radio observations of the field were performed.
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