XMM-Newton and Chandra observations of the globular cluster NGC 6388

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 $\simeq$ 5.7$\times$103 $M_{\odot}$. 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 $L_{\rm X}^{\rm Obs}$ $\simeq$ 2.7$\times$1033 erg s-1. If one of these sources is the X-ray counterpart of the intermediate-mass black hole in NGC 6388, the corresponding upper limit on the accretion efficiency, with respect to the Eddington luminosity, is 3$\times$10-9. This measurement could be tightened if moderately deep radio observations of the field were performed.