The velocity dispersion profile of NGC 6388 from resolved-star spectroscopy: No evidence of a central cusp and new constraints on the black hole mass

By combining high spatial resolution and wide-field spectroscopy performed, respectively, with SINFONI and FLAMES at the ESO/VLT we measured the radial velocities of more than 600 stars in the direction of NGC 6388, a Galactic globular cluster which is suspected to host an intermediate-mass black hole. Approximately 55% of the observed targets turned out to be cluster members. The cluster velocity dispersion has been derived from the radial velocity of individual stars: 52 measurements in the innermost 2″, and 276 stars located between 18″ and 600″. The velocity dispersion profile shows a central value of ∼13 km s-1, a flat behavior out to ∼60″ and a decreasing trend outward. The comparison with spherical and isotropic models shows that the observed density and velocity dispersion profiles are inconsistent with the presence of a central black hole more massive than ∼2000 M ⊙. These findings are at odds with recent results obtained from integrated light spectra, showing a velocity dispersion profile with a steep central cusp of 23-25 km s-1 at r < 2″ and suggesting the presence of a black hole with a mass of ∼1.7 × 104 M ⊙. We also found some evidence of systemic rotation with amplitude A rot ∼ 8 km s-1 in the innermost 2″ (0.13 pc), decreasing to A rot = 3.2 km s -1 at 18″ < r < 160″.