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, a flat behavior out to ~60" and a decreasing trend outwards. 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 Msol. 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 at r<2" and suggesting the presence of a black hole with a mass of 17,000 Msol (Lutzgendorf et al. 2011). We also found some evidence of systemic rotation with amplitude Arot ~8 km/s in the innermost 2" (0.13 pc), decreasing to Arot= 3.2 km/s at 18"<r<160".