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 similar to 13 km s(-1), a flat behavior out to similar 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 similar to 2000 M-circle dot. 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 similar to 1.7 x 10(4) M-circle dot. We also found some evidence of systemic rotation with amplitude A(rot) similar to 8 km s(-1) in the innermost 2 '' (0.13 pc), decreasing to A(rot) = 3.2km s(-1) at 18 '' < r < 160 ''.