RMS velocity of the cluster at different external potential. In the left panel, we show the rms contour lines of the velocity calculated via Eq. (8), providing its dependency on the virial radius and the total BH mass in the cluster. The contours illustrate the velocities at specific radii and masses. The bottom right panel provides contour lines of the velocity of the cluster defined by Eq. (9), assuming an additional contraction calculated by Kroupa et al. (2020). The different colors indicate various values of η_g.