We analyzed a sample of high and low surface brightness (HSB and LSB) disc galaxies and elliptical galaxies to investigate the correlation between the circular velocity (Vc) and the central velocity dispersion (sigma). We better defined the previous Vc-sigma correlation for HSB and elliptical galaxies, especially at the lower end of the sigma values. Elliptical galaxies with Vc based on dynamical models or directly derived from the HI rotation curves follow the same relation as the HSB galaxies in the V-sigma plane. On the contrary, the LSB galaxies follow a different relation, since most of them show either higher Vc (or lower sigma) with respect to the HSB galaxies. This argues against the relevance of baryon collapse in the radial density profile of the dark matter haloes of LSB galaxies. Moreover, if the Vc-sigma relation is equivalent to one between the mass of the dark matter halo and that of the supermassive black hole, these results suggest that the LSB galaxies host a supermassive black hole with a smaller mass compared to HSB galaxies of equal dark matter halo. On the other hand, if the fundamental correlation of SMBH mass is with the halo Vc, then LSBs should have larger black hole masses for given bulge sigma.
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