On the Relation between Circular Velocity and Central Velocity Dispersion in High and Low Surface Brightness Galaxies^*

In order to investigate the correlation between the circular velocity V_c and the central velocity dispersion of the spheroidal component σ_c, we analyzed these quantities for a sample of 40 high surface brightness (HSB) disk galaxies, eight giant low surface brightness (LSB) spiral galaxies, and 24 elliptical galaxies characterized by flat rotation curves. Galaxies have been selected to have a velocity gradient ≤2 km s^-1 kpc^-1 for R ≥ 0.35R₂₅. We used these data to better define the previous V_c-σ_c correlation for spiral galaxies (which turned out to be HSB) and elliptical galaxies, especially at the lower end of the σ_c values. We find that the V_c-σ_c relation is described by a linear law out to velocity dispersions as low as σ_c ≈ 50 km s^-1, while in previous works a power law was adopted for galaxies with σ_c > 80 km s^-1. Elliptical galaxies with V_c based on dynamical models or directly derived from the H I rotation curves follow the same relation as the HSB galaxies in the V_c-σ_c plane. On the other hand, the LSB galaxies follow a different relation, since most of them show either higher V_c or lower σ_c with respect to the HSB galaxies. This argues against the relevance of baryon collapse to the radial density profile of the dark matter halos of LSB galaxies. Moreover, if the V_c-σ_c relation is equivalent to one between the mass of the dark matter halo and that of the supermassive black hole, then these results suggest that the LSB galaxies host a supermassive black hole (SMBH) with a smaller mass compared to HSB galaxies with an equal dark matter halo. On the other hand, if the fundamental correlation of SMBH mass is with the halo circular velocity, then LSB galaxies should have larger black hole masses for a given bulge dispersion. Elliptical galaxies with V_c derived from H I data and LSB galaxies were not considered in previous studies.