Linear relation between HI circular velocity and stellar velocity dispersion in early-type galaxies, and slope of the density profiles

We report a tight linear relation between the HI circular velocity measured at 6 R-e and the stellar velocity dispersion measured within 1 R-e for a sample of 16 early-type galaxies with stellar mass between 10(10) and 10(11) M-circle dot. The key difference from previous studies is that we only use spatially resolved v(circ)(H I) measurements obtained at large radius for a sizeable sample of objects. We can therefore link a kinematical tracer of the gravitational potential in the dark-matter dominated outer regions of galaxies with one in the inner regions, where baryons control the distribution of mass. We find that v(cir)c(H I) = 1.33 sigma(e) with an observed scatter of just 12 per cent. This indicates a strong coupling between luminous and dark matter from the inner-to the outer regions of early-type galaxies, analogous to the situation in spirals and dwarf irregulars. The v(circ)(H I)-sigma(e) relation is shallower than those based on v(circ) measurements obtained from stellar kinematics and modelling at smaller radius, implying that v(circ) declines with radius - as in bulge-dominated spirals. Indeed, the value of v(circ)(H I) is typically 25 per cent lower than the maximum v(circ) derived at similar to 0.2 R-e from dynamical models. Under the assumption of power-law total density profiles. rho proportional to r(-gamma), our data imply an average logarithmic slope = 2.18 +/- 0.03 across the sample, with a scatter of 0.11 around this value. The average slope and scatter agree with recent results obtained from stellar kinematics alone for a different sample of early-type galaxies.