We report a tight linear relation between the H i 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 } \mathrm { M } _ { \odot } .
The key difference from previous studies is that we only use spatially resolved v _ { \mathrm { 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 _ { \mathrm { circ } } ( H i ) = 1.33 \sigma _ { \mathrm { e } } with an observed scatter of just 12 percent .
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 _ { \mathrm { circ } } ( H i ) - \sigma _ { \mathrm { e } } relation is shallower than those based on v _ { \mathrm { circ } } measurements obtained from stellar kinematics and modelling at smaller radius , implying that v _ { \mathrm { circ } } declines with radius – as in bulge-dominated spirals .
Indeed , the value of v _ { \mathrm { circ } } ( H i ) is typically 25 percent lower than the maximum v _ { \mathrm { circ } } derived at \sim 0.2 R _ { \mathrm { e } } from dynamical models .
Under the assumption of power-law total density profiles \rho \propto r ^ { - \gamma } , our data imply an average logarithmic slope \langle \gamma \rangle = 2.18 \pm 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 .