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We report a tight linear relation between the HI circular velocity measuredat 6 $R_{\rm e}$ and the stellar velocity dispersion measured within 1 $R_{\rme}$ 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 isthat we only use spatially resolved $v_\mathrm{circ}$(HI) measurements obtainedat large radius for a sizeable sample of objects. We can therefore link akinematical tracer of the gravitational potential in the dark-matter dominatedouter regions of galaxies with one in the inner regions, where baryons controlthe distribution of mass. We find that $v_\mathrm{circ}$(HI) = 1.33$\sigma_\mathrm{e}$ with an observed scatter of just 12 percent. This indicatesa strong coupling between luminous and dark matter from the inner- to the outerregions of early-type galaxies, analogous to the situation in spirals and dwarfirregulars. The $v_\mathrm{circ}$(HI)-$\sigma_\mathrm{e}$ relation is shallowerthan those based on $v_\mathrm{circ}$ measurements obtained from stellarkinematics and modelling at smaller radius, implying that \vcirc\ declines withradius -- as in bulge-dominated spirals. Indeed, the value of$v_\mathrm{circ}$(HI) is typically 25 percent lower than the maximum$v_\mathrm{circ}$ derived at $\sim0.2\ R_\mathrm{e}$ from dynamical models.Under the assumption of power-law total density profiles $\rho \proptor^{-\gamma}$, our data imply an average logarithmic slope$\langle\gamma\rangle=2.18\pm0.03$ across the sample, with a scatter of 0.11around this value. The average slope and scatter agree with recent resultsobtained from stellar kinematics alone for a different sample of early-typegalaxies.

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