Constraints on galaxy halo profiles from galaxy-galaxy lensing and Tully-Fisher/Fundamental Plane relations

Observations of galaxy-galaxy lensing from the Sloan Digital Sky Survey (SDSS) are combined with the Tully-Fisher and Fundamental Plane relations to derive constraints on galactic halo profiles. We show that for both early- and late-type galaxies around L-* the rotation velocity decreases significantly from its peak value at the optical radius to the virial radius r(200) , v (opt) /v (200) similar to 1.8 with about 20 per cent uncertainty. Such a decrease is expected in models in which the halo profile is very concentrated, so that it declines at steeper than the isothermal rate at large radii. This large decrease can be explained as a result of both a concentrated dark matter profile and a significant stellar contribution to the rotation velocity at the optical radii. We model the stellar component with a thin rotationally supported disc or a Hernquist profile and use an adiabatic dark matter response model to place limits on the halo concentration as a function of the stellar mass-to-light ratio. For reasonable values of the latter we find concentrations c(200) consistent with cold dark matter (CDM) predictions, suggesting there is no evidence for low concentrations for the majority of haloes in the Universe. We also discuss the origin of the Faber-Jackson relation L proportional tosigma(4) in light of the L proportional tov (200) (5/2) relation found for early-type galaxies above L-* from galaxy-galaxy lensing. This leads to a decrease in v(opt) /v (200) with luminosity above L-*, so that at 7L(*) the ratio is 1.4. This is expected from the Fundamental Plane relation as a result of a reduction in the baryonic contribution to the total mass at the optical radius and a decrease in the optical to virial rotation velocity in the dark matter profile. These results imply that relations such as the Tully-Fisher and the Faber-Jackson relation are not simply those between the mass of the dark matter halo and the galaxy luminosity, but are also significantly influenced by the baryonic effects on the rotation velocity at optical radii.