We present a joint gravitational lensing and stellar dynamical analysis of fifteen massive field early-type galaxies – selected from the Sloan Lens ACS ( SLACS ) Survey – using Hubble Space Telescope ACS images and luminosity weighted stellar velocity dispersions obtained from the Sloan Digital Sky Survey database .
The sample of lens galaxies is well-defined ( see Paper I ) , with a redshift range of z =0.06–0.33 and an average stellar velocity dispersion of \langle \sigma _ { ap } \rangle = 263 km s ^ { -1 } ( rms of 44 km s ^ { -1 } ) inside a 3-arcsec fiber diameter .
The following numerical results are found : ( i ) A joint-likelihood gives an average logarithmic density slope for the total mass density of \langle \gamma ^ { \prime } \rangle = 2.01 ^ { +0.02 } _ { -0.03 } ( 68 % C.L .
; \rho _ { tot } \propto r ^ { - \gamma ^ { \prime } } ) inside \langle { R } _ { Einst } \rangle = 4.2 \pm 0.4 kpc ( rms of 1.6 kpc ) .
The inferred intrinsic rms spread in logarithmic density slopes is \sigma _ { \gamma ^ { \prime } } = 0.12 , which might still include some minor systematic uncertainties .
A range for the stellar anisotropy parameter \beta = [ -0.25 , +0.25 ] results in \Delta \langle \gamma ^ { \prime } \rangle = [ +0.05 , -0.09 ] .
Changing from a Hernquist to a Jaffe luminosity density profile increases \langle \gamma ^ { \prime } \rangle by 0.05 .
( ii ) The average position-angle difference between the light distribution and the total mass distribution is found to be \langle \Delta \theta \rangle = 0 \pm 3 degrees ( rms of 10 degrees ) , setting an upper limit of \langle \gamma _ { ext } \rangle \lesssim 0.035 on the average external shear .
The total mass has an average ellipticity \langle q _ { SIE } \rangle =0.78 \pm 0.03 ( rms of 0.12 ) , which correlates extremely well with the stellar ellipticity , q _ { * } , resulting in \langle q _ { SIE } / q _ { * } \rangle = 0.99 \pm 0.03 ( rms of 0.11 ) for \sigma \gtrsim 225 km s ^ { -1 } .
At lower velocity dispersions , inclined S0 galaxies dominate , leading to a higher ratio ( up to 1.6 ) .
This suggests that the dark-matter halo surrounding these galaxies is less flattened than their stellar component .
Assuming an oblate mass distribution and random orientations , the distribution of ellipticities implies \langle q _ { 3 } \rangle \equiv \langle ( c / a ) _ { \rho } \rangle = 0.66 with an error of \sim 0.2 .
( iii ) The average projected dark-matter mass fraction is inferred to be \langle f _ { DM } \rangle = 0.25 \pm 0.06 ( rms of 0.22 ) inside \langle { R } _ { E } \rangle , using the stellar mass-to-light ratios derived from the Fundamental Plane as priors .
( iv ) Combined with results from the Lenses Structure & Dynamics ( LSD ) Survey at z \gtrsim 0.3 , we find no significant evolution of the total density slope inside one effective radius for galaxies with \sigma _ { ap } \geq 200 km s ^ { -1 } : a linear fit gives \alpha _ { \gamma ^ { \prime } } \equiv d \langle \gamma ^ { \prime } \rangle / dz = 0.23 \pm 0.16 ( 1 \sigma ) for the range z =0.08–1.01 .
We conclude that massive early-type galaxies at z =0.06–0.33 on average have an isothermal logarithmic density slope inside half an effective radius , with an intrinsic spread of at most 6 % ( 1 \sigma ) .
The small scatter and absence of significant evolution in the inner density slopes suggest a collisional scenario where gas and dark matter strongly couple during galaxy formation , leading to a total mass distribution that rapidly converge to dynamical isothermality .