Article

# Density profile, velocity anisotropy and line-of-sight external convergence of SLACS gravitational lenses

The Astrophysical Journal (Impact Factor: 5.99). 04/2009; 728(1). DOI: 10.1088/0004-637X/728/1/33

Source: arXiv

**ABSTRACT**

Data from 58 strong-lensing events surveyed by the Sloan Lens ACS Survey are

used to estimate the projected galaxy mass inside their Einstein radii by two

independent methods: stellar dynamics and strong gravitational lensing. We

perform a joint analysis of these two estimates inside models with up to three

degrees of freedom with respect to the lens density profile, stellar velocity

anisotropy, and line-of-sight (LOS) external convergence, which incorporates

the effect of the large-scale structure on strong lensing. A Bayesian analysis

is employed to estimate the model parameters, evaluate their significance and

compare models. We find that the data favor Jaffe's light profile over

Hernquist's, but that any particular choice between these two does not change

the qualitative conclusions with respect to the features of the system that we

investigate. The density profile is compatible with an isothermal, being

sightly steeper and having an uncertainty in the logarithmic slope of the order

of 5% in models that take into account a prior ignorance on anisotropy and

external convergence. We identify a considerable degeneracy between the density

profile slope and the anisotropy parameter, which largely increases the

uncertainties in the estimates of these parameters, but we encounter no

evidence in favor of an anisotropic velocity distribution on average for the

whole sample. An LOS external convergence following a prior probability

distribution given by cosmology has a small effect on the estimation of the

lens density profile, but can increase the dispersion of its value by nearly

40%.

used to estimate the projected galaxy mass inside their Einstein radii by two

independent methods: stellar dynamics and strong gravitational lensing. We

perform a joint analysis of these two estimates inside models with up to three

degrees of freedom with respect to the lens density profile, stellar velocity

anisotropy, and line-of-sight (LOS) external convergence, which incorporates

the effect of the large-scale structure on strong lensing. A Bayesian analysis

is employed to estimate the model parameters, evaluate their significance and

compare models. We find that the data favor Jaffe's light profile over

Hernquist's, but that any particular choice between these two does not change

the qualitative conclusions with respect to the features of the system that we

investigate. The density profile is compatible with an isothermal, being

sightly steeper and having an uncertainty in the logarithmic slope of the order

of 5% in models that take into account a prior ignorance on anisotropy and

external convergence. We identify a considerable degeneracy between the density

profile slope and the anisotropy parameter, which largely increases the

uncertainties in the estimates of these parameters, but we encounter no

evidence in favor of an anisotropic velocity distribution on average for the

whole sample. An LOS external convergence following a prior probability

distribution given by cosmology has a small effect on the estimation of the

lens density profile, but can increase the dispersion of its value by nearly

40%.

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**ABSTRACT:**Based on 58 SLACS strong-lens early-type galaxies with direct total-mass and stellar-velocity dispersion measurements, we find that inside one effective radius massive elliptical galaxies with M_eff >= 3x10^10 M_sun are well-approximated by a power-law ellipsoid with an average logaritmic density slope of <gamma'_LD> = -dlog(rho_tot)/dlog(r)=2.085^{+0.025}_{-0.018} (random error on mean) for isotropic orbits with beta_r=0, +-0.1 (syst.) and sigma_gamma' <= 0.20^{+0.04}_{-0.02} intrinsic scatter (all errors indicate the 68 percent CL). We find no correlation of gamma'_LD with galaxy mass (M_eff), rescaled radius (i.e. R_einst/R_eff) or redshift, despite intrinsic differences in density-slope between galaxies. Based on scaling relations, the average logarithmic density slope can be derived in an alternative manner, fully independent from dynamics, yielding <gamma'_SR>=1.959 +- 0.077. Agreement between the two values is reached for =0.45 +- 0.25, consistent with mild radial anisotropy. This agreement supports the robustness of our results, despite the increase in mass-to-light ratio with total galaxy mass: M_eff ~ L_{V,eff}^(1.363+-0.056). We conclude that massive early-type galaxies are structurally close-to homologous with close-to isothermal total density profiles (<=10 percent intrinsic scatter) and have at most some mild radial anisotropy. Our results provide new observational limits on galaxy formation and evolution scenarios, covering four Gyr look-back time. Comment: Accepted for publication by ApJL; 4 pages, 2 figures - [Show abstract] [Hide abstract]

**ABSTRACT:**Galaxy-scale strong gravitational lenses with measured stellar velocity dispersions allow a test of the weak-field metric on kiloparsec scales and a geometric measurement of the cosmological distance-redshift relation, provided that the mass-dynamical structure of the lensing galaxies can be independently constrained to a sufficient degree. We combine data on 53 galaxy-scale strong lenses from the Sloan Lens ACS Survey with a well-motivated fiducial set of lens-galaxy parameters to find (1) a constraint on the post-Newtonian parameter gamma = 1.01 +/- 0.05 and (2) a determination of Omega_Lambda = 0.75 +/- 0.17 under the assumption of a flat universe. These constraints assume that the underlying observations and priors are free of systematic error. We evaluate the sensitivity of these results to systematic uncertainties in (1) total mass-profile shape, (2) velocity anisotropy, (3) light-profile shape, and (4) stellar velocity dispersion. Based on these sensitivities, we conclude that while such strong-lens samples can in principle provide an important tool for testing general relativity and cosmology, they are unlikely to yield precision measurements of gamma and Omega_Lambda unless the properties of the lensing galaxies are independently constrained with substantially greater accuracy than at present. Comment: 8 pages, 5 figures; Accepted to ApJ - [Show abstract] [Hide abstract]

**ABSTRACT:**We use data from 58 strong lensing events surveyed by the Sloan Lens ACS Survey to estimate the projected galaxy mass inside their Einstein radii by two independent methods: stellar dynamics and strong gravitational lensing. We perform a joint analysis of both estimates examining the galaxy-lens density profile (that we approximate by a power law), the anisotropy of the velocity distribution (represented by an effective constant parameter), and a possible line-of-sigh (l.o.s.) mass contamination (which is suggested by various independent works in the literature). For each model, a likelihood analysis is performed to find the parameters that produce the best agreement between the dynamical and lensing masses, and the parameter confidence levels. The Bayesian evidence is calculated to allow a comparison among the models. We find a degeneracy among the slope of the density profile, the anisotropy parameter and the l.o.s. mass contamination. For a density profile close to isothermal, a l.o.s. mass contamination of the order of a few percent is possible, being less probable with larger anisotropy.