Limits on the power-law mass and luminosity density profiles of elliptical galaxies from gravitational lensing systems

Abstract

We use 118 strong gravitational lenses observed by the SLACS, BELLS, LSD and SL2S surveys to constrain the total mass profile and the profile of luminosity density of stars (light-tracers) in elliptical galaxies up to redshift z ∼ 1. Assuming power-law density profiles for the total mass density, ρ = ρ 0 (r/r 0 ) −α , and luminosity density, ν = ν 0 (r/r 0 ) −δ , we investigate the power law index and its first derivative with respect to the redshift. Using Monte Carlo simulations of the posterior likelihood taking the Planck's best-fitted cosmology as a prior, we find γ = 2.132 ± 0.055 with a mild trend ∂γ/∂z l = −0.067 ± 0.119 when α = δ = γ, suggesting that the total density profile of massive galaxies could have become slightly steeper over cosmic time. Furthermore, similar analyses performed on sub-samples defined by different lens redshifts and velocity dispersions, indicate the need of treating low, intermediate and high-mass galaxies separately. Allowing δ to be a free parameter, we obtain α = 2.070 ± 0.031, ∂α/∂z l = −0.121 ± 0.078, and δ = 2.710 ± 0.143. The model in which mass traces light is rejected at > 95% confidence and our analysis robustly indicates the presence of dark matter in the form of a mass component that is differently spatially extended than the light. In this case, intermediate-mass elliptical galaxies (200 km/s < σ ap 300 km/s) show the best consistency with the singular isothermal sphere as an effective model of galactic lenses.

Revisiting Studies of the Statistical Property of a Strong Gravitational Lens System and Model-Independent Constraint on the Curvature of the Universe

“…Considering the effects of aperture (θ ap ) with atmospheric blurring (σ atm ) and luminosity-weighted averaging (see Schwab et al (2010);Cao et al (2016) for details), the constraints become: α = 2.05 ± 0.05 and δ = 2.61 ± 0.15 at 68% confidence level, as shown in upper-right panel of figure 4, which is consistent with previous works (Koopmans et al 2009;Sonnenfeld et al 2013b;Oguri et al 2014;Cao et al 2016).…”

Test of Parametrized Post-Newtonian Gravity With Galaxy-Scale Strong Lensing Systems

“…σ atm is the seeing recorded by the spectroscopic guide cameras during observing sessions (Cao et al 2016). The above equation tells us that we can constrain the PPN parameter γ on a sample of lenses with known redshifts of the lens and of the source, with measured velocity dispersion and the Einstein radius, provided we have reliable knowledge about cosmological model and about parameters describing the mass distribution of lensing galaxies (α, β, δ).…”

“…Following our previous analysis (Cao et al 2016) concerning power-law mass and luminosity density profiles of elliptical galaxies, we used a mass-selected sample of strong lensing systems, taken from a comprehensive compilation of strong lensing systems observed by four surveys: SLACS, BELLS, LSD and SL2S. The sample has been defined by restricting the velocity dispersions of lensing galaxies to the intermediate range: 200km/s < σ ap ≤ 300km/s.…”

Finding strong gravitational lenses in the Kilo Degree Survey with Convolutional Neural Networks

“…In fact, the total mass (dark plus baryonic) within the Einstein radius depends almost solely on the space-time geometry of the lensing system (the source and the lens redshift and the cosmological parameters). For this reason, strong lensing is a unique tool, if combined with central velocity dispersion measurements and stellar population analysis, to estimate the fraction of dark matter in the central regions of galaxy-scale halos (e.g., Gavazzi et al E-mail: petrillo@astro.rug.nl 2007; Jiang & Kochanek 2007;Grillo et al 2010;Cardone et al 2009;Cardone & Tortora 2010;Tortora et al 2010;More et al 2011;Ruff et al 2011;Sonnenfeld et al 2015), and to constrain the slope of the inner mass density profile (e.g., Treu & Koopmans 2002a,b;Koopmans et al 2006;Koopmans & Treu 2003;More et al 2008;Barnabè et al 2009;Koopmans et al 2009;Cao et al 2016). …”