We measure the total mass-density profiles out to three effective radii for a sample of 63 z \sim 0.5 , massive early-type galaxies ( ETGs ) acting as strong gravitational lenses through a joint analysis of lensing and stellar dynamics .
The compilation is selected from three galaxy-scale strong-lens samples including the Baryon Oscillation Spectroscopic Survey ( BOSS ) Emission-Line Lens Survey ( BELLS ) , BELLS for GALaxy-Ly \alpha EmitteR sYstems Survey , and Strong Lensing Legacy Survey ( SL2S ) .
Utilizing the wide source-redshift coverage ( 0.8–3.5 ) provided by these three samples , we build a statistically significant ensemble of massive ETGs for which robust mass measurements can be achieved within a broad range of Einstein radii up to three effective radii .
Characterizing the three-dimensional total mass-density distribution by a power-law profile as \rho \propto r ^ { - \gamma } , we find that the average logarithmic density slope for the entire sample is \langle \gamma \rangle = 2.000 _ { -0.032 } ^ { +0.033 } ( 68 \% CL ) with an intrinsic scatter \delta = 0.180 _ { -0.028 } ^ { +0.032 } .
Further parameterizing \langle \gamma \rangle as a function of redshift z and ratio of Einstein radius to effective radius R _ { ein } / R _ { eff } , we find the average density distributions of these massive ETGs become steeper at larger radii and later cosmic times with magnitudes \mathrm { d } \langle \gamma \rangle / \mathrm { d } z = -0.309 _ { -0.160 } ^ { +0.166 } and \mathrm { d } \langle \gamma \rangle / \mathrm { d } \log _ { 10 } \frac { R _ { ein } } { R _ { eff } } = 0.19 % 4 _ { -0.083 } ^ { +0.092 } .