A Mass Model for the Lensing Cluster SDSS J1004+4112: Constraints from the Third Time Delay
Raquel Forés-Toribio, J. A. Muñoz, C. S. Kochanek, E. Mediavilla
Abstract
Abstract We have built a new model for the lens system SDSS J1004+4112 including the recently measured time delay of the fourth quasar image. This time delay has a strong influence on the inner mass distribution of the lensing cluster ( ρ ∝ r − α ) allowing us to determine <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>α</mml:mi> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>1.18</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.03</mml:mn> <mml:mo stretchy="false">(</mml:mo> <mml:mo>−</mml:mo> <mml:mn>0.18</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.02</mml:mn> <mml:mo stretchy="false">(</mml:mo> <mml:mo>+</mml:mo> <mml:mn>0.11</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> at the 68% (95%) confidence level in agreement with hydrodynamical simulations of massive galaxy clusters. We find an offset between the brightest cluster galaxy and the dark matter halo of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>3.8</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.7</mml:mn> <mml:mo stretchy="false">(</mml:mo> <mml:mo>−</mml:mo> <mml:mn>1.3</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.6</mml:mn> <mml:mo stretchy="false">(</mml:mo> <mml:mo>+</mml:mo> <mml:mn>1.4</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> kpc at 68% (95%) confidence which is compatible with other galaxy cluster measurements. As an observational challenge, the estimated time delay between the leading image C and the faint ( I = 24.7) fifth image E is roughly 8 yr.