A perturbative scheme connects any static spherical density profile to gravitational deflection angles and lensed image positions through the Tolman-Oppenheimer-Volkoff equations.
The Fundamental Plane of Gravitational Lens Galaxies and The Evolution of Early-Type Galaxies in Low Density Environments
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abstract
Most gravitational lenses are early-type galaxies in relatively low density environments -- a ``field'' rather than a ``cluster'' population. We show that field early-type galaxies with 0 < z < 1, as represented by the lens galaxies, lie on the same fundamental plane as those in rich clusters at similar redshifts. We then use the fundamental plane to measure the combined evolutionary and K-corrections for early-type galaxies in the V, I and H bands. Only for passively evolving stellar populations formed at z > 2 (H_0=65 km/s Mpc, Omega_0=0.3, Lambda_0=0.7) can the lens galaxies be matched to the local fundamental plane. The high formation epoch and the lack of significant differences between the field and cluster populations contradict many current models of the formation history of early-type galaxies. Lens galaxy colors and the fundamental plane provide good photometric redshift estimates with an empirical accuracy of -0.03 +/- 0.11 for the 17 lenses with known redshifts. A mass model dominated by dark matter is more consistent with the data than either an isotropic or radially anisotropic constant M/L mass model, and a radially anisotropic model is better than an isotropic model.
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From Matter Density to Deflection Angle and Gravitational Lensing Using a Perturbative Method
A perturbative scheme connects any static spherical density profile to gravitational deflection angles and lensed image positions through the Tolman-Oppenheimer-Volkoff equations.