Cold Dark Matter and Strong Gravitational Lensing: Concord or Conflict?

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Abstract
Using the number and sizes of observed gravitational lenses, I derive upper limits on the dark matter content of elliptical galaxies. On average, dark matter can account for no more than 33% of the total mass within one effective radius (Re) of elliptical galaxies or 40% of the mass within 2Re (95% confidence upper limits). I show that galaxies built from cold dark matter (CDM) mass distributions are too concentrated to comfortably satisfy these limits; a high-density (ΩM = 1) CDM cosmology is ruled out at better than 95% confidence, while a low-density, flat cosmology is only marginally consistent with the lens data. Thus, lensing adds to the evidence from spiral galaxy dynamics that CDM mass distributions are too concentrated on kiloparsec scales to agree with real galaxies and extends the argument to elliptical galaxies. Lensing also provides a unique probe of the very inner regions of galaxies, because images are predicted to form near the centers of lens galaxies but are not observed. The lack of central images in deep maps of radio lenses places strong lower limits on the central densities of galaxies. The central densities of CDM galaxies are too low on ~10 pc scales. Supermassive black holes can help suppress central images, but they must lie well off the observed black hole-bulge mass correlation in order to satisfy current limits on central images. Self-interacting dark matter, or any other modification to regular cold dark matter, must simultaneously reduce the densities on kiloparsec scales and increase the densities on parsec scales in order to satisfy the unique constraints from lensing.