Detecting dark matter substructure spectroscopically in strong gravitational lenses

The cold dark matter (CDM) model for galaxy formation predicts that a significant fraction of mass in the dark matter haloes that surround L ∼ L* galaxies is bound in substructures of mass 10 4-107 M⊙. The number of observable baryonic substructures (such as dwarf galaxies and globular clusters) falls short of these predictions by at least an order of magnitude. We present a method for searching for substructure in the haloes of gravitational lenses that produce multiple images of quasi-stellar objects (QSOs), such as four-image Einstein Cross lenses. Current methods based on broad-band flux ratios cannot cleanly distinguish between substructure, differential extinction, scattering in the radio by ionized regions in the lens galaxy, microlensing by stars and, most importantly, ambiguities in the host lens model These difficulties may be overcome by utilizing the prediction that, when substructure is present, the magnification will be a function of source size. QSO broad-line and narrow-line emission regions are ∼1 pc and > 100 pc in size, respectively. The radio emission region is typically intermediate to these and the continuum emission region is much smaller. When narrow-line region (NLR) features are used as a normalization, the relative intensity and equivalent width of broad-line region (BLR) features will respectively reflect substructure-leasing and microlensing effects. Spectroscopic observations of just a few image pairs would probably be able to extract the desired substructure signature cleanly and distinguish it from microlensing - depending on the actual level of projected mass in substructure. In the rest-optical, the Hβ/[O III] region is ideal, since the narrow wavelength range also largely eliminates differential reddening problems. In the rest-ultraviolet, the region longward of and including Lyα may also work. Simulations of Q2237+0305 are done as an example, to determine the level of substructure that is detectable in this way. Possible systematic difficulties are also discussed. This is an ideal experiment to be carried out with near-infrared integral field unit spectrographs on 8-m class telescopes, and will provide a fundamentally new probe of the internal structure of dark matter haloes.