Strong lensing statistics in large, zlsim 0.2, surveys: bias in the lens galaxy population

Abstract

Large current and future surveys, like the Two-degree Field Survey (2dF), the Sloan Digital Sky Survey (SDSS) and the proposed Kilo-Degree Survey (KIDS), are likely to provide us with many new strong gravitational lenses. Taking cosmological parameters as known, we calculate the expected lensing statistics of the galaxy population in large, low-redshift surveys. Galaxies are modelled using realistic, multiple components: a dark matter halo, a bulge component and disc. We use semi-analytic models of galaxies coupled with dark matter haloes in the Millennium Run to model the lens galaxy population. Replicating the selection criteria of the 2dF, we create a mock galaxy catalogue. We predict that a fraction of 7.5 ± 0.2 x 10 -5 of radio sources will be lensed by galaxies within a survey like the 2dF below z < 0.2. We find that proper inclusion of the baryonic component is crucial for calculating lensing statistics - pure dark matter haloes produce lensing cross-sections several orders of magnitude lower. With a simulated sample of lensed radio sources, the predicted lensing galaxy population consists mainly of ellipticals (∼80 per cent) with an average lens velocity dispersion of 191 ± 3 km s -1 , producing typical image separations of ∼1.5 arcsec. The lens galaxy population lies on the fundamental plane but its velocity dispersion distribution is shifted to higher values compared to all early-type galaxies. We show that magnification bias affects lens statistics very strongly and increases the 4:2 image ratio drastically. Taking this effect into account, we predict that the ratio of 4:2 image systems is 18 ± 5 per cent, marginally consistent with the observed ratio found in the Cosmic Lens All-Sky Survey (CLASS). We also find that the population of four-image lens galaxies differs markedly from the population of lens galaxies in two-image systems. We find that while most lenses tend to be ellipticals, galaxies that produce four-image systems preferentially tend to be lower velocity dispersion systems with more pronounced disc components. Our key result is the explicit demonstration that the population of lens galaxies differs markedly from the galaxy population as a whole: lens galaxies have a higher average luminosity and, for a given luminosity, they reside in more massive haloes than the overall sample of ellipticals. This bias restricts our ability to infer galaxy evolution parameters from a sample of lensing galaxies.