B.6.1. The Mechanics of Surveys

There are two basic approaches to searching for gravitational lenses depending on whether you start with a list of potentially lensed sources or a list of potential lens galaxies. Of the two, only a search of sources for lensed sources has a significant cosmological sensitivity - for a non-evolving population of lenses in a flat cosmological model we will find in Section B.6.3 that the number of lensed sources scales with the volume between the observer and the source D_s³. If you search potential lens galaxies for those which have actually lensed a source, then the cosmological dependence enters only through distance ratios, D_ds / D_s, and you require a precise knowledge of the source redshift distribution. Thus, while lenses found in this manner are very useful for many projects (mass distributions, galaxy evolution etc.), they are not very useful for determining the cosmological model. This changes for the case of cluster lenses where you may find multiple lensed sources at different redshifts behind the same lens (e.g. Soucail, Kneib & Gorse [2004]).

Most lenses have been found by searching for lensed sources because the number of targets which must be surveyed is considerably smaller. This is basically a statement about the relative surface densities of candidate sources and lenses. The typical lens is a galaxy with an Einstein radius of approximately b 1."0 so it has a cross section of order b². If you search N lenses with such a cross section for signs of a lensed source, you would expect to find N b² _source lenses where _source is the surface density of detectable sources. If you search N sources for a lens galaxy in front of them, you would expect to find N b² _lens lenses, where _lens is the surface density of lens galaxies. Since the surface density of massive galaxies is significantly higher than the surface density of easily detectable higher redshift sources (_lens >> _source), you need examine fewer sources than lens galaxies to find the same number of lensed systems. This is somewhat mitigated by the fact the surface density of potential lens galaxies is high enough to allow you to examine many potential lenses in a single observation, while the surface density of sources is usually so low that they can be examined only one at a time.

For these reasons, we present a short synopsis of searches for sources behind lenses and devote most of this section to the search for lenses in front of sources. The first method for finding sources behind lenses is a simple byproduct of redshift surveys. Redshift surveys take spectra of the central regions of low redshift galaxies allowing the detection of spectral features from any lensed images inside the aperture used for the spectrum. Thus, the lens Q2237+0305 was found in the CfA redshift survey (Huchra et al. [1985]) and SDSS0903+5028 (Johnston et al. [2003]) was found in the SDSS survey. Theoretical estimates (Kochanek [1992b], Mortlock & Webster [2000c]) suggest that the discovery rate should one per 10⁴-10⁵ redshift measurements, but this does not seem to be borne out by the number of systems discovered in this age of massive redshift surveys (the origin of the lower rate in the 2dF survey is discussed by Mortlock & Webster [2001]). Miralda-Escude & Lehár ([1992]) proposed searching for lensed optical (emission line) rings, a strategy successfully used by Warren et al. ([1996]) to find 0047-2808 and by Ratnatunga, Griffiths & Ostrander ([1999]) to find lenses in the HST Medium Deep Survey (MDS). There is also a hybrid approach whose main objective is simply to find lenses with minimal follow up observations by looking for high redshift radio lobes that have non-stellar optical counterparts (Lehár et al. [2001]). Since radio lobes have no intrinsic optical emission, a lobe superposed on a galaxy is an excellent lens candidate. The present limitation on this method is the low angular resolution of the available all sky radio surveys (FIRST, NVSS) and the magnitude limits and star/galaxy separation problems of the current all-sky optical catalogs. Nonetheless, several systems have been discovered by this technique.

The majority of lens surveys, however, have focused on either optical quasars or radio sources because they are source populations known to lie at relatively high redshift (z_s 1) and that are easily detected even when there is an intervening lens galaxy. Surveys of optical quasars (Crampton, McClure & Fletcher [1992], Yee, Fillipenko & Tang [1993], Maoz et al. [1993], Surdej et al. [1993], Kochanek, Falco & Schild [1995]) have the advantage that the sources are bright, and the disadvantages that the bright sources can mask the lens galaxy and that the selection process is modified by dust in the lens galaxy and emission from the lens galaxy. We will discuss these effects in Section B.9. While many more lensed quasars have been discovered since these efforts, none of the recent results have been presented as a survey. Surveys of all radio sources (the MIT/Greenbank survey, Burke, Lehár & Conner [1992]) have the advantage that most lensed radio sources are produced by extended, steep spectrum sources (see Kochanek & Lawrence [1990]), and the disadvantage that the complex intrinsic structures of extended radio sources make the follow up observations difficult. Surveys of flat spectrum radio sources (the CLASS survey, Browne et al. [2003], the PANELS survey, Winn, Hewitt & Schechter [2001]) have the advantage that the follow up observations are relatively simple because most unlensed flat spectrum sources are (nearly) point sources. There are disadvantages as well - because the source structure is so simple, flat spectrum lenses tend to provide fewer constraints on mass models than steep spectrum lenses. The radio sources tend to be optically faint, making it difficult to determine their redshifts in many cases.

The second issue for any survey is to understand the method by which the sources were originally identified. For example, it is important to know whether the flux of a lensed source in the input catalog is the total flux of all the images or only a part of the flux (e.g. the flux of the brightest image). This will have a significant effect on the statistical corrections for using a flux-limited catalog, a correction known in gravitational lensing as the "magnification bias" (see Section B.6.6). All large, published surveys were essentially drawn from samples which would include the total flux of a lensed system. It is also important to know whether the survey imposed any criterion for the sources being point-like, since lensed sources are not, or any color criterion that might be violated by lensed sources with bright lens galaxies or significant extinction.

The third issue for any survey is to consider the desired selection function of the observations. This is some combination of resolution, dynamic range and field of view. These determine the range of lens separations that are detectable, the nature of any background sources, and the cost of any follow up observations. Any survey is a trade-off between completeness (what fraction of all lenses in sample that can be discovered), false positives (how many objects selected as lenses candidates that are not), and the cost of follow-up observations. The exact strategy is not critical provided it is well-understood. The primary advantages of the surveys of flat spectrum radio sources are the relatively low false positive rates and follow up costs produced by using a source population consisting almost entirely of point sources with no contaminating background population. This does not mean that the flat spectrum surveys are free of false positives - core-jet sources can initially look like asymmetric two-image lenses. On small angular scales ( 3."0) the quasar surveys share this advantage, but for wider separations there is contamination from binary quasars (see Section B.7.2) and Galactic stars (see Kochanek [1993a]).