B.6.5. Spiral Galaxy Lenses

Discussions of lens statistics, or even lenses in general, focus on early-type galaxies (E/S0). The reason is that spiral lenses are relatively rare. The only morphologically obvious spirals are B0218+357 (Sc, York et al. [2004]), B1600+434 (S0/Sa, Jaunsen & Hjorth [1997]), PKS1830-211 (Sb/Sc, Winn et al. [2002b]), PMNJ2004-1349 (Sb/Sc, Winn, Hall & Schechter [2003]), and Q2237+0305 (Sa, Huchra et al. [1985]). Other small separation systems may well be spiral galaxies, but we do not have direct evidence from imaging. There are studies of individual spiral lenses or the statistics of spiral lenses by Maller, Flores & Primack ([1997]), Keeton & Kochanek ([1998]), Koopmans et al. ([1998]), Maller et al. ([2000]), Trott & Webster ([2002]), and Winn, Hall & Schechter ([2003]).

The reason lens samples are dominated by early-type galaxies is that the early-type galaxies are more massive even if slightly less numerous (e.g. Fukugita & Turner [1991], see Section B.6.2). The relative numbers of early-type and late-type lenses should be the ratio of their optical depths, (n_l / n_e)(_l / _e)⁴, based on the comoving densities and characteristic velocity dispersions of the early and late-type galaxies. For example, in the Kochanek et al. ([2001]) K-band luminosity function n_l / n_e 2.2 while the ratio of the characteristic velocity dispersions is _*l / _*e = 0.68 giving an expected fraction of 32% spiral. This is modestly higher than the values using other luminosity functions (usually closer to 20%) or the observed fraction. Because the typical separation of the spiral lenses will also be smaller by a factor of (_*l / _*e)² = 0.46, they will be much harder to resolve given the finite resolution of lens surveys. Thus, survey selections functions discriminate more strongly against late-type lenses than against early-type lenses. The higher prevalence of dust in late-type lenses adds a further bias against them in optical surveys.