Cosmological Constant and Statistical Lensing of Giant Arcs

Abstract

Using a singular isothermal sphere model for the matter distribution of foreground clusters of galaxies, we study the statistics of giant arcs in flat cosmologies with and without a cosmological constant. We find that the relative number of arcs predicted within $z=1$ in a universe with $Ω_0=0.3$ and $λ_0 \equiv Λ/(3H_0^2)=0.7$ is a factor of $\sim2$ larger than the one in the Einstein-de Sitter universe ($Ω_0=1, λ_0=0$). For a luminosity-dependent evolution model of the number density of background galaxies that accounts for the over-density of faint blue galaxies at $z_s\approx0.4$, the Einstein- de Sitter cosmological model predicts that about $5\%$ of clusters of galaxies with an X-ray luminosity $L_x > 2 \times 10^{44}$ erg s$^{-1}$ should have giant arcs with length-to-width ratio larger than 10. This is a factor of $\sim4$ lower than the observed fraction in the gravitational lensing survey of distant X-ray selected EMSS clusters of galaxies, indicating that the matter distribution of clusters of galaxies deviates significantly from simple isothermal spheres or/and the presence of a significant cosmological constant. It is profitable to further study the constraint on the cosmological constant from giant arcs using more realistic cluster models.

19 pages, compressed uuencoded PS file with two figures included, ApJ in press