User:TallJimbo/WeakLensing/Clusters

Galaxy clusters are the largest gravitationally-bound structures in the Universe with approximately 80% of their content in the form of dark matter ; their gravitational fields deflect light-rays traveling near the cluster. As seen from Earth, this effect can cause dramatic distortions of a background source object detectable by eye such as multiple images, arcs, and rings (cluster strong lensing). More generally, the effect causes small, but statistically coherent, distortions of background sources on the order of 10% (cluster weak lensing). Abell 1689, CL0024+17, and the Bullet Cluster are among the most prominent examples of lensing clusters.

History
The effects of cluster strong lensing were first detected by Roger Lynds of the National Optical Astronomy Observatories and Vahe Petrosian of Stanford University who discovered giant luminous arcs in a survey of galaxy clusters in the late 1970s. Lynds and Petrosian published their findings in 1986 without knowing the origin of the arcs. In 1987, Genevieve Soucail of the Toulouse Observatory and her collaborators presented data of a blue ring-like structure in Abell 370 and proposed a gravitational lensing interpretation. The first cluster weak lensing analysis was conducted in 1990 by J. Anthony Tyson of Bell Laboratories and collaborators. Tyson et al. detected a coherent alignment of the ellipticities of the faint blue galaxies behind both Abell 1689 and CL 1409+52. Lensing has been used as a tool to investigate a tiny fraction of the thousands of known galaxy clusters.

Historically, lensing analyses were conducted on galaxy clusters detected via their baryon content (e.g. from optical or X-ray surveys). The sample of galaxy clusters studied with lensing was thus subject to various selection effects; for example, the most optical and X-ray luminous clusters were investigated. In 2006, David Wittman of the University of California at Davis and collaborators published the first sample of galaxy clusters detected via their lensing signals, completely independent of their baryon content. However, clusters discovered through lensing are subject to mass selection effects as the more massive clusters produce lensing signals with higher signal-to-noise.

Observational products
The projected mass density can be recovered from the measurement of the ellipticities of the lensed background galaxies through techniques that can be classifed into two types: direct reconstruction and inversion. However, a mass distribution reconstructed without knowledge of the magnification suffers from a limitation known as the mass sheet degeneracy, where the cluster surface mass density κ can be determined only up to a transformation $$\kappa \rightarrow \kappa^{\prime} = \lambda \kappa+(1-\lambda)$$ where λ is an arbitrary constant. In principle, this degeneracy can be broken if an independent measurement of the magnification is available because the magnification is not invariant under the aforementioned degeneracy transformation.

Given a centroid for the cluster, which can determined by using a reconstructed mass distribution or optical or X-ray data, a parametric model such as a singular isothermal sphere (SIS) profile or a Navarro-Frenk-White (NFW) profile can be fit to the shear profile as a function of clustrocentric radius. Knowledge of the lensing cluster redshift and the redshift distribution of the background galaxies is also necessary for estimation of the mass and size from a model fit; these redshifts can be measured precisely using spectroscopy or estimated using photometry. Individual mass estimates from weak lensing can only be derived for the most massive clusters, and the accuracy of these mass estimates are limited by projections along the line of sight.

Scientific implications
Cluster mass estimates determined by lensing are valuable because the method requires no assumption about the dynamical state or star formation history of the cluster in question. Comparison of the dark matter distribution mapped using lensing with the distribution of the baryons using optical and X-ray data reveals the interplay of the dark matter with the stellar and gas components. A notable example of such a joint analysis is the so-called Bullet Cluster.

In a cosmological context, cluster lensing profiles can be used to constrain models of structure formation. In principle, since the number density of clusters as a function of mass and redshift is sensitive to the underlying cosmology, cluster counts derived from large weak lensing surveys should be able to investigate cosmological parameters. In practice, however, projections along the line of sight cause many false positives. Weak lensing can also be used to calibrate the mass-observable relation via a stacked weak lensing signal around an ensemble of clusters, although this relation is expected to have an intrinsic scatter. In order for lensing clusters to be a precision probe of cosmology in the future, the projection effects and the scatter in the lensing mass-observable relation need to be thoroughly characterized and modeled.