Weak gravitational lensing

While the presence of any mass bends the path of light passing near it, this effect rarely produces the giant arcs and multiple images associated with strong gravitational lensing. Most lines of sight in the universe are thoroughly in the weak lensing regime, in which the deflection is impossible to detect in a single background source. However, even in these cases, the presence of the foreground mass can be detected, by way of a systematic alignment of background sources around the lensing mass. Weak gravitational lensing is thus an intrinsically statistical measurement, but it provides a way to measure the masses of astronomical objects without requiring assumptions about their composition or dynamical state. While the presence of any mass bends the path of light passing near it, this effect rarely produces the giant arcs and multiple images associated with strong gravitational lensing. Most lines of sight in the universe are thoroughly in the weak lensing regime, in which the deflection is impossible to detect in a single background source. However, even in these cases, the presence of the foreground mass can be detected, by way of a systematic alignment of background sources around the lensing mass. Weak gravitational lensing is thus an intrinsically statistical measurement, but it provides a way to measure the masses of astronomical objects without requiring assumptions about their composition or dynamical state. Gravitational lensing acts as a coordinate transformation that distorts the images of background objects (usually galaxies) near a foreground mass. The transformation can be split into two terms, the convergence and shear. The convergence term magnifies the background objects by increasing their size, and the shear term stretches them tangentially around the foreground mass. To measure this tangential alignment, it is necessary to measure the ellipticities of the background galaxies and construct a statistical estimate of their systematic alignment. The fundamental problem is that galaxies are not intrinsically circular, so their measured ellipticity is a combination of their intrinsic ellipticity and the gravitational lensing shear. Typically, the intrinsic ellipticity is much greater than the shear (by a factor of 3-300, depending on the foreground mass). The measurements of many background galaxies must be combined to average down this 'shape noise'. The orientation of intrinsic ellipticities of galaxies should be almost entirely random, so any systematic alignment between multiple galaxies can generally be assumed to be caused by lensing. Another major challenge for weak lensing is correction for the point spread function (PSF) due to instrumental and atmospheric effects, which causes the observed images to be smeared relative to the 'true sky'. This smearing tends to make small objects more round, destroying some of the information about their true ellipticity. As a further complication, the PSF typically adds a small level of ellipticity to objects in the image, which is not at all random, and can in fact mimic a true lensing signal. Even for the most modern telescopes, this effect is usually at least the same order of magnitude as the gravitational lensing shear, and is often much larger. Correcting for the PSF requires building for the telescope a model for how it varies across the field. Stars in our own galaxy provide a direct measurement of the PSF, and these can be used to construct such a model, usually by interpolating between the points where stars appear on the image. This model can then be used to reconstruct the 'true' ellipticities from the smeared ones. Ground-based and space-based data typically undergo distinct reduction procedures due to the differences in instruments and observing conditions. Angular diameter distances to the lenses and background sources are important for converting the lensing observables to physically meaningful quantities. These distances are often estimated using photometric redshifts when spectroscopic redshifts are unavailable. Redshift information is also important in separating the background source population from other galaxies in the foreground, or those associated with the mass responsible for the lensing. With no redshift information, the foreground and background populations can be split by an apparent magnitude or a color cut, but this is much less accurate. Galaxy clusters are the largest gravitationally bound structures in the Universe with approximately 80% of cluster content in the form of dark matter. The gravitational fields of these clusters deflect light-rays traveling near them. 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. 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+524. 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, only the most 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. Clusters discovered through lensing are subject to mass selection effects because the more massive clusters produce lensing signals with higher signal-to-noise. The projected mass density can be recovered from the measurement of the ellipticities of the lensed background galaxies through techniques that can be classified 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 κ → κ ′ = λ κ + ( 1 − λ ) {displaystyle kappa ightarrow kappa ^{prime }=lambda kappa +(1-lambda )} where λ is an arbitrary constant. 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.