1. INTRODUCTION AND HISTORICAL PERSPECTIVE

In the early days of modern cosmology, soon after it was realized that the Universe was expanding (Hubble 1929; Lemaître 1931; Hubble 1931); Zwicky (1933) suggested that some unseen matter was the likely dominant mass component in clusters of galaxies. With remarkable prescience, Zwicky (1937) further noted that gravitational lensing by clusters would be an invaluable tool to: (i) trace and measure the amount of this unseen mass, now referred to as dark matter and currently thought to pervade the cosmos; and (ii) study magnified distant objects lying behind clusters. Zwicky's bold predictions were based on a profound and intuitive understanding of the properties of gravitational lensing. However at that time, inadequate imaging technology coupled with the lack of theoretical understanding of structure formation in the Universe hampered further observational progress and discoveries of gravitational lensing effects.

Although the existence of clusters of galaxies has been recognized for nearly two centuries - they were first recognized by Messier and Herschel as "remarkable concentrations of nebulae on the sky" (see the review of Biviano 2000 and references therein) the study of clusters began in earnest only really in the 1950s. In particular, the publication of the first comprehensive cluster catalog of the nearby Universe by Abell in 1958, can be considered as a milestone that spurred the study of clusters of galaxies transforming it into an active observational research area.

In comparison, gravitational lensing theory developed much later in the 1960s with early theoretical studies demonstrating the usefulness of lensing for astronomy. In particular, Sjur Refsdal derived the basic equations of gravitational lens theory (Refsdal 1964a) and subsequently showed how the gravitational lensing phenomenon can be used to determine Hubble's constant by measuring the time delay between two lensed images (Refsdal 1964b). Following the discovery of quasars, Barnothy (1965) proposed gravitational lensing as a tool for the study of quasars. With the discovery of the first double quasar Q0957+561 by Walsh, Carswell & Weymann (1979) gravitational lensing really emerged in astronomy as an active observational field of study.

The study of clusters of galaxies as astronomical objects on the other hand, came of age in the 1970s and early 1980s specially with the discovery of the X-ray emitting intra-cluster medium (Lea et al. 1973; Gull & Northover 1976; Bahcall & Sarazin 1977; Serlemistos et al. 1977; Cavaliere & Fusco-Femiano 1978) and the numerous studies of the stellar populations of galaxies in clusters (Bautz & Morgan 1970; Sandage 1976; Leir & van den Bergh 1977; Hoessl, Gunn & Thuan 1980; Dressler 1980). However, there was no discussion of their lensing properties in theoretical papers till the 1980s. The paper by Narayan, Blandford & Nityananda (1984) is one of the earliest theoretical papers that explored in detail the possibility that clusters can act as powerful lenses. As an example, this paper explained large separation multiple quasars as likely "cluster-assisted" lensing systems. Although such a possibility had been already proposed by Young et al. (1980), who discovered a cluster of galaxies near the first double quasar Q0957+561, it was not so obvious for most other systems.

The likely explanation for the lack of interest in cluster lensing research was probably the belief that clusters were rather diffuse/extended systems and therefore not dense enough to act as powerful light deflectors. Only with the establishment of the role of cold dark matter in structure formation, did it become clear that clusters are indeed repositories of vast amounts of dark matter that enable them to act as efficient lenses in the Universe. The theory of structure formation in the context of a cold dark matter dominated Universe was developed in a seminal paper by Blumenthal et al. (1984). An attractive feature of this cold dark matter hypothesis was its considerable predictive power: the post-recombination fluctuation spectrum was calculable, and it in turn governs the formation of galaxies and clusters. At that time, good agreement with the data was obtained for a Zel'dovich spectrum of primordial fluctuations. Several decades later, a version of this paradigm the Λ Cold Dark Matter (ΛCDM hereafter) model which postulates the existence of a non-zero cosmological constant Ω_Λ is currently well established and is in remarkable agreement with a wide range of current observations on cluster and galaxy-scales.

Nevertheless, it still came as quite a surprise when in 1986, Lynds & Petrosian (1986) and Soucail et al. (1987) independently discovered the first "giant arcs": the strongly elongated images of distant background galaxies in the core of massive clusters (see Figure 1). This new phenomenon was then immediately identified by Paczynśki (1987) as the consequence of gravitational lensing by the dense centers of clusters, and was soon confirmed by the measurement of the redshift of the arc in Abell 370 (Soucail et al. 1988). The discovery of giant arcs revealed the existence of the strong lensing regime, however as we know now, it only represents the tip of the iceberg!

Figure 1. The galaxy cluster Abell 370 as observed by CFHT in 1985 (left) with one of the first CCD cameras (R-band), in which the first gravitationally lensed arc was later identified (Lynds & Petrosian 1986; Soucail et al. 1987a, 1987b). For comparison, the image on the right shows the Hubble Space Telescope image of the same cluster Abell 370 taken with the WFPC-2 camera with the F675W filter in December 1995 (Soucail et al 1999). Most of the bright galaxies seen are cluster members at z = 0.375, whereas the arc, i.e. the highly elongated feature, is the image of a background galaxy at redshift z = 0.724 (Soucail et al. 1988). The image is oriented such that North is on top, East to the left and the field of view is roughly 40 x 60 arcsec2.

Coupled with the growing theoretical understanding of the structure and assembly history of clusters, this observational discovery of cluster lensing opened up an entire new vista to probe the detailed distribution of dark matter in these systems. In 1990, Antony Tyson while obtaining deep CCD imaging of clusters, identified a "systematic alignment" of faint galaxies around cluster cores (Tyson, Wenk & Valdes 1990). He then suggested that this weak alignment produced by the distortion due to lensing by clusters could be used to map dark matter at larger radii in clusters than strong lensing afforded. These two key discoveries of strong and weak lensing respectively opened up a rich, new field in astronomy, the study of "cluster lenses", which we discuss further in this review.

These observational discoveries stoked the theoretical community to produce a number of key papers in the first half of the 1990s that developed the theoretical framework for strong and weak lensing techniques. Several of the seminal papers date from this period, and theorists delved into quantifying this new territory of gravitational lensing. Some of the significant early papers are: Schneider (1984); Blandford & Narayan (1986); Blandford, Kochanek, Kovner & Narayan (1989); Kochanek (1990); Miralda-Escude (1991); Kaiser (1992); Kaiser & Squires (1993). It is important to underline that significant advances in technology spurred the field dramatically during these years. The discovery of the lensing phenomenon in clusters was made possible thanks to the successful development of CCD imaging that allowed deeper and sharper optical images of the sky, as well as deep spectroscopy - essential to measure the spectrum and the redshifts of the faint lensed background galaxies. Another technological revolution was in preparation at that time, a telescope above the atmosphere: the Hubble Space Telescope (HST). HST has dramatically impacted cluster lensing studies, and, in particular, that of the strong lensing regime. Although launched in 1991, HST did not make a strong impact at first, as its unforeseen "blurred vision" made the faint images of distant galaxies inadequate for lensing work. Nevertheless, even with the first HST-WFPC1 (Wide Field Planetary Camera) images of Abell 370 and AC114 one could already see the potential power of Hubble for lensing studies.

In December 1993, with the first successful servicing mission and the installation of the odd shaped WFPC2 camera, Hubble recovered its image sharpness, and it is not surprising that one of the first image releases following the installation of WFPC2 was the astonishing view of the cluster lens Abell 2218 (Kneib et al. 1996), which is iconic and has been included in most recent introductory astronomy textbooks.

Image sharpness is one of the key pre-requisites for studying lensing by clusters (e.g. Smail & Dickinson 1995), and unsurprisingly another requirement is a large image field of view. The strong lensing regime in clusters corresponds to the inner one arc-minute region around the cluster center. Typically, cluster virial radii are of the order of a few Mpc, which corresponds to ∼ 15 arcminutes for a cluster at z ∼ 0.2. Therefore, to go beyond the inner regions and to measure the weak lensing signal from cluster outskirts, cameras with a sufficiently large field of view are required to ideally cover the full size of a cluster in one shot (e.g. Kaiser et al 1998, Joffre et al 2000).

From the second half of the 1990s we have seen the rapid development of wide field imaging cameras such as: the UH8k followed by CFHT12k at CFHT (Canada France Hawaii Telescope); Suprime at the Subaru Telescope; WFI at the 2.2m telescope at ESO (European Southern Observatory); the Megacam camera at CFHT; the Gigacam of Pan-STARRS (PS-1); the OmegaCam of the VST and soon the Dark Energy Camera at CTIO (Cerro Tololo Inter-American Observatory). These cameras are composed of a mosaic of many large format CCDs (4k × 2k or larger) allowing coverage of a large field (ranging from a quarter of a square degree up to a few square degrees). The making of these instruments was strongly motivated by the detection of the weak lensing distortion of faint galaxies produced by foreground clusters and intervening large scale structure, the latter effect is commonly referred to as "cosmic shear".

In parallel, techniques to accurately measure the gravitational shear were also developed. The most well documented is the “KSB” technique (Kaiser, Squires & Broadhurst 1995) which is implemented in the commonly used imcat software package, ¹ which has been since improved by several groups. The accuracy of shape measurements for distorted background images is key to exploiting lensing effects. The difficulty in the shear measurement arises as galaxy ellipticities need to be measured extremely accurately given that there are other confounding sources that generate distortions. Spurious distortions are induced by the spatially and temporally variable PSF (Point Spread Function) as well as by intrinsic shape correlations that are unrelated to lensing (Crittenden et al. 2001; 2002). Corrections that carefully take into account these additional and variable sources of image distortion have been incorporated into shape measurement algorithms like lensfit ² (Miller et al. 2007; Kitching et al. 2008). Although the “KSB” technique has been quite popular due to its speed and efficiency, many new implementations for extracting the shear signal with the rapid increase in the speed and processing power of computers are currently available.

The first weak lensing measurements of clusters were reported with relatively small field of view cameras (Fahlman et al. 1994; Bonnet et al. 1994) but were soon extended to the larger field of view mosaic cameras (e.g. Dahle et al. 2002; Clowe & Schneider 2001, 2002; Bardeau et al. 2005, 2007). Two-dimensional dark matter mapping gets rapidly noisy as one extends over more than ∼2 arcminutes from the cluster center due to a rapidly diminishing lensing signal. However, radial averaging of the shear field provides an effective way to probe the mass profile of clusters out to their virial radius and even beyond. This technique of inverting the measured shear profile to constrain the mass distribution of clusters is currently widely used. Combining constraints from the strong and weak lensing regime has enabled us to derive the dark matter density profile over a wide range of physical scales. As a consequence, gravitational lensing has become a powerful method to address fundamental questions pertinent to cluster growth and assembly.

Theoretically, as it is known that clusters are dominated by dark matter, enormous progress has been made in tracking their formation and evolution using large cosmological N-body simulations since the 1980s. Gravitational lensing is sensitive to the total mass of clusters, thereby enabling detailed comparison of the mass distribution and properties inferred observationally with simulated clusters. Lensing observations have therefore allowed important tests of the standard structure formation paradigm.

At the turn of the second millennium the new role of lensing clusters is its growing use as natural telescopes to study very high-redshift galaxies that formed during the infancy of the Universe (e.g. Franx et al. 1997; Pelló et al. 1999; Ellis et al. 2001). This became possible with deep spectroscopy on 4 m and then 8-10 m class telescopes that enable probing the high-redshift Universe, primarily by exploiting the lensing amplification and magnification ³ produced by these natural telescopes (Pelló et al 2001). Capitalizing on the achromatic nature of cluster lensing, various observatories functioning at different wavelengths of the electromagnetic spectrum have been deployed for these studies. In particular, the discovery and study of the population of sub-millimeter galaxies using SCUBA at the James Clerk Maxwell Telescope (JCMT hereafter; see the reviews by Blain et al. 2002; Smail et al. 2002; Kneib et al. 2004; Knudsen et al. 2005; Borys et al. 2005, Knudsen et al. 2008), the Caltech interferometer at Owens Valley (e.g. Frayer et al. 1998; Sheth et al. 2004), the IRAM interferometer (e.g. Neri et al. 2003; Kneib et al. 2005), the Very Large Array (VLA) (e.g. Smail et al. 2002; Ivison et al. 2002; Chapman et al. 2002) and Sub-Millimeter Array (SMA) (e.g. Knudsen et al. 2010) greatly benefited from the boost provided by the magnification effect of gravitational lensing in cluster fields. Similarly, observation of lensed galaxies in the mid-infrared with the ISOCAM mid-infrared camera on the Infra-red Space Observatory (ISO) satellite (Altieri et al. 1999; Metcalfe et al. 2003), followed with the Spitzer observatory (Egami et al. 2005) and now with the Herschel space observatory (Egami et al. 2010; Altieri et al. 2010) have pushed the limits of our knowledge of distant galaxies further. Gravitational lensing is now recognized as a powerful technique to count the faintest galaxies in their different classes: Extremely Red Objects (Smith et al. 2001); Lyman-α emitters at z ∼ 4−6 (Hu et al. 2002; Santos et al. 2004, Stark et al. 2007); Lyman-break galaxies at z ∼ 6−10 (Richard et al. 2008) as well as to study in detail the rare, extremely magnified individual sources (Pettini et al. 2000; Kneib et al. 2004; Egami et al. 2005, Smail et al. 2007, Swinbank et al. 2007, 2010) in the distant Universe.

Since March 2002, the installation of the new ACS camera onboard HST has provided further observational advances in the study and unprecedented use of cluster lenses (see Figure 2). These are exemplified in the very deep and spectacular ACS images of Abell 1689 (Broadhurst et al. 2005; Halkola, Seitz & Pannella 2006). This color image reveals more than 40 multiple-image systems in the core of this cluster (Limousin et al. 2007) and well over a hundred lensed images in total. The dramatic increase in the number of strong lensing constraints that these observations provide in the cluster core has spurred important and significant new developments in mass reconstruction techniques (e.g. Diego et al. 2005a, b; Jullo et al. 2007, 2009; Coe et al. 2008). With this amount of high quality data the construction of extremely high-resolution mass models of the cluster core are now possible. Mass models with high precision have enabled the use of this cluster to constrain the cosmological parameters Ω_m and Ω_Λ (Link and Pierce 1998; Golse et al. 2004; Gilmore & Natarajan 2009; Jullo et al. 2010; D'Aloisio & Natarajan 2011). First observational constraints were attempted by Soucail et al. (2004), and more recent work by Jullo et al. (2010) has demonstrated the feasibility of this technique involving detailed modeling of deep ACS images coupled with comprehensive redshift determinations for the numerous multiple-image systems. Combining these cosmological constraints from the cluster lens Abell 1689 with those obtained from independent X-ray measurements and a flat Universe prior from WMAP, Jullo et al. (2010) find results that are competitive with the other more established methods like SuperNovae (Riess et al. 1998; Perlmutter et al. 1999) and Baryonic Acoustic Oscillations (Eisenstein et al. 2005). Therefore, in the very near future cluster strong lensing is likely to provide us with a viable complementary technique to constrain the geometry of the Universe and probe the equation of state of Dark Energy, which is a key unsolved problem in cosmology today.

Figure 2. Color image of two cluster lenses observed by HST-ACS: Left panel - Abell 2218 at z = 0.175 and Right panel - Cl0024+1654 at z = 0.395.

¹ IMCAT software is available at http://www.ifa.hawaii.edu/~kaiser/imcat/ Back.

² LENSFIT software is available at - http://www.physics.ox.ac.uk/lensfit/ Back.

³ the magnification refers to the spatial stretching of the images by the gravitational lensing effect, however the magnification cannot be recognized when the lensed object is not resolved by the observations (if the object is compact or if the PSF is broad) leading to an apparent amplification of the flux of the lensed object. In some cases, a lensed object can be tangentially magnified but radially amplified, the use of the terms magnification and amplification are thus sometimes mixed. Back.