SOBRECARGAS POR GENERACION

One of the most useful and important properties of gravitational lensing is that it is sensitive to any kind of matter that acts gravitationally. This makes it very effective for the study of the mass profiles of galaxy clusters where the hot intra cluster gas emitting X-rays is not necessarily in hydrostatic equilibrium, the velocity dispersion

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measurements are affected by complex dynamical structure and most of the mass is in the form of dark matter that cannot be observed directly. With gravitational lensing one measures all the mass from the gas and stars and dark matter. Additionally the dynamical state of the cluster does not affect the results.

In galaxy clusters the dense central regions (typically several hundred kpc) are efficient strong lenses producing multiple images and spectacular giant arcs. The giant arcs constrain the mass within the Einstein radius1 of the cluster tightly. The cluster centre needs to be well determined for this to yield accurate masses if only one arc is visible. By identifying counter images of the arc on the opposite side of the cluster, mass estimates can be significantly improved.

Clusters where one can identify many multiply imaged sources are more interest- ing. With multiple images at many different projected cluster centric distances one can effectively measure the mass of the cluster at different radii and accurate radial mass profiles in the central regions can be obtained. If the redshifts of the sources can also be estimated we can effectively break the mass sheet degeneracy mentioned earlier.

Regions outside the Einstein ring and the strong lensing regime distort that shapes of background galaxies and the mass can be estimated using weak lensing mass recon- struction algorithms. This means that the mass profiles of clusters can be extended out and beyond the virial radii of clusters (typically around 2 Mpc).

There is a region between the strong and weak lensing regimes where there are no multiple images but the images are significantly curved (flexion) and the current weak lensing mass reconstruction techniques cannot make full use of the information contained in the shapes of the images of background galaxies. The work to include also this region in the mass reconstruction is starting with papers treating flexion appearing in astro-ph (Goldberg & Natarajan, 2002; Okura et al., 2006; Goldberg & Leonard, 2006; Melchior et al., 2006). This could hopefully reduce the discrepancies sometimes seen between the cluster profile parameters derived from strong and weak lensing, e.g. in Abell 1689.

The masses and mass profiles of clusters are of great astronomical interest for sev- eral reasons. Since most of the matter, not only in clusters but also in galaxies and the universe as a whole, is expected to be in some form of cold dark matter the exact distri- bution of the mass in clusters can give us clues how dark matter interacts with normal baryonic matter and itself. Large cores in clusters could, for example, indicate that dark matter is self-interacting: the interactions between dark matter particles would lead to dissipation of energy and create flat cores for clusters. Accurate masses for large numbers of clusters and groups in the universe are needed to constrain also cos- mological models. The initial conditions for structure formation are well know from

1_{A spherically symmetric lens produces a ring like image of a background source, if the source is} located directly behind the lens. The ring is called an Einstein ring and its radius the Einstein radius.

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the imprint left on the cosmic microwave background radiation and the evolution of the inhomogeneities to the present day can be calculated using numerical simulations. What is needed, is an equally good reference point at later evolutionary stages of the universe.

The first strong lensing clusters were discovered when giant luminous arcs were identified in CL2244-02 (Lynds & Petrosian, 1986) and A370 (Soucail et al., 1987). The nature of the arcs was not immediately recognised but spectroscopy of the arcs revealed them to be at high redshifts making gravitational lensing the only viable ex- planation for the highly elongated structures. Since then many more clusters with giant arcs and multiple images have been found.

Great effort has gone into the detailed studies of many clusters with weak and strong lensing methods as well as X-ray and dynamical mass estimates. Ideally one should obtain the same mass for a cluster regardless of the method but due to different approximations and assumptions in the methods the measured masses can have dis- crepancies as large as factor of 3 e.g. clusters A2218 (Kneib et al. 1995; Abdelsalam et al. 1998 although recent studies by Girardi et al. 1997; Cannon et al. 1999 claim to resolve this problem.) and A1689 (Girardi et al. 1997; Clowe & Schneider 2001; King et al. 2002; Xue & Wu 2002; Andersson & Madejski 2004). In some other clusters however a good agreement is found. An example of such a cluster is CL2244 (Ota et al., 1998).

The discrepancies are most likely associated with complicated dynamical states of the clusters. Mergers and subcomponents in the mass structure of a cluster can increase the measured line of sight velocity dispersions. The X-rays mass estimates are affected by non-spherical mass distributions in clusters and deviations from hydrostatic equilibrium. Lensing on the other hand is affected by mass structures along the line of sight not associated with the cluster and unknown redshifts of the background sources. The key to our understanding of galaxy clusters is to use all the methods at our disposal. Another hotly debated issue is related to the exact profile of galaxy clusters. Weak lensing is most sensitive around the scale radius where both NFW and isothermal spheres have logarithmic gradients close to -2. This makes it very difficult to reject one of the profiles with high confidence using weak lensing alone. The inner slope can be obtained with strong lensing but also here controversy prevails with NFW matching the observations well in some clusters (e.g. CL0024, Kneib et al., 2003) and isothermal sphere in others (e.g. MS2137, Gavazzi et al., 2003).

1.2.3.1 Abell 1689

Abell 1689 is a very massive cluster at a redshift 0.18 that has been studied extensively with spectroscopy, X-rays and gravitational lensing. Most of the lensing work done so far is in the weak lensing regime, although some models based on the prominent giant arc have been constructed.

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The first dynamical mass estimates measured a very high velocity dispersion of almost 2400 km/s Teague et al. (1990). This has since been reduced by a reanalysis of the data to a more moderate value of 1500 km/s (Girardi et al., 1997). The reanalysis revealed A1689 to have 3 significant substructures with well defined velocities that overlap spatially. Considering them all as one structure gives the very high dispersion of Teague et al. (1990). The 3 separate structure are a likely reason for the problems associated with the very different mass estimates from the 3 methods. The separate structures can increase the observed velocity dispersion of the cluster as well as complicates the mass estimates based on the X-ray emitting gas.

Of the mass estimates, X-ray (Allen, 1998; Xue & Wu, 2002; Andersson & Made- jski, 2004) produces consistently the lowest mass estimates. Most recently Andersson & Madejski (2004) obtain a velocity dispersion of only 918 km/s.

Weak lensing has been used in many various forms to estimate the mass of the clus- ter (Tyson & Fischer, 1995; Taylor et al., 1998; Dye et al., 2001; Clowe & Schneider, 2001; King et al., 2002,?; Clowe, 2003; Broadhurst et al., 2005b). The weak lensing results generally favour a fairly small velocity dispersion of 1000-1200 km/s for an isothermal sphere, although there are also exceptions of the rule (Taylor et al., 1998; Dye et al., 2001).

For a long time the only strong lensing analysis of A1689 was that of Miralda- Escude & Babul (1995) who used two prominent arcs to construct a simple two halo model for the cluster. One of the haloes has a velocity dispersion of 1450 km/s and the other 700 km/s. This is in fairly good agreement with the dynamical mass estimate presented in Girardi et al. (1997).

What has been lacking until very recently is a thorough investigation using the full potential of a strong lensing analysis in this cluster. This deficit will be dealt with in this thesis.

That no proper strong lensing model exists is mainly due to the lack of deep im- ages of the cluster taken with the Hubble Space Telescope. The use of space based observations is necessary in order to be able to resolve the many faint multiple images expected to be identifiable in the cluster. In this work we will use recent HST WFPC2 and ACS images in 6 passbands (WFPC2: F555W, F814W, ACS: F475W, F625W, F775W, F850L) in the HST Science Archive. Essentially the same data set has been used in several other recent strong lensing models of the cluster (Broadhurst et al., 2005a; Diego et al., 2005b; Zekser et al., 2006)

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