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Register a new userMass-sheet degeneracy: Fundamental limit on the cluster mass reconstruction from statistical (weak) lensing
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Weak gravitational lensing is considered to be one of the most powerful tools to study the mass and the mass distribution of galaxy clusters. However, weak lensing mass reconstructions are plagued by the so-called mass-sheet degeneracy--the surface mass density kappa of the cluster can be determined only up to a degeneracy transformation kappa to kappa = lambda kappa + (1 -lambda), where lambda is an arbitrary constant. This transformation fundamentally limits the accuracy of cluster mass determinations if no further assumptions are made. We describe here a method to break the mass-sheet degeneracy in weak lensing mass maps using distortion and redshift information of background galaxies and illustrate this by two simple toy models. Compared to other techniques proposed in the past, it does not rely on any assumptions on cluster potential; it can be easily applied to non-parametric mass-reconstructions and no assumptions on boundary conditions have to be made. In addition it does not make use of weakly constrained information (such as the source number counts, used in the magnification effect). Our simulations show that we are effectively able to break the mass-sheet degeneracy for supercritical lenses, but that for undercritical lenses the mass-sheet degeneracy is very difficult to be broken, even under idealised conditions.
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Weak lensing applied to deep optical images of clusters of galaxies provides a powerful tool to reconstruct the distribution of the gravitating mass associated to these structures. We use the shear signal extracted by an analysis of deep exposures of a region centered around the galaxy cluster Abell 209, at redshift z=0.2, to derive both a map of the projected mass distribution and an estimate of the total mass within a characteristic radius. We use a series of deep archival R-band images from CFHT-12k, covering an area of 0.3 deg^2. We determine the shear of background galaxy images using a new implementation of the modified Kaiser-Squires-Broadhurst pipeline for shear determination, which we has been tested against the ``Shear TEsting Program 1 and 2 simulations. We use mass aperture statistics to produce maps of the 2 dimensional density distribution, and parametric fits using both Navarro-Frenk-White (NFW) and singular-isothermal-sphere profiles to constrain the total mass. The projected mass distribution shows a pronounced asymmetry, with an elongated structure extending from the SE to the NW. This is in general agreement with the optical distribution previously found by other authors. A similar elongation was previously detected in the X-ray emission map, and in the distribution of galaxy colours. The circular NFW mass profile fit gives a total mass of M_{200} = 7.7^{+4.3}_{-2.7} 10^{14} solar masses inside the virial radius r_{200} = 1.8pm 0.3 Mpc. The weak lensing profile reinforces the evidence for an elongated structure of Abell 209, as previously suggested by studies of the galaxy distribution and velocities.
In Schneider, King & Erben (2000) we developed likelihood techniques to compare the constraints on cluster mass profiles that can be obtained using the shear and magnification information. This work considered circularly symmetric power-law models for clusters at fairly low redshifts where the redshift distribution of source galaxies could be neglected. Here this treatment is extended to encompass NFW profiles which are a good description of clusters from cosmological N-body simulations, and NFW clusters at higher redshifts where the influence of various scenarios for the knowledge of the redshift distribution are examined. Since in reality the overwhelming majority of clusters have ellipsoidal rather than spherical profiles, the singular isothermal ellipsoid (SIE) is investigated. We also briefly consider the impact of substructure on such a likelihood analysis. In general, we find that the shear information provides a better constraint on the NFW profile under consideration, so this becomes the focus of what follows. The ability to differentiate between the NFW and power-law profiles strongly depends on the size of the data field, and on the number density of galaxies for which an ellipticity can be measured. For higher redshift NFW profiles, there is very little reduction (~1.5%) in the dispersion of parameter estimates when spectroscopic redshifts, as opposed to photometric redshift estimates, are available for the galaxies used in the lensing analysis.
Weak gravitational lensing is considered to be one of the most powerful tools to study the mass and the mass distribution of galaxy clusters. However, the mass-sheet degeneracy transformation has limited its success. We present a novel method for a cluster mass reconstruction which combines weak and strong lensing information on common scales and can, as a consequence, break the mass-sheet degeneracy. We extend the weak lensing formalism to the inner parts of the cluster and combine it with the constraints from multiple image systems. We demonstrate the feasibility of the method with simulations, finding an excellent agreement between the input and reconstructed mass also on scales within and beyond the Einstein radius. Using a single multiple image system and photometric redshift information of the background sources used for weak and strong lensing analysis, we find that we are effectively able to break the mass-sheet degeneracy, therefore removing one of the main limitations on cluster mass estimates. We conclude that with high resolution (e.g. HST) imaging data the method can more accurately reconstruct cluster masses and their profiles than currently existing lensing techniques.
Merging clusters of galaxies are unique in their power to directly probe and place limits on the self-interaction cross-section of dark matter. Detailed observations of several merging clusters have shown the intracluster gas to be displaced from the centroids of dark matter and galaxy density by ram pressure, while the latter components are spatially coincident, consistent with collisionless dark matter. This has been used to place upper limits on the dark matter particle self-inteaction cross-section of order 1 cm^2/g. The cluster Abell 520 has been seen as a possible exception. We revisit A520 presenting new HST ACS mosaic images and a Magellan image set. We perform a detailed weak lensing analysis and show that the weak lensing mass measurements and morphologies of the core galaxy-filled structures are mostly in good agreement with previous works. There is however one significant difference -- we do not detect the previously claimed dark core that contains excess mass with no significant galaxy overdensity at the location of the X-ray plasma. This peak has been suggested to be indicative of a large self-interaction cross-section for dark matter (at least ~5 sigma larger than the upper limit of 0.7 cm^2/g determined by observations of the Bullet Cluster). We find no such indication and instead find that the mass distribution of A520, after subtraction of the X-ray plasma mass, is in good agreement with the luminosity distribution of the cluster galaxies. We conclude that A520 shows no evidence to contradict the collisionless dark matter scenario.
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