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Register a new userCluster mass estimation from lens magnification
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Authors
Eelco van Kampen
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The mass of a cluster of galaxies can be estimated from its lens magnification, which can be determined from the variation in number counts of background galaxies. In order to derive the mass one needs to make assumptions for the lens shear, which is unknown from the variation in number counts alone. Furthermore, one needs to go beyond the weak lensing (linear) approximation as most of the observational data is concentrated in the central parts of clusters, where the lensing is strong. By studying the lensing properties of a complete catalogue of galaxy cluster models, one can find reasonable approximations about the lens shear as a function of the lens convergence. We show that using these approximations one can fairly well reconstruct the surface mass distribution from the magnification alone.
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The surface mass density of a cluster of galaxies, and thus its total mass, can be estimated from its lens magnification. The magnification can be determined from the variation in number counts of its background galaxies. In the weak lensing approximation the surface mass density is a linear function of the magnification. However, most observational data is concentrated in the central parts of clusters, so one needs to go beyond the weak lensing approximation, and consider the lens shear as well, which is unknown from the variation in number counts alone. We studied the lensing properties of a catalogue of numerical cluster models in order to find the best possible approximation for the shear which still allows straightforward determination of the surface mass density. We show that by using such an approximation one can fairly well reconstruct the surface mass distribution from the magnification alone. It is demonstrated that the mass estimated using the weak lens magnification approximation is usually at least twice the true mass. We illustrate our technique on existing data, and show that the resulting masses compare well to other estimates.
We present the first application of lens magnification to measure the absolute mass of a galaxy cluster; Abell 1689. The absolute mass of a galaxy cluster can be measured by the gravitational lens magnification of a background galaxy population by the cluster potential. The lensing signal is complicated by the variation in number counts due to galaxy clustering and shot-noise, and by additional uncertainties in relating magnification to mass in the strong lensing regime. Clustering and shot-noise can be dealt with using maximum likelihood methods. Local approximations can then be used to estimate the mass from magnification. Alternatively if the lens is axially symmetric we show that the amplification equation can be solved nonlocally for the surface mass density and the tangential shear. In this paper we present the first maps of the total mass distribution in Abell 1689, measured from the deficit of lensed red galaxies behind the cluster. Although noisier, these reproduce the main features of mass maps made using the shear distortion of background galaxies but have the correct normalisation, finally breaking the ``sheet-mass degeneracy that has plagued lensing methods based on shear. We derive the cluster mass profile in the inner 4 (0.48 Mpc/h). These show a profile with a near isothermal surface mass density kappa = (0.5+/-0.1)(theta/1)^{-1} out to a radius of 2.4 (0.28Mpc/h), followed by a sudden drop into noise. We find that the projected mass interior to 0.24 h^{-1}$Mpc is M(<0.24 Mpc/h)=(0.50+/- 0.09) times 10^{15} Msol/h. We compare our results with masses estimated from X-ray temperatures and line-of-sight velocity dispersions, as well as weak shear and lensing arclets and find all are in fair agreement for Abell 1698.
Gravitational lensing magnification is measured with a significance of 9.7 sigma on a large sample of galaxy clusters in the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). This survey covers ~154 deg^2 and contains over 18,000 cluster candidates at redshifts 0.2 <= z <= 0.9, detected using the 3D-Matched Filter cluster-finder of Milkeraitis et al. (2010). We fit composite-NFW models to the ensemble, accounting for cluster miscentering, source-lens redshift overlap, as well as nearby structure (the 2-halo term), and recover mass estimates of the cluster dark matter halos in range of ~10^13 M_sun to 2*10^14 M_sun. Cluster richness is measured for the entire sample, and we bin the clusters according to both richness and redshift. A mass-richness relation M_200 = M_0 (N_200 / 20)^beta is fit to the measurements. For two different cluster miscentering models we find consistent results for the normalization and slope, M_0 = (2.3 +/- 0.2)*10^13 M_sun, beta = 1.4 +/- 0.1 and M_0 = (2.2 +/- 0.2)*10^13 M_sun, beta = 1.5 +/- 0.1. We find that accounting for the full redshift distribution of lenses and sources is important, since any overlap can have an impact on mass estimates inferred from flux magnification.
Using the power of gravitational lensing magnification by massive galaxy clusters, the Hubble Frontier Fields provide deep views of six patches of the high redshift Universe. The combination of deep Hubble imaging and exceptional lensing strength has revealed the greatest numbers of multiply-imaged galaxies available to constrain models of cluster mass distributions. However, even with $mathcal{O}(100)$ images per cluster, the uncertainties associated with the reconstructions are not negligible. The goal of this paper is to show the diversity of model magnification predictions. We examine 7 and 9 mass models of Abell 2744 and MACS J0416, respectively, submitted to the Mikulski Archive for Space Telescopes for public distribution in September 2015. The dispersion between model predictions increases from 30% at common low magnifications ($musim2$) to 70% at rare high magnifications ($musim40$). MACS J0416 exhibits smaller dispersions than Abell 2744 for $2<mu<10$. We show that magnification maps based on different lens inversion techniques typically differ from each other by more than their quoted statistical errors. This suggests that some models underestimate the true uncertainties, which are primarily due to various lensing degeneracies. Though the exact mass sheet degeneracy is broken, its generalized counterpart is not broken at least in Abell 2744. Other, local degeneracies are also present in both clusters. Our comparison of models is complementary to the comparison of reconstructions of known synthetic mass distributions. By focusing on observed clusters, we can identify those that are best constrained, and therefore provide the clearest view of the distant Universe.
In the context of strong gravitational lensing, the magnification of image is of crucial importance to constrain various lens models. For several commonly used quadruple lens models, the magnification invariants, defined as the sum of the signed magnifications of images, have been analytically derived when the image multiplicity is a maximum. In this paper, we further study the magnification of several disk lens models, including (a) exponential disk lens, (b) Gaussian disk lens, (c) modified Hubble profile lens, and another two of the popular three-dimensional symmetrical lens model, (d) NFW lens and (e) Einasto lens. We find that magnification invariant does also exist for each lens model. Moreover, our results show that magnification invariants can be significantly changed by the characteristic surface mass density $kappa_{rm c}$.
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