[Paper Review] Gravitational `Convergence' and Cluster Masses

Tom Broadhurst|arXiv (Cornell University)|Dec 1, 1995

Cosmology and Gravitation Theories3 citations

TL;DR

This paper introduces a method to measure gravitational convergence and cluster masses using colour-dependent magnification biases in lensed galaxies. By exploiting the redshift-dependent colour distribution of background galaxies, it isolates convergence from weak lensing data, enabling model-independent mass estimates without requiring high spatial resolution.

ABSTRACT

Two colour photometry of the cluster A1689 reveals a `relative magnification-bias' between lensed blue and red background galaxies, arising from a dependence of the faint galaxy count-slope on colour. The colour distribution is skewed blueward of the far field, allowing us to measure the cluster magnification and to understand the notorious blueness of large arcs. We show that the magnification information can be combined with the usual image distortion measurements to isolate the local `convergence' component of lensing and hence derive the projected mass. This is achieved through a simple local relation between the convergence and the observables, which can be applied generally over the surface a cluster. In the weak lensing limit, the convergence reduces to a dependence on the magnification alone, so that in the outskirts of clusters the surface-density of matter is obtained directly from the surface-density of background galaxies. Hence, useful lensing work requires colour information but not necessarily good seeing. Interestingly, convergence varies slowly at high redshift, saturating at a level depending on the Horizon distance, allowing a useful model-independent measurement of the Global Geometry.

Motivation & Objective

• To address the challenge of measuring gravitational convergence in galaxy clusters using weak lensing data.
• To overcome the limitation of traditional lensing methods that require high-resolution imaging and complex modeling.
• To develop a method that uses colour information to isolate convergence from magnification effects.
• To enable direct measurement of surface mass density in cluster outskirts using only galaxy counts and colours.
• To provide a model-independent probe of global geometry through convergence at high redshift.

Proposed method

• Uses two-colour photometry of background galaxies in cluster A1689 to detect a colour-dependent magnification bias.
• Identifies a blueward skew in the colour distribution of faint background galaxies, indicating magnification bias.
• Derives a local relation between convergence and observable magnification and colour, valid across cluster surfaces.
• Applies this relation in the weak lensing limit, where convergence depends only on magnification, simplifying mass reconstruction.
• Combines convergence measurements with standard image distortion data to isolate the projected mass distribution.
• Demonstrates that colour information alone can yield surface mass density without requiring good seeing conditions.

Experimental results

Research questions

• RQ1 Can convergence be measured independently of shear in weak gravitational lensing using colour information?
• RQ2 How does the magnification bias of background galaxies depend on their colour and redshift?
• RQ3 Can surface mass density be derived directly from galaxy counts and colours without high-resolution imaging?
• RQ4 What is the behavior of convergence at high redshift, and can it provide constraints on global geometry?
• RQ5 How does the relative magnification bias between blue and red galaxies affect arc formation and cluster mass estimates?

Key findings

• A relative magnification bias between blue and red background galaxies is detected due to the colour dependence of the faint galaxy count slope.
• The colour distribution of background galaxies is skewed blueward in the far field, enabling measurement of magnification and convergence.
• Convergence can be isolated using a simple local relation between convergence and observables (magnification and colour), valid across cluster surfaces.
• In the weak lensing regime, convergence reduces to a function of magnification alone, allowing direct measurement of surface mass density from galaxy counts.
• Convergence varies slowly at high redshift and saturates at a level dependent on the horizon distance, offering a model-independent probe of global geometry.
• The method enables accurate cluster mass measurements without requiring high spatial resolution, relying only on colour information and galaxy counts.