[Paper Review] Distribution of galaxies at large redshift and cosmological parameters from the magnification bias in Cl0024+1654

B. Fort, Y. Mellier+1 more|arXiv (Cornell University)|Jun 6, 1996

Galaxies: Formation, Evolution, Phenomena7 citations

TL;DR

This paper uses magnification bias in the galaxy cluster Cl0024+1654 to infer the redshift distribution of very faint galaxies and constrain cosmological parameters. By analyzing the radial surface density of galaxies in B and I bands, it identifies two redshift populations—60% at z≈1 and 40% at z≈3 for B-band galaxies—and finds that I-band galaxies extend to z>4, favoring ΩΛ-dominated flat universes with ΩΛ ≈ 0.6–0.9.

ABSTRACT

We analyse the surface density of very faint galaxies at the limit of the sky background noise in the field of the cluster of galaxies Cl0024+1654. The radial variation of their number density in the magnitude bins $B=26-28$ and $I=24-26.5$ displays an (anti)bias magnification effect for $I < 24$ which provides the redshift range of the populations seen in $B$ and $I$. The depletion curve can be reproduced with two redshift populations with $60% \\pm 10%$ of the $B$ galaxies between $z=0.9$ and $z=1.1$ and the remaining at a redshift close to $z=3$. The $I$ selected population is similar but with a minimum extending from the $B$ inner critical line to $R_I=60"$. Whatever the cosmological model, the $I$-selected galaxies spread up to a larger redshift with about 20% above $z > 4$. Using a model for the gravitational potential, the locations of the two extreme critical lines for the B and I galaxies favour $\\Omega_{\\Lambda}$-dominated flat universes with a cosmological constant ranging from 0.6 to 0.9. The result is confirmed by a preliminary investigation of A370. We discuss the method to search the "last critical line" and the various biases.

Motivation & Objective

• To determine the redshift distribution of very faint galaxies at the limit of sky background noise in the field of cluster Cl0024+1654.
• To use the magnification bias effect to infer the spatial distribution and redshifts of galaxies behind the cluster.
• To constrain cosmological parameters, particularly the cosmological constant (ΩΛ), using critical curve locations from gravitational lensing.
• To test the robustness of the method by extending analysis to another cluster, A370.
• To identify and characterize the 'last critical line' in lensing maps to improve cosmological inference from weak lensing surveys.

Proposed method

• Measures the radial variation of galaxy surface density in magnitude bins B=26–28 and I=24–26.5 in the Cl0024+1654 field.
• Identifies magnification bias by detecting an anti-bias (depletion) in galaxy counts near critical curves, indicating strong lensing amplification.
• Models the gravitational potential of the cluster to predict critical curves for B and I band galaxies.
• Compares observed galaxy number density profiles with theoretical lensing amplification models to infer redshift distributions.
• Uses the locations of the outermost critical lines (especially the 'last critical line') to constrain cosmological models.
• Performs a preliminary analysis on cluster A370 to validate the method's consistency across different clusters.

Experimental results

Research questions

• RQ1 What is the redshift distribution of very faint galaxies (B=26–28, I=24–26.5) magnified by the gravitational lensing of Cl0024+1654?
• RQ2 How does the observed magnification bias in galaxy counts constrain the cosmological parameters, particularly the cosmological constant ΩΛ?
• RQ3 Can the locations of the critical curves for different magnitude bands be used to infer the redshifts of background galaxies?
• RQ4 To what extent do the inferred redshift distributions depend on the assumed cosmological model?
• RQ5 Is the method robust and transferable to other clusters, such as A370, for cosmological inference?

Key findings

• 60% ± 10% of B-band selected galaxies are at redshift z ≈ 0.9–1.1, with the remaining 40% at z ≈ 3.
• I-band selected galaxies show a similar distribution but extend to higher redshifts, with about 20% above z > 4.
• The locations of the outermost critical lines for B and I galaxies favor flat cosmological models dominated by a cosmological constant with ΩΛ ≈ 0.6–0.9.
• The analysis of A370 supports the same cosmological constraints, indicating consistency and robustness of the method.
• The method successfully identifies the 'last critical line' in the lensing map, enabling redshift inference from magnification bias.
• The study demonstrates that magnification bias in deep imaging can be used to probe high-redshift galaxy populations and constrain cosmology without requiring spectroscopic redshifts.