A Bayesian approach to strong lensing modelling of galaxy clusters

By E. Jullo, Jean-Paul Kneib, M. Limousin, 'Ard'is El'iasd'ottir, P. J. Marshall, Tomás Verdugo. 2007

466 citations recorded by the source corpus.

In this paper, we describe a procedure for modelling strong lensing galaxy clusters with parametric methods, and to rank models quantitatively using the Bayesian evidence. We use a publicly available Markov chain Monte-Carlo (MCMC) sampler (‘bayesys’), allowing us to avoid local minima in the likelihood functions. To illustrate the power of the MCMC technique, we simulate three clusters of galaxies, each composed of a cluster-scale halo and a set of perturbing galaxy-scale subhalos. We ray-trace three light beams through each model to produce a catalogue of multiple images, and then use the MCMC sampler to recover the model parameters in the three different lensing configurations. We find that, for typical Hubble Space Telescope (HST)-quality imaging data, the total mass in the Einstein radius is recovered with ∼1–5% error according to the considered lensing configuration. However, we find that the mass of the galaxies is strongly degenerated with the cluster mass when no multiple images appear in the cluster centre. The mass of the galaxies is generally recovered with a 20% error, largely due to the poorly constrained cut-off radius. Finally, we describe how to rank models quantitatively using the Bayesian evidence. We confirm the ability of strong lensing to constrain the mass profile in the central region of galaxy clusters in this way. Ultimately, such a method applied to strong lensing clusters with a very large number of multiple images may provide unique geometrical constraints on cosmology. The implementation of the MCMC sampler used in this paper has been done within the framework of the lenstool software package, which is publicly availablewww.oamp.fr/cosmology/lenstool..

Subfields: Astronomy and Astrophysics, Computer Vision and Pattern Recognition, Ecology

View Paper: https://www.semanticscholar.org/paper/faed0b68861a358f5c31657706eb2e486a5f5be9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. Richard S. Ellis
2. L. Hernquist
3. R. Bouwens
4. P. Hopkins
5. J. Dunlop
6. P. Oesch
7. G. Illingworth
8. D. Stark

In Computer Vision and Pattern Recognition

1. M. Oguri
2. J. Richard
3. Jean-Paul Kneib
4. E. Jullo
5. A. Leonard
6. A. van der Wel
7. L. Bradley
8. Richard S. Ellis

In Ecology

1. M. Oguri
2. J. Richard
3. E. Jullo
4. Jean-Paul Kneib
5. Julia Gutkin
6. T. Treu
7. Richard S. Ellis
8. T. Broadhurst

Citations in the corpus

• LoCuSS: first results from strong-lensing analysis of 20 massive galaxy clusters at z= 0.2 (2009, methodology): “The models are fitted to the multiple-image constraints using the new Bayesian Markov chain Monte-Carlo (hereafter MCMC) sampler, described in detail in Jullo et al. (2007).”
• Ultraviolet emission lines in young low-mass galaxies at z ≃ 2: physical properties and implications for studies at z > 7 (2014, methodology): “The magnification factors and associated uncertainties are computed up-to-date cluster mass models using the LENSTOOL program (Kneib 1993, Jullo et al. 2007).”
• The Mass Distribution of SDSS J1004$+$4112 Revisited (2010, methodology): “Critical curves are computed using a marching squares technique (Jullo et al. 2007).”
• Mass and magnification maps for the Hubble Space Telescope Frontier Fields clusters: implications for high-redshift studies (2014, methodology): “Our collaboration uses LENSTOOL2 (Jullo et al. 2007), an algorithm we developed collectively over the years.”
• A Comprehensive Study of Galaxies at z ∼ 9–16 Found in the Early JWST Data: Ultraviolet Luminosity Functions and Cosmic Star Formation History at the Pre-reionization Epoch (2022, methodology): “The RELICS survey (Coe et al. 2019) team provides the mass models13 developed with the LENSTOOL (Jullo et al. 2007; Fox et al. 2022) and GLAFIC (Oguri 2010) codes, both of which are constructed using HST data.”
• Multiscale cluster lens mass mapping - I. Strong lensing modelling (2009, methodology): “In addition, Kneib et al. (1996) have shown that the complementary modelling of galaxy-scale halos hosting bright cluster member galaxies significantly improves the fit (see Jullo et al. 2007, for a throughout description of the analytical modelling of clusters).”
• Masses of Galaxy Clusters from Gravitational Lensing (2013, methodology): “Combining information from both regimes is relatively straightforward when considering parametric methods, such as the one developed by Jullo et al. (2007), which as used by Limousin et al. (2010) to study the massive z = 0.545 cluster MACS J1423.”
• CLASH: THE ENHANCED LENSING EFFICIENCY OF THE HIGHLY ELONGATED MERGING CLUSTER MACS J0416.1−2403 (2012, methodology): “0 are its PIEMD parameters (Jullo et al. 2007).”
• LENS MODELS AND MAGNIFICATION MAPS OF THE SIX HUBBLE FRONTIER FIELDS CLUSTERS (2014, methodology): “′′3 (following Jullo et al. 2007; Limousin et al. 2007).14 Moreover, identifying features by eye works better than automated measurement in scenarios where im- 14 We also ran an identical set of models using a positional error ages are close to the critical curves and the magnification gradient…”
• CLASH: THREE STRONGLY LENSED IMAGES OF A CANDIDATE z ≈ 11 GALAXY (2012, methodology): “We assumed core radii rcore = 300 pc and luminosity scaling relations as in Jullo et al. (2007): velocity dispersion σ0 ∝ L1/4 and cutoff radius rcut ∝ L1/2, resulting in all galaxies having equal mass-to-light ratios.”
• The Frontier Fields lens modelling comparison project (2016, methodology): “The model is optimized with the Bayesian Markov chain Monte-Carlo sampler, described in detail in Jullo et al. (2007).”
• ARE ULTRA-FAINT GALAXIES AT z = 6–8 RESPONSIBLE FOR COSMIC REIONIZATION? COMBINED CONSTRAINTS FROM THE HUBBLE FRONTIER FIELDS CLUSTERS AND PARALLELS (2015, methodology): “The CATS HFF mass models are built using the Lenstool16 software (Kneib 1993; Jullo et al. 2007; Jullo & Kneib 2009).”
• The extreme faint end of the UV luminosity function at z ∼ 6 through gravitational telescopes: a comprehensive assessment of strong lensing uncertainties (2018, methodology): “…lensing models constructed by the CATS team (clusters as telescopes) using version 7.0 of the Lenstool2 2 http://projets.lam.fr/projects/lenstool/wiki software, which follows a parametric approach to map the mass distribution in the cluster (Kneib 1993; Jullo et al. 2007; Jullo & Kneib 2009).”
• Resolved spectroscopy of gravitationally lensed galaxies: recovering coherent velocity fields in subluminous z ~ 2-3 galaxies (2009, methodology): “We will follow the methodology defined by earlier relevant articles (Kneib et al. 1993, 1996; Smith et al. 2005; Jullo et al. 2007) within which further details can be found.”
• The behaviour of dark matter associated with four bright cluster galaxies in the 10 kpc core of Abell 3827 (2015, methodology): “To model the strong gravitational lens system, we use two independent software packages: GRALE (Liesenborgs, De Rijcke & Dejonghe 2006) and LENSTOOL (Jullo et al. 2007).”
• Weighing simulated galaxy clusters using lensing and X-ray (2009, methodology): “We refer the reader to the paper by Jullo et al. (2007) for a more detailed description of the many options available in this software.”
• THE DENSITY PROFILES OF MASSIVE, RELAXED GALAXY CLUSTERS. I. THE TOTAL DENSITY OVER THREE DECADES IN RADIUS (2012, methodology): “Inferring mass models from data Our analysis is based on the Lenstool code (Kneib et al. 1993; Jullo et al. 2007), which has been widely used for studying strong lenses.”