Galaxy mass profiles from strong lensing I: The circular power-law model

Abstract

In this series of papers we develop a formalism for constraining mass profiles in strong gravitational lenses with extended images, using fluxes in addition to positional information. We start in this paper with a circular power-law profile and show that the slope $\gamma$ is uniquely determined by only two observables: the flux ratio $f_1/f_2$ and the image position ratio ${\theta }_1/{\theta }_2$ of the two images. We derive an analytic expression relating these two observables to the slope, a result which does not depend on the Einstein angle or the structure or brightness of the source. We then find an expression for the uncertainty on the slope ${\sigma }_{\gamma }$ that depends only on the position ratio ${\theta }_1/{\theta }_2$ and the total S/N in the images. For example, in a system with position ratio ${\theta }_1/{\theta }_2=0.5$, S/N $=100$ and $\gamma =2$ we find that $\gamma$ is constrained to a precision of $\pm 0.03$. We then test these results against a series of mock observations. We invert the images and fit an 11 parameter model, including ellipticity and position angle for both lens and source and measure the uncertainty on $\gamma$. We find agreement with the theoretical estimate for all mock observations. In future papers we will examine the radial range of the galaxy over which the constraint on the slope applies, and extend the analysis to elliptical lenses.

arXiv comment12 pages, 5 figures. Accepted for publication in MNRAS

References in corpus (48)

• emcee: The MCMC Hammer
• The Sloan Lens ACS Survey. III - The Structure and Formation of Early-type Galaxies and their Evolution since z~1
• Strong Lensing by Galaxies
• The Sloan Lens ACS Survey. V. The Full ACS Strong-Lens Sample
• Dissecting the Gravitational Lens B1608+656. II. Precision Measurements of the Hubble Constant, Spatial Curvature, and the Dark Energy Equation of State
• The initial mass function of early-type galaxies
• The Structure & Dynamics of Massive Early-type Galaxies: On Homology, Isothermality and Isotropy inside one Effective Radius
• Baryon effects on the internal structure of LCDM halos in the EAGLE simulations
• H0LiCOW - IX. Cosmographic analysis of the doubly imaged quasar SDSS 1206+4332 and a new measurement of the Hubble constant
• H0LiCOW I. $H_0$ Lenses in COSMOGRAIL's Wellspring: Program Overview
• Detection of lensing substructure using ALMA observations of the dusty galaxy SDP.81
• Galaxy Masses
• The internal structure and formation of early-type galaxies: the gravitational--lens system MG2016+112 at z=1.004
• Two-dimensional kinematics of SLACS lenses: III. Mass structure and dynamics of early-type lens galaxies beyond z ~ 0.1
• The Structure and Dynamics of Luminous and Dark Matter in the Early-Type Lens Galaxy of 0047-281 at z=0.485
• Dark Matter Contraction and the Stellar Content of Massive Early-type Galaxies: Disfavoring "Light" Initial Mass Functions
• H0LiCOW IV. Lens mass model of HE 0435-1223 and blind measurement of its time-delay distance for cosmology
• Source-position transformation -- an approximate invariance in strong gravitational lensing
• Detection of substructure with adaptive optics integral field spectroscopy of the gravitational lens B1422+231
• AutoLens: Automated Modeling of a Strong Lens's Light, Mass and Source
• Two-dimensional kinematics of SLACS lenses: II. Combined lensing and dynamics analysis of early-type galaxies at z = 0.08 - 0.33
• H0LiCOW III. Quantifying the effect of mass along the line of sight to the gravitational lens HE 0435-1223 through weighted galaxy counts
• Decomposition of the visible and dark matter in the Einstein ring 0047-2808 by semi-linear inversion
• Constraints on Galaxy Density Profiles from Strong Gravitational Lensing: The Case of B 1933+503
• Constraints on the Inner Mass Profiles of Lensing Galaxies from Missing Odd Images
• The BOSS Emission-Line Lens Survey. IV. : Smooth Lens Models for the BELLS GALLERY Sample
• The X-Shooter Lens Survey - I. Dark-Matter Domination and a Salpeter-type IMF in a Massive Early-type Galaxy
• Gravitational lens time delays for distant supernovae: break the degeneracy between radial mass profiles and the Hubble constant
• Models of the Cosmic Horseshoe Gravitational Lens
• Quantifying Environmental and Line-of-Sight Effects in Models of Strong Gravitational Lens Systems
• Lens galaxies in the Illustris simulation: power-law models and the bias of the Hubble constant from time-delays
• The elliptical power law profile lens
• Models for the lens and source of B0218+357 - A LensClean approach to determine H0
• A multipole-Taylor expansion for the potential of gravitational lens MG J0414+0534
• Survey of Gravitationally-lensed Objects in HSC Imaging (SuGOHI). II. Environments and Line-of-Sight Structure of Strong Gravitational Lens Galaxies to z ~ 0.8
• High resolution observations and mass modelling of the CLASS gravitational lens B1152+199
• H0LiCOW II. Spectroscopic survey and galaxy-group identification of the strong gravitational lens system HE0435-1223
• A Unifying Framework for Self-consistent Gravitational Lensing and Stellar Dynamics Analyses of Early-Type Galaxies
• Cosmography from two-image lens systems: overcoming the lens profile slope degeneracy
• SHARP - V. Modelling gravitationally-lensed radio arcs imaged with global VLBI observations
• On the Choice of Lens Density Profile in Time Delay Cosmography
• Early-type galaxy density profiles from IllustrisTNG: I. Galaxy correlations and the impact of baryons
• Generalised model-independent characterisation of strong gravitational lenses IV: formalism-intrinsic degeneracies
• Galaxy density profiles and shapes -- I. simulation pipeline for lensing by realistic galaxy models
• Modelling mass distribution in elliptical galaxies: mass profiles and their correlation with velocity dispersion profiles
• SEAGLE - I: A pipeline for simulating and modeling strong lenses from cosmological hydrodynamic simulations
• The SWELLS Survey. VI. hierarchical inference of the initial mass functions of bulges and discs
• Zooming into the Cosmic Horseshoe: new insights on the lens profile and the source shape

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• GIGA-Lens: Fast Bayesian Inference for Strong Gravitational Lens Modeling
• Testing strong lensing subhalo detection with a cosmological simulation
• Statistical strong lensing. III. Inferences with complete samples of lenses
• Euclid: A complete Einstein ring in NGC 6505
• The dynamical structure of broken power-law and double power-law models for dark matter haloes
• Galaxy mass profiles from strong lensing II: The elliptical power-law model
• Galaxy mass profiles from strong lensing III: The two-dimensional broken power-law model
• Detecting the hidden population of low-mass haloes in strong lenses