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Register a new userAnalysis of luminosity distributions and shape parameters of strong gravitational lensing elliptical galaxies
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Luminosity profiles of galaxies acting as strong gravitational lenses can be tricky to study. Indeed, strong gravitational lensing images display several lensed components, both point-like and diffuse, around the lensing galaxy. Those objects limit the study of the galaxy luminosity to its inner parts. Therefore, the usual fitting methods perform rather badly on such images. Previous studies of strong lenses luminosity profiles using software such as GALFIT or IMFITFITS and various PSF-determining methods have resulted in discrepant results. The present work aims at investigating the causes of those discrepancies, as well as at designing more robust techniques for studying the morphology of early-type lensing galaxies with the ability to subtract a lensed signal from their luminosity profiles. We design a new method to independently measure each shape parameter, namely, the position angle, ellipticity, and half-light radius of the galaxy. Our half-light radius measurement method is based on an innovative scheme for computing isophotes that is well suited to measuring the morphological properties of gravitational lensing galaxies. Its robustness regarding various specific aspects of gravitational lensing image processing is analysed and tested against GALFIT. It is applied to a sample of systems from the CASTLES database. Simulations show that when restricted to small, inner parts of the lensing galaxy, the technique presented here is more trustworthy than GALFIT. It gives more robust results than GALFIT, which shows instabilities regarding the fitting region, the value of the Sersic index, and the signal-to-noise ratio. It is therefore better suited than GALFIT for gravitational lensing galaxies. It is also able to study lensing galaxies that are not much larger than the PSF. New values for the half-light radius of the objects in our sample are presented and compared to previous works.
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We show how the combination of observations related to strong gravitational lensing and stellar dynamics in ellipticals offers a new way to measure the cosmological matter and dark-energy density parameters. A gravitational lensing estimate of the mass enclosed inside the Einstein circle can be obtained by measuring the Einstein angle, once the critical density of the system is known. A model-dependent dynamical estimate of this mass can also be obtained by measuring the central velocity dispersion of the stellar component. By assuming the well-tested homologous 1/r^{2} profile for the total density distribution in the lens elliptical galaxies, these two mass measurements can be properly compared. Thus, a relation between the Einstein angle and the central stellar velocity dispersion is derived, and the cosmological matter and the dark-energy density parameters can be estimated from this. We determined the accuracy of the cosmological parameter estimates by means of simulations that include realistic measurement uncertainties on the relevant quantities. Interestingly, the expected constraints on the cosmological parameter plane are complementary to those coming from other observational techniques. Then, we applied the method to the data sets of the Sloan Lens ACS and the Lenses Structure and Dynamics Surveys, and showed that the concordance value between 0.7 and 0.8 for the dark-energy density parameter is included in our 99% confidence regions. The small number of lenses available to date prevents us from precisely determining the cosmological parameters, but it still proves the feasibility of the method. When applied to samples made of hundreds of lenses that are expected to become available from forthcoming surveys, this technique will be an important tool for measuring the geometry of the Universe.
We investigate how strong gravitational lensing can test contemporary models of massive elliptical (ME) galaxy formation, by combining a traditional decomposition of their visible stellar distribution with a lensing analysis of their mass distribution. As a proof of concept, we study a sample of three ME lenses, observing that all are composed of two distinct baryonic structures, a `red central bulge surrounded by an extended envelope of stellar material. Whilst these two components look photometrically similar, their distinct lensing effects permit a clean decomposition of their mass structure. This allows us to infer two key pieces of information about each lens galaxy: (i) the stellar mass distribution (without invoking stellar populations models) and (ii) the inner dark matter halo mass. We argue that these two measurements are crucial to testing models of ME formation, as the stellar mass profile provides a diagnostic of baryonic accretion and feedback whilst the dark matter mass places each galaxy in the context of LCDM large scale structure formation. We also detect large rotational offsets between the two stellar components and a lopsidedness in their outer mass distributions, which hold further information on the evolution of each ME. Finally, we discuss how this approach can be extended to galaxies of all Hubble types and what implication our results have for studies of strong gravitational lensing.
We discuss constraints on the mass density distribution (parameterized as $rhopropto r^{-gamma}$) in early-type galaxies provided by strong lensing and stellar kinematics data. The constraints come from mass measurements at two `pinch radii. One `pinch radius $r_1=2.2 R_{Einst}$ is defined such that the Einstein (i.e. aperture) mass can be converted to the spherical mass almost independently of the mass-model. Another `pinch radius $r_2=R_{opt}$ is chosen so that the dynamical mass, derived from the line-of-sight velocity dispersion, is least sensitive to the anisotropy of stellar orbits. We verified the performance of this approach on a sample of simulated elliptical galaxies and on a sample of 15 SLACS lens galaxies at $0.01 leq z leq 0.35$, which have already been analysed in Barnabe et al. (2011) by the self-consistent joint lensing and kinematic code. For massive simulated galaxies the density slope $gamma$ is recovered with an accuracy of $sim 13%$, unless $r_1$ and $r_2$ happen to be close to each other. For SLACS galaxies, we found good overall agreement with the results of Barnabe et al. (2011) with a sample-averaged slope $gamma=2.1pm0.05$. While the two-pinch-radii approach has larger statistical uncertainties, it is much simpler and uses only few arithmetic operations with directly observable quantities.
The combination of strong gravitational lensing and stellar kinematics provides a powerful and robust method to investigate the mass and dynamical structure of early-type galaxies. We demonstrate this approach by analysing two massive ellipticals from the XLENS Survey for which both high-resolution HST imaging and X-Shooter spectroscopic observations are available. We adopt a flexible axisymmetric two-component mass model for the lens galaxies, consisting of a generalised NFW dark halo and a realistic self-gravitating stellar mass distribution. For both systems, we put constraints on the dark halo inner structure and flattening, and we find that they are dominated by the luminous component within one effective radius. By comparing the tight inferences on the stellar mass from the combined lensing and dynamics analysis with the values obtained from stellar population studies, we conclude that both galaxies are characterised by a Salpeter-like stellar initial mass function.
Strong gravitational lensing along with the distance sum rule method can constrain both cosmological parameters as well as density profiles of galaxies without assuming any fiducial cosmological model. To constrain galaxy parameters and cosmic curvature $(Omega_{k0})$, we use the distance ratio data from a recently compiled database of $161$ galactic scale strong lensing systems. We use databases of supernovae type-Ia (Pantheon) and Gamma Ray Bursts (GRBs) for calculating the luminosity distance. To study the model of the lens galaxy, we consider a general lens model namely, the Extended Power-Law model. Further, we take into account two different parametrisations of the mass density power-law index $(gamma)$ to study the dependence of $gamma$ on redshift. The best value of $Omega_{k0}$ suggests a closed universe, though a flat universe is accommodated at $68%$ confidence level. We find that parametrisations of $gamma$ have a negligible impact on the best fit value of the cosmic curvature parameter. Furthermore, measurement of time delay can be a promising cosmographic probe via time delay distance that includes the ratio of distances between the observer, the lens and the source. We again use the distance sum rule method with time-delay distance dataset of H0LiCOW to put constraints on the Cosmic Distance Duality Relation (CDDR) and the cosmic curvature parameter $(Omega_{k0})$. For this we consider two different redshift-dependent parametrisations of the distance duality parameter $(eta)$. The best fit value of $Omega_{k0}$ clearly indicates an open universe. However, a flat universe can be accommodated at $95%$ confidence level. Further, at $95%$ confidence level, no violation of CDDR is observed. We believe that a larger sample of strong gravitational lensing systems is needed in order to improve the constraints on the cosmic curvature and distance duality parameter.
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