Strong Lensing Events Research Articles

The Galaxy–Galaxy Strong Lensing Cross Section and the Internal Distribution of Matter in ΛCDM Substructure

Strong gravitational lensing offers a powerful probe of the detailed distribution of matter in lenses, while magnifying and bringing faint background sources into view. Observed strong lensing by massive galaxy clusters, which are often in complex dynamical states, has also been used to map their dark matter (DM) substructures on smaller scales. Deep high-resolution imaging has revealed the presence of strong lensing events associated with these substructures, namely galaxy-scale sub-halos. However, an inventory of these observed galaxy–galaxy strong lensing (GGSL) events is noted to be discrepant with state-of-the-art ΛCDM simulations. Cluster sub-halos appear to be over-concentrated compared to their simulated counterparts yielding an order-of-magnitude higher value of GGSL. In this paper, we explore the possibility of resolving this observed discrepancy by redistributing the mass within observed cluster sub-halos in ways that are consistent within the ΛCDM paradigm of structure formation. Lensing mass reconstructions from data provide constraints on the mass enclosed within apertures and are agnostic to the detailed mass profile within them. Therefore, as the detailed density profile within cluster sub-halos currently remains unconstrained by data, we are afforded the freedom to redistribute the enclosed mass. We investigate if rearranging the mass to a more centrally concentrated density profile helps alleviate the GGSL discrepancy. We report that refitting cluster sub-halos to the ubiquitous ΛCDM-motivated Navarro–Frenk–White profile, and further modifying them to include significant baryonic components, does not resolve this tension. A resolution to this persisting GGSL discrepancy may require more careful exploration of alternative DM models.

Simulating high-realistic galaxy scale strong lensing in galaxy clusters to train deep learning methods

AbstractGalaxy-galaxy strong lensing in galaxy clusters is a unique tool for studying the subhalo mass distribution, as well as for testing predictions from cosmological simulations. We describe a novel method that simulates realistic lensed features embedded inside the complexity of observed data by exploiting high-precision cluster lens models. Such methodology is used to build a large dataset with which Convolutional Neural Networks have been trained to identify strong lensing events in galaxy clusters. In particular, we inject lensed sources around cluster members using the images acquired by the Hubble Space Telescope. The resulting simulated mock data preserve the complexity of observation by taking into account all the physical components that could affect the morphology and the luminosity of the lensing events. The trained networks achieve a purity-completeness level of ∼ 91% in detecting such events. The methodology presented can be extended to other data-intensive surveys carried out with the next-generation facilities.

The probability of galaxy–galaxy strong lensing events in hydrodynamical simulations of galaxy clusters

Context. An excess of galaxy–galaxy strong lensing (GGSL) in galaxy clusters compared to expectations from the Λ cold-dark-matter (CDM) cosmological model has recently been reported. Theoretical estimates of the GGSL probability are based on the analysis of numerical hydrodynamical simulations in ΛCDM cosmology. Aims. We quantify the impact of the numerical resolution and active galactic nucleus (AGN) feedback scheme adopted in cosmological simulations on the predicted GGSL probability, and determine if varying these simulation properties can alleviate the gap with observations. Methods. We analyze cluster-size halos (M200 > 5 × 1014 M⊙) simulated with different mass and force resolutions and implementing several independent AGN feedback schemes. Our analysis focuses on galaxies with Einstein radii in the range 0.″5 ≤ θE ≤ 3″. Results. We find that improving the mass resolution by factors of 10 and 25, while using the same galaxy formation model that includes AGN feedback, does not affect the GGSL probability. We find similar results regarding the choice of gravitational softening. On the contrary, adopting an AGN feedback scheme that is less efficient at suppressing gas cooling and star formation leads to an increase in the GGSL probability by a factor of between 3 and 6. However, we notice that such simulations form overly massive galaxies whose contribution to the lensing cross section would be significant but that their Einstein radii are too large to be consistent with the observations. The primary contributors to the observed GGSL cross sections are galaxies with smaller masses that are compact enough to become critical for lensing. The population with these required characteristics appears to be absent from simulations. Conclusion. Based on these results, we reaffirm the tension between observations of GGSL and theoretical expectations in the framework of the ΛCDM cosmological model. The GGSL probability is sensitive to the galaxy formation model implemented in the simulations. Still, all the tested models have difficulty simultaneously reproducing the stellar mass function and the internal structure of galaxies.

Galaxies in the central regions of simulated galaxy clusters

Context. Recent observations found that observed cluster member galaxies are more compact than their counterparts in ΛCDM hydrodynamic simulations, as indicated by the difference in their strong gravitational lensing properties, and they reported that measured and simulated galaxy–galaxy strong lensing events on small scales are discrepant by one order of magnitude. Among the possible explanations for this discrepancy, some studies suggest that simulations with better resolution and implementing different schemes for galaxy formation could produce simulations that are in better agreement with the observations. Aims. In this work, we aim to assess the impact of numerical resolution and of the implementation of energy input from AGN feedback models on the inner structure of cluster sub-haloes in hydrodynamic simulations. Methods. We compared several zoom-in re-simulations of a sub-sample of cluster-sized haloes obtained by varying mass resolution and softening the length and AGN energy feedback scheme. We studied the impact of these different setups on the sub-halo (SH) abundances, their radial distribution, their density and mass profiles, and the relation between the maximum circular velocity, which is a proxy for SH compactness Results. Regardless of the adopted numerical resolution and feedback model, SHs with masses of MSH ≲ 1011 h−1 M⊙, the most relevant mass range for galaxy–galaxy strong lensing, have maximum circular velocities ∼30% smaller than those measured from strong lensing observations. We also find that simulations with less effective AGN energy feedback produce massive SHs (MSH ≳ 1011 h−1 M⊙) with higher maximum circular velocity and that their Vmax − MSH relation approaches the observed one. However, the stellar-mass number count of these objects exceeds the one found in observations, and we find that the compactness of these simulated SHs is the result of an extremely over-efficient star formation in their cores, also leading to larger than observed SH stellar mass. Conclusions. Regardless of the resolution and galaxy formation model adopted, simulations are unable to simultaneously reproduce the observed stellar masses and compactness (or maximum circular velocities) of cluster galaxies. Thus, the discrepancy between theory and observations that emerged previous works. It remains an open question as to whether such a discrepancy reflects limitations of the current implementation of galaxy formation models or the ΛCDM paradigm.

Imaginary images and Stokes phenomena in the weak plasma lensing of coherent sources

ABSTRACT The study of astrophysical plasma lensing, such as in the case of extreme scattering events, has typically been conducted using the geometric limit of optics, neglecting wave effects. However, for the lensing of coherent sources such as pulsars and fast radio bursts, wave effects can play an important role. Asymptotic methods, such as the so-called Eikonal limit, also known as the stationary phase approximation, have been used to include first-order wave effects; however, these methods are discontinuous at Stokes lines. Stokes lines are generic features of a variety of lens models, and are regions in parameter space where imaginary images begin to contribute to the overall intensity modulation of lensed sources. Using the mathematical framework of Picard–Lefschetz theory to compute diffraction integrals, we argue that these imaginary images contain as much information as their geometric counterparts, and may potentially be observable in data. Thus, weak-lensing events where these imaginary images are present can be as useful for inferring lens parameters as strong-lensing events in which multiple geometric images are present.

The AARTFAAC 60 MHz transients survey

ABSTRACT We report the experimental set-up and overall results of the AARTFAAC wide-field radio survey, which consists of observing the sky within 50° of Zenith, with a bandwidth of 3.2 MHz, at a cadence of 1 s, for 545 h. This yielded nearly 4 million snapshots, two per second, of on average 4800 square degrees and a sensitivity of around 60 Jy. We find two populations of transient events, one originating from PSR B0950+08 and one from strong ionospheric lensing events, as well as a single strong candidate for an extragalactic transient, with a peak flux density of 80 ± 30 Jy and a dispersion measure of $73\pm 3\, \mathrm{~pc~cm^{-3}}$. We also set a strong upper limit of 1.1 all-sky per day to the rate of any other populations of fast, bright transients. Lastly, we constrain some previously detected types of transient sources by comparing our detections and limits with other low-frequency radio transient surveys.

Model-independent Estimations for the Cosmic Curvature from the Latest Strong Gravitational Lensing Systems

Abstract Model-independent measurements for the cosmic spatial curvature, which is related to the nature of cosmic spacetime geometry, play an important role in cosmology. On the basis of the distance sum rule in the Friedmann–Lemaître–Robertson–Walker metric, (distance ratio) measurements of strong gravitational lensing (SGL) systems, together with distances from SNe Ia observations, have been proposed to directly estimate the spatial curvature without any assumptions for the theories of gravity and contents of the universe. However, previous studies indicated that a spatially closed universe was strongly preferred. In this paper, we re-estimate the cosmic curvature with the latest SGL data, which includes 163 well-measured systems. In addition, possible factors, e.g., a combination of SGL data from different surveys and stellar masses of the lens galaxy, which might affect estimations for the spatial curvature, are considered in our analysis. We find that, except for the case where only SGL systems from the Sloan Lens ACS Survey are considered, a spatially flat universe is consistently favored at very high confidence levels by the latest observations. It has been suggested that an increasing number of well-measured strong lensing events might significantly reduce the bias of estimation for the cosmic curvature.

SHALOS: StatisticalHerschel-ATLAS lensed objects selection

Context. The statistical analysis of large sample of strong lensing events can be a powerful tool to extract astrophysical or cosmological valuable information. Their selection using submillimetre galaxies has been demonstrated to be very effective with more than ∼200 proposed candidates in the case ofHerschel-ATLAS data and several tens in the case of the South Pole Telescope. However, the number of confirmed events is still relatively low, i.e. a few tens, mostly because of the lengthy observational validation process on individual events.Aims. In this work we propose a new methodology with a statistical selection approach to increase by a factor of ∼5 the number of such events within theHerschel-ATLAS data set. Although the methodology can be applied to address several selection problems, it has particular benefits in the case of the identification of strongly lensed galaxies: objectivity, minimal initial constrains in the main parameter space, and preservation of statistical properties.Methods. The proposed methodology is based on the Bhattacharyya distance as a measure of the similarity between probability distributions of properties of two different cross-matched galaxies. The particular implementation for the aim of this work is called SHALOS and it combines the information of four different properties of the pair of galaxies: angular separation, luminosity percentile, redshift, and the ratio of the optical to the submillimetre flux densities.Results. The SHALOS method provides a ranked list of strongly lensed galaxies. The number of candidates within ∼340 deg2of theHerschel-ATLAS surveyed area for the final associated probability,Ptot > 0.7, is 447 and they have an estimated mean amplification factor of 3.12 for a halo with a typical cluster mass. Additional statistical properties of the SHALOS candidates, as the correlation function or the source number counts, are in agreement with previous results indicating the statistical lensing nature of the selected sample.

Optical analysis of a CMB cosmic string candidate

The complexity of the cosmological scenario regarding cosmic strings (CSs) stands still in the way of a complete understanding. We describe here a promising strategy for the possible detection of these elusive physical entities. It is based on the search of strong gravitational lensing events in the location area of the CS candidate (CSc-1), which was declared in a previous work by CMB analysis. Using photometric and geometric criteria, we identified pairs of candidates of lensed galaxies (LGCs) in the "string field" (SF), which were then compared with the average density of background galaxy pairs in a set of "control fields" (CFs). We found an excess of $22\%$ (per sq. deg.) of the LGCs in SF, which exceeds the estimated cosmic dispersion. We also found that the number of LGCs is in excess of $29.2\%$ in the angular separation bin $[8'', 9'']$. Finally, we analysed the possibility of a preferred orientation of the line connecting the centres of the LGCs. The orientation is statistically significant for an angular separation bin $[4'',6'']$. Therefore, we found two "windows" for the preferred angular separation for LGCs along the possible CS. However, the confirmation of the gravitational lensing origin of our LGCs requires spectroscopic observations which seem to be justified by the present results. We plan to acquire their spectra as well as to continue the study of the spectral and morphological features of the LGCs in the CSc-1 field and to analyse the other CS-candidates using the same strategy.

Effect of gravitational lensing on the distribution of gravitational waves from distant binary black hole mergers

The detailed observation of the distribution of redshifts and chirp masses of binary black hole mergers is expected to provide a clue to their origin. In this paper, we develop a hybrid model of the probability distribution function of gravitational lensing magnification taking account of both strong and weak gravitational lensing, and use it to study the effect of gravitational lensing magnification on the distribution of gravitational waves from distant binary black hole mergers detected in ongoing and future gravitational wave observations. We find that the effect of gravitational lensing magnification is significant at high ends of observed chirp mass and redshift distributions. While a high mass tail in the observed chirp mass distribution is produced by highly magnified gravitational lensing events, we find that highly demagnified images of strong lensing events produce a high redshift ($z_{\rm obs}> 15$) tail in the observed redshift distribution, which can easily be observed in the third-generation gravitational wave observatories. Such a demagnified, apparently high redshift event is expected to be accompanied by a magnified image that is observed typically $10-100$ days before the demagnified image. For highly magnified events that produce apparently very high chirp masses, we expect pairs of events with similar magnifications with time delays typically less than a day. This work suggests the critical importance of gravitational lensing (de-)magnification on the interpretation of apparently very high mass or redshift gravitational wave events.

Using Strong Gravitational Lensing to Identify Fossil Group Progenitors

Abstract Fossil galaxy systems are classically thought to be the end result of galaxy group/cluster evolution, as galaxies experiencing dynamical friction sink to the center of the group potential and merge into a single, giant elliptical that dominates the rest of the members in both mass and luminosity. Most fossil systems discovered lie within z < 0.2, which leads to the question, what were these systems’ progenitors? Such progenitors are expected to have imminent or ongoing major merging near the brightest group galaxy that, when concluded, will meet the fossil criteria within the look forward time. Since strong gravitational lensing preferentially selects groups merging along the line of sight, or systems with a high mass concentration like fossil systems, we searched the CASSOWARY survey of strong-lensing events with the goal of determining whether lensing systems have any predisposition to being fossil systems or progenitors. We find that ∼13% of lensing groups are identified as traditional fossils while only ∼3% of nonlensing control groups are. We also find that ∼23% of lensing systems are traditional fossil progenitors compared to ∼17% for the control sample. Our findings show that strong-lensing systems are more likely to be fossil/pre-fossil systems than comparable nonlensing systems. Cumulative galaxy luminosity functions of the lensing and nonlensing groups also indicate a possible, fundamental difference between strong-lensing and nonlensing systems’ galaxy populations, with lensing systems housing a greater number of bright galaxies even in the outskirts of groups.

Periodic self-lensing from accreting massive black hole binaries

Nearly 150 massive black hole binary (MBHB) candidates at sub-pc orbital separations have been reported in recent literature. Nevertheless, the definitive detection of even a single such object remains elusive. If at least one of the black holes is accreting, the light emitted from its accretion disc will be lensed by the other black hole for binary orbital inclinations near to the line of sight. This binary self-lensing could provide a unique signature of compact MBHB systems. We show that, for MBHBs with masses in the range 10^6 - 10^10 solar masses and with orbital periods less than ~10 yr, strong lensing events should occur in one to 10s of percent of MBHB systems that are monitored for an entire orbit. Lensing events will last from days for the less massive, shorter period MBHBs up to a year for the most massive ~10 year orbital period MBHBs. At small inclinations of the binary orbit to the line of sight, lensing must occur and will be accompanied by periodicity due to the relativistic Doppler boost. Flares at the same phase as the otherwise average flux of the Doppler modulation would be a smoking gun signature of self-lensing and can be used to constrain binary parameters. For MBHBs with separation >100 Schwarzschild radii, we show that finite-sized source effects could serve as a probe of MBH accretion disc structure. Finally, we stress that our lensing probability estimate implies that ~10 of the known MBHB candidates identified through quasar periodicity should exhibit strong lensing flares.

UP TO 100,000 RELIABLE STRONG GRAVITATIONAL LENSES IN FUTURE DARK ENERGY EXPERIMENTS

The Euclid space telescope will observe ∼105 strong galaxy–galaxy gravitational lens events in its wide field imaging survey over around half the sky, but identifying the gravitational lenses from their observed morphologies requires solving the difficult problem of reliably separating the lensed sources from contaminant populations, such as tidal tails, as well as presenting challenges for spectroscopic follow-up redshift campaigns. Here I present alternative selection techniques for strong gravitational lenses in both Euclid and the Square Kilometre Array, exploiting the strong magnification bias present in the steep end of the Hα luminosity function and the H i mass function. Around 103 strong lensing events are detectable with this method in the Euclid wide survey. While only ∼1% of the total haul of Euclid lenses, this sample has ∼100% reliability, known source redshifts, high signal-to-noise, and a magnification-based selection independent of assumptions of lens morphology. With the proposed Square Kilometre Array dark energy survey, the numbers of reliable strong gravitational lenses with source redshifts can reach 105.

Arc Statistics

The existence of an arc statistics problem was at the center of a strong debate in the last fifteen years. With the aim to clarify if the optical depth for giant gravitational arcs by galaxy clusters in the so called concordance model is compatible with observations, several studies were carried out which helped to significantly improve our knowledge of strong lensing clusters, unveiling their extremely complex internal structure. In particular, the abundance and the frequency of strong lensing events like gravitational arcs turned out to be a potentially very powerful tool to trace the structure formation. However, given the limited size of observational and theoretical data-sets, the power of arc statistics as a cosmological tool has been only minimally exploited so far. On the other hand, the last years were characterized by significant advancements in the field, and several cluster surveys that are ongoing or planned for the near future seem to have the potential to make arc statistics a competitive cosmological probe. Additionally, recent observations of anomalously large Einstein radii and concentrations in galaxy clusters have reinvigorated the debate on the arc statistics problem. In this paper, we review the work done so far on arc statistics, focussing on what is the lesson we learned and what is likely to improve in the next years.

Gravitational lensing properties of an isothermal universal halo profile

N-body simulations predict that dark matter halos with different mass scales are described by a universal model, the Navarro-Frenk-White (NFW) density profiles. As a consequence of baryonic cooling effects, these halos will become more concentrated, and similar to an isothermal sphere over a large range in radii (∼ 300 h−1 kpc). The singular isothermal sphere (SIS) model however has to be truncated artificially at large radii since it extends to infinity. We model a massive galaxy halo as a combination of an isothermal sphere and an NFW density profile. We give an approximation for the mass concentration at different baryon fractions and present exact expressions for the weak lensing shear and flexion for such a halo. We compare the lensing properties with the SIS and NFW profiles. We find that the combined profile can generate higher order lensing signals at small radii and is more efficient in generating strong lensing events. In order to distinguish such a halo profile from the SIS or NFW profiles, one needs to combine strong and weak lensing constraints for small and large radii.

THE NEXT GENERATION VIRGO CLUSTER SURVEY (NGVS). I. INTRODUCTION TO THE SURVEY*

ABSTRACT The Next Generation Virgo Cluster Survey (NGVS) is a program that uses the 1 deg2 MegaCam instrument on the Canada–France–Hawaii Telescope to carry out a comprehensive optical imaging survey of the Virgo cluster, from its core to its virial radius—covering a total area of 104 deg2—in the u*griz bandpasses. Thanks to a dedicated data acquisition strategy and processing pipeline, the NGVS reaches a point-source depth of g ≈ 25.9 mag (10σ) and a surface brightness limit of μ g ∼ 29 mag arcsec−2 (2σ above the mean sky level), thus superseding all previous optical studies of this benchmark galaxy cluster. In this paper, we give an overview of the technical aspects of the survey, such as areal coverage, field placement, choice of filters, limiting magnitudes, observing strategies, data processing and calibration pipelines, survey timeline, and data products. We also describe the primary scientific topics of the NGVS, which include: the galaxy luminosity and mass functions; the color–magnitude relation; galaxy scaling relations; compact stellar systems; galactic nuclei; the extragalactic distance scale; the large-scale environment of the cluster and its relationship to the Local Supercluster; diffuse light and the intracluster medium; galaxy interactions and evolutionary processes; and extragalactic star clusters. In addition, we describe a number of ancillary programs dealing with “foreground” and “background” science topics, including the study of high-inclination trans-Neptunian objects; the structure of the Galactic halo in the direction of the Virgo Overdensity and Sagittarius Stream; the measurement of cosmic shear, galaxy–galaxy, and cluster lensing; and the identification of distant galaxy clusters, and strong-lensing events.

DENSITY PROFILE, VELOCITY ANISOTROPY, AND LINE-OF-SIGHT EXTERNAL CONVERGENCE OF SLACS GRAVITATIONAL LENSES

Data from 58 strong-lensing events surveyed by the Sloan Lens ACS Survey are used to estimate the projected galaxy mass inside their Einstein radii by two independent methods: stellar dynamics and strong gravitational lensing. We perform a joint analysis of these two estimates inside models with up to three degrees of freedom with respect to the lens density profile, stellar velocity anisotropy, and line-of-sight (LOS) external convergence, which incorporates the effect of the large-scale structure on strong lensing. A Bayesian analysis is employed to estimate the model parameters, evaluate their significance and compare models. We find that the data favor Jaffe's light profile over Hernquist's, but that any particular choice between these two does not change the qualitative conclusions with respect to the features of the system that we investigate. The density profile is compatible with an isothermal, being sightly steeper and having an uncertainty in the logarithmic slope of the order of 5% in models that take into account a prior ignorance on anisotropy and external convergence. We identify a considerable degeneracy between the density profile slope and the anisotropy parameter, which largely increases the uncertainties in the estimates of these parameters, but we encounter no evidence in favor of an anisotropic velocity distribution on average for the whole sample. An LOS external convergence following a prior probability distribution given by cosmology has a small effect on the estimation of the lens density profile, but can increase the dispersion of its value by nearly 40%.

Strong lensing in the MARENOSTRUM UNIVERSE

The strong lensing events that are observed in compact clusters of galaxies can, both statistically and individually, return important clues about the structural properties of the most massive structures in the Universe. Substantial work is ongoing in order to understand the degree of similarity between the lensing cluster population and the population of clusters as a whole, with members of the former being likely more massive, compact, and substructured than members of the latter. In this work we exploit synthetic clusters extracted from the MareNostrum Universe cosmological simulation in order to estimate the correlation between the strong lensing efficiency and other bulk properties of lensing clusters, such as the virial mass and the bolometric X-ray luminosity. We found that a positive correlation exist between all these quantities, with the substantial scatter being smaller for the luminosity-cross section relation. We additionally used the relation between the lensing efficiency and the virial mass in order to construct a synthetic optical depth that agrees well with the true one, while being extremely faster to be evaluated. We finally estimated what fraction of the total giant arc abundance is recovered when galaxy clusters are selected according to their dynamical activity or their X-ray luminosity. Our results show that there is a high probability for high-redshift strong lensing clusters to be substantially far away from dynamical equilibrium, and that 30–40% of the total amount of giant arcs are lost if looking only at very X-ray luminous objects.

Strong lensing in the MARENOSTRUM UNIVERSE

<i>Context. <i/>Strong lensing is one of the most direct probes of mass distribution in the inner regions of galaxy clusters. It can be used to constrain the density profiles and to measure the mass of the lenses. Moreover, the abundance of strong lensing events can be used to constrain structure formation and cosmological parameters through the so-called “arc-statistics” approach. However, several issues related to the use of strong lensing clusters in cosmological applications are still controversial, leading to the suspicion that several biases may affect this very peculiar class of objects.<i>Aims. <i/>With this study we aim a better understanding of the properties of galaxy clusters that can potentially act as strong lenses.<i>Methods. <i/>We do so by investigating the properties of a large sample of galaxy clusters extracted from the <i>N<i/>-body/hydrodynamical simulation MareNostrum Universe. We perform ray-tracing simulations with each of them and identify those objects capable of producing strong lensing effects. We explore the correlation between the cross section for lensing and many properties of clusters, such as mass, three-dimensional and projected shapes, their concentrations, the X-ray luminosity, and the dynamical activity.<i>Results. <i/>We quantify the minimal cluster mass required for producing both multiple images and large distortions. While we do not measure a significant excess of triaxiality in strong lensing clusters, we find that the probability of strong alignments between the major axes of the lenses and the line of sight is a growing function of the lensing cross section. In projection, the strong lenses appear rounder within <i>R<i/><sub>200<sub/>, but we find that their cores tend to be more elliptical as the lensing cross section increases. As a result of the orientation bias, we also find that the cluster concentrations estimated from the projected density profiles tend to be biased high. The X-ray luminosity of strong lensing clusters tend to be higher than for normal lenses of similar mass and redshift. This is particularly significant for the least massive lenses. Finally, we find that the strongest lenses generally exhibit an excess of kinetic energy within the virial radius, thus indicating that they are more dynamically active than the usual clusters.<i>Conclusions. <i/>We conclude that strong lensing clusters are a very peculiar class of objects, affected by many selection biases that need to be properly modeled when using them to study the inner structure of galaxy clusters or to constrain the cosmological parameters.

Density profile and line-of-sight mass contamination of SLACS gravitational lenses

We use data from 58 strong lensing events surveyed by the Sloan Lens ACS Survey to estimate the projected galaxy mass inside their Einstein radii by two independent methods: stellar dynamics and strong gravitational lensing. We perform a joint analysis of both estimates examining the galaxy-lens density profile (that we approximate by a power law), the anisotropy of the velocity distribution (represented by an effective constant parameter), and a possible line-of-sigh (l.o.s.) mass contamination (which is suggested by various independent works in the literature). For each model, a likelihood analysis is performed to find the parameters that produce the best agreement between the dynamical and lensing masses, and the parameter confidence levels. The Bayesian evidence is calculated to allow a comparison among the models. We find a degeneracy among the slope of the density profile, the anisotropy parameter and the l.o.s. mass contamination. For a density profile close to isothermal, a l.o.s. mass contamination of the order of a few percent is possible, being less probable with larger anisotropy.