Strong-lensing Cross Sections Research Articles

The galaxy–galaxy strong lensing cross-sections of simulated ΛCDM galaxy clusters

ABSTRACT We investigate a recent claim that observed galaxy clusters produce an order of magnitude more galaxy–galaxy strong lensing (GGSL) than simulated clusters in a Λ cold dark matter (CDM) cosmology. We take galaxy clusters from the c-eagle hydrodynamical simulations and calculate the expected amount of GGSL for sources placed behind the clusters at different redshifts. The probability of a source lensed by one of the most massive c-eagle clusters being multiply imaged by an individual cluster member is in good agreement with that inferred for observed clusters. We show that numerically converged results for the GGSL probability require higher resolution simulations than had been used previously. On top of this, different galaxy formation models predict cluster substructures with different central densities, such that the GGSL probabilities in ΛCDM cannot yet be robustly predicted. Overall, we find that GGSL within clusters is not currently in tension with the ΛCDM cosmological model.

Strong lensing cross-sections for isothermal models. I. Finite source effects in the circular case

The strong galaxy-galaxy lensing produces highly magnified and distorted images of background galaxies in the form of arcs and Einstein rings. Statistically, these effects are quantified, for example, in the number counts of highly luminous sub-millimeter galaxies and of gravitational arcs. Two key quantities to model these statistics are the magnification and the arc cross sections. These are usually computed using either the circular infinitesimal source approximation or ray-tracing simulations for sources of finite size. In this work, we use an analytic solution for gravitational arcs to obtain these cross sections as a function of image magnification and length-to-width ratio in closed form, for finite sources. These analytical solutions provide simple interpretations to the numerical results, can be employed to test the computational codes, and can be used for fast a computation of the abundance of distant sources and arcs. In this paper, the lens is modeled by a Singular Isothermal Sphere, which is an excellent approximation to radial density profile of Early-Type galaxies, and the sources are also axisymmetric. We derive expressions for the geometrical properties of the images, such as the area and several definitions of length and width. We obtain the magnification cross section in exact form and derive a simple analytic approximation covering the arc and Einstein ring regimes. The arc cross section is obtained down to the formation of an Einstein ring and given in terms of elementary functions. Perturbative expansions of these results are worked out, showing explicitly the correction terms for finite sources.

SEARCHING FOR COOLING SIGNATURES IN STRONG LENSING GALAXY CLUSTERS: EVIDENCE AGAINST BARYONS SHAPING THE MATTER DISTRIBUTION IN CLUSTER CORES

The process by which the mass density profile of certain galaxy clusters becomes centrally concentrated enough to produce high strong lensing (SL) cross-sections is not well understood. It has been suggested that the baryonic condensation of the intra-cluster medium (ICM) due to cooling may drag dark matter to the cores and thus steepen the profile. In this work, we search for evidence of ongoing ICM cooling in the first large, well-defined sample of strong lensing selected galaxy clusters in the range 0.1 < z < 0.6. Based on known correlations between the ICM cooling rate and both optical emission line luminosity and star formation, we measure, for a sample of 89 strong lensing clusters, the fraction of clusters that have [OII]3727 emission in their brightest cluster galaxy (BCG). We find that the fraction of line-emitting BCGs is constant as a function of redshift for z > 0.2 and shows no statistically significant deviation from the total cluster population. Specific star formation rates, as traced by the strength of the 4000 angstrom break, D_4000, are also consistent with the general cluster population. Finally, we use optical imaging of the SL clusters to measure the angular separation, R_arc, between the arc and the center of mass of each lensing cluster in our sample and test for evidence of changing [OII] emission and D_4000 as a function of R_arc, a proxy observable for SL cross-sections. D_4000 is constant with all values of R_arc, and the [OII] emission fractions show no dependence on R_arc for R_arc > 10" and only very marginal evidence of increased weak [OII] emission for systems with R_arc < 10". These results argue against the ability of baryonic cooling associated with cool core activity in the cores of galaxy clusters to strongly modify the underlying dark matter potential, leading to an increase in strong lensing cross-sections.

Predicting the number of giant arcs expected in the next-generation wide-field surveys from space

In this paper, we estimate the number of gravitational arcs detectable in a wide-field survey such as that which will be operated by the Euclid space mission, assuming a Λ cold dark matter cosmology. We use the publicly available code moka to obtain realistic deflection angle maps of mock gravitational lenses. The maps are processed by a ray-tracing code to estimate the strong lensing cross-sections of each lens. Our procedure involves (1) the generation of a light-cone which is populated with lenses drawn from a theoretical mass function, (2) the modelling of each single lens using a triaxial halo with a Navarro–Frenk–White density profile and theoretical concentration–mass relation, including substructures, (3) the determination of the lensing cross-section as a function of redshift for each lens in the light-cone and (4) the simulation of mock observations to characterize the redshift distribution of sources that will be detectable in the Euclid images. We focus on the so-called giant arcs, i.e. gravitational arcs characterized by large length-to-width ratios (l/w > 5, 7.5 and 10). We quantify the arc detectability at different significances above the level of the background. Performing 128 different realizations of a 15 000 deg2 survey, we find that the number of arcs detectable at 1σ above the local background will be , and for l/w ≥ 5, 7.5 and 10, respectively. The expected arc numbers decrease to , and for a detection limit at 3σ above the background level. From our analysis, we find that most of the lenses which contribute to the lensing optical depth are located at redshifts 0.4 < zl < 0.7 and that the 50 per cent of the arcs are images of sources at zs > 3. This is the first step towards the full characterization of the population of strong lenses that will be observed by Euclid. Given these results, we conclude that Euclid is a powerful instrument for strong lensing related science, which will be useful for several applications, ranging from arc and Einstein ring statistics to the measurement of the matter content in the cluster cores.

Moka: a new tool for strong lensing studies

Strong gravitational lensing is a powerful tool for probing the matter distribution in the cores of massive dark matter haloes. Recent and ongoing analyses of galaxy cluster surveys (MACS, CFHTLS, SDSS, SGAS, CLASH, LoCuSS) have adressed the question of the nature of the dark matter distribution in clusters. N-body simulations of cold dark-matter haloes consistently find that haloes should be characterized by a concentration-mass relation that decreases monotonically with halo mass, and populated by a large amount of substructures, representing the cores of accreted progenitor halos. It is important for our understanding of dark matter to test these predictions. We present MOKA, a new algorithm for simulating the gravitational lensing signal from cluster-sized haloes. It implements the most recent results from numerical simulations to create realistic cluster-scale lenses with properties independent of numerical resolution. We perform systematic studies of the strong lensing cross section as a function of halo structures. We find that the strong lensing cross sections depend most strongly on the concentration and on the inner slope of the density profile of a halo, followed in order of importance by halo triaxiality and the presence of a bright central galaxy.

Cluster strong lensing in the Millennium simulation: the effect of galaxies and structures along the line-of-sight

We use ray-tracing through the Millennium simulation to study how secondary matter structures along the line-of-sight and the stellar mass in galaxies affect strong cluster lensing, in particular the cross-section for giant arcs. Furthermore, we investigate the distribution of the cluster Einstein radii and the radial distribution of giant arcs. We find that additional structures along the line-of-sight increase the strong-lensing optical depth by ~10-25%, while strong-lensing cross-sections of individual clusters are frequently boosted by as much as ~50%. The enhancement is mainly due to structures that are not correlated with the lens. Cluster galaxies increase the strong-lensing optical depth by up to a factor of 2, while interloping galaxies are not significant. We conclude that these effects need to be taken into account for predictions of the giant arc abundance, but they are not large enough to fully account for the reported discrepancy between predicted and observed abundances. Furthermore, we find that Einstein radii defined via the area enclosed by the critical curve are 10-30% larger than those defined via radial surface mass density profiles. The contributions of radial and tangential arcs to the radial distribution of arcs can be clearly distinguished. The radial distribution of tangential arcs is very broad and extends out to several Einstein radii. Thus, individual arcs are not well suited for constraining Einstein radii.

Strong-lensing optical depths in a ΛCDM universe – II. The influence of the stellar mass in galaxies

We investigate how strong gravitational lensing in the concordanceCDM cosmology is affected by the stellar mass in galaxies. We extend our previous studies, based on ray trac- ing through the Millennium Simulation, by including the stellar components predicted by galaxy formation models. We find that the inclusion of these components greatly enhances the probability for strong lensing compared to a 'dark matter only' universe. The identification of the 'lenses' associated with strong-lensing events reveals that the stellar mass of galaxies (i) significantly enhances the strong-lensing cross-sections of group and cluster haloes and (ii) gives rise to strong lensing in smaller haloes, which would not produce noticeable effects in the absence of the stars. Even if we consider only image splittings � 10 arcsec, the luminous matter can enhance the strong-lensing optical depths by up to a factor of 2.

Strong lensing optical depths in a CDM universe

We investigate strong gravitational lensing in the concordance ΛCDM cosmology by carrying out ray tracing along past light cones through the Millennium Simulation, the largest simulation of cosmic structure formation ever carried out. We extend previous ray-tracing methods in order to take full advantage of the large volume and the excellent spatial and mass resolution of the simulation. As a function of source redshift we evaluate the probability that an image will be highly magnified, will be highly elongated or will be one of a set of multiple images. We show that such strong lensing events can almost always be traced to a single dominant lensing object and we study the mass and redshift distribution of these primary lenses. We fit analytic models to the simulated dark haloes in order to study how our optical depth measurements are affected by the limited resolution of the simulation and of the lensing planes that we construct from it. We conclude that such effects lead us to underestimate total strong lensing cross-sections by about 15 per cent. This is smaller than the effects expected from our neglect of the baryonic components of galaxies. Finally we investigate whether strong lensing is enhanced by material in front of or behind the primary lens. Although strong lensing lines of sight are indeed biased towards higher than average mean densities, this additional matter typically contributes only a few per cent of the total surface density.

Characterizing the Cluster Lens Population

We present a detailed investigation into which properties of CDM halos make them effective strong gravitational lenses. Strong-lensing cross sections of 878 clusters from an N-body simulation are measured by ray-tracing through 13,594 unique projections. We measure concentrations, axis ratios, orientations, and the substructure of each cluster, and compare the lensing-weighted distribution of each quantity to that of the cluster population as a whole. The concentrations of lensing clusters are on average 34% larger than the typical cluster in the universe. Despite this bias, the anomalously high concentrations (c > 14) recently measured by several groups appear to be inconsistent with the concentration distribution in our simulations, which predict that <2% of lensing clusters should have concentrations this high. No correlation is found between lensing cross section and substructure. We introduce several types of simplified dark matter halos and use them to isolate which properties of CDM clusters make them effective lenses. The abundance of giant arcs is primarily determined by the mass distribution within an average overdensity of ~10,000. A multiple-lens-plane ray-tracing algorithm is used to show that projections of large-scale structure increase the giant arc abundance modestly, by <7%. We revisit the claimed excess of giant arcs behind high redshift clusters in the RCS survey and find that the number of high-redshift (z > 0.6) lenses is in good agreement with ΛCDM, although our simulations predict more low-redshift (z < 0.6) lenses than observed.

A fast method for computing strong-lensing cross sections: application to merging clusters

Strong gravitational lensing by irregular mass distributions, such as galaxy clusters, is generally not well quantified by cross sections of analytic mass models. Computationally expensive ray-tracing methods have so far been necessary for accurate cross-section calculations. We describe a fast, semi-analytic method here which is based on surface integrals over high-magnification regions in the lens plane and demonstrate that it yields reliable cross sections even for complex, asymmetric mass distributions. The method is faster than ray-tracing simulations by factors of $\sim30$ and thus suitable for large cosmological simulations, saving large amounts of computing time. We apply this method to a sample of galaxy cluster-sized dark matter haloes with simulated merger trees and show that cluster mergers approximately double the strong-lensing optical depth for lens redshifts $z_\mathrm{l}\gtrsim0.5$ and sources near $z_\mathrm{s} = 2$. We believe that this result hints at one possibility for understanding the recently detected high arcs abundance in clusters at moderate and high redshifts, and is thus worth further studies.

Strong lensing efficiency of galaxy clusters in dark energy cosmologies

We study the efficiency for producing strong gravitational lensing events of galaxy clusters numerically simulated in different dark-energy cosmologies with constant and time-variable equation of state, and we compare the results with those obtained in standard ACDM and OCDM models. Our main results are (1) that the expected abundance of gravitational arcs with large length-to-width ratio depends on the equation of state of dark energy at the epoch of formation of the halo; and (2) that the high sensitivity of strong-lensing cross sections of galaxy clusters to dynamical processes like mergers, which was found in earlier studies, varies substantially between different cosmologies, being stronger for models in which halos are less concentrated. As expected, the largest differences in the lensing optical depth occur at intermediate and high redshift.

The impact of gas physics on strong cluster lensing

Previous studies of strong gravitational lensing by galaxy clusters neglected the potential impact of the intracluster gas. Here, we compare simulations of strong cluster lensing including gas physics at increasing levels of complexity, i.e. with adiabatic, cooling, star-forming, feedback-receiving, and thermally conducting gas, and with different implementations of the artificial viscosity in the SPH simulations. Each cluster was simulated starting from the same initial conditions such as to allow directly comparing the simulated clusters. We compare the clusters' shapes, dynamics and density profiles and study their strong-lensing cross sections computed by means of ray-tracing simulations. We find that the impact of adiabatic gas depends on the amount of turbulence that builds up, which means that the artificial viscosity plays an important role. With the common viscosity implementation, adiabatic gas has little effect on strong cluster lensing, while lower viscosity allows stronger turbulence, thus higher non-thermal pressure and a generally broader gas distribution which tends to lower lensing cross sections. Conversely, cooling and star formation steepen the core density profiles and can thus increase the strong-lensing efficiency considerably.

MERGERS, COSMIC RAYS, AND NONTHERMAL PROCESSES IN CLUSTERS OF GALAXIES

Clusters of galaxies generally form by the gravitational merger of smaller clusters and groups. Major cluster mergers are the most energetic events in the Universe since the Big Bang. The basic properties of cluster mergers and their effects are discussed. Mergers drive shocks into the intracluster gas, and these shocks heat the intracluster gas. As a result of the impulsive heating and compression associated with mergers, there is a large transient increase in the X-ray luminosities and temperatures of merging clusters. These merger boost can affect X-ray surveys of clusters and their cosmological interpretation. Similar boosts occur in the strong lensing cross-sections and Sunyaev-Zeldovich effect in merging clusters. Merger shock and turbulence associated with mergers should also (re)accelerate nonthermal relativistic particles. As a result of particle acceleration in shocks and turbulent acceleration following mergers, clusters of galaxies should contain very large populations of relativistic electrons and ions. Observations and models for the radio, extreme ultraviolet, hard X-ray, and gamma-ray emission from nonthermal particles accelerated in these shocks will also be described. Gamma-ray observations with GLAST seem particularly promising.

CD galaxy contribution to the strong lensing cross-sections of galaxy clusters

We perform ray-tracing simulations evaluating the effect of a cD galaxy on the strong lensing properties of five galaxy cluster haloes obtained from N-body simulations. The cD galaxy is modelled using both axially symmetric and elliptical models and assuming several masses for its dark matter halo. The effect of the cD orientation with respect to the mass distribution of the host galaxy cluster is also investigated. The simulations are carried out in an open and a flat model universe with cosmological constant. We find that the enhancement of the cluster lensing cross-sections for long and thin arcs owing to the presence of a massive cD at the cluster centre is typically less than 100 per cent, depending on the model used for the cD galaxy and its orientation. The impact of the cD on the cluster efficiency for producing radially magnified images is larger only for those clusters with a lensing cross-section for radial arcs that is very small in absence of the central galaxy. We conclude that the presence of a cD galaxy at the cluster centre can only moderately influence the cluster efficiency for strong lensing and, in particular, fails to explain the discrepancy between the observed number of giant arcs in galaxy clusters and their abundance predicted from lensing simulations in the currently most favoured ACDM model.

Strong gravitational lensing by spiral galaxies

We investigate gravitational lensing using a realistic model of disc galaxies. Most of the mass is contained in a large spherical isothermal dark matter halo, but the potential is modified significantly in the core by a gravitationally dominant exponential disc. The method used is adapted from a very general multilens ray-tracing technique developed by Mo¨ller. We investigate the effects of the disc-to-halo mass ratio, the disc scalelength, the disc inclination to the line of sight and the lens redshift on two strong-lensing cross-sections: the cross-section for multiple imaging and the cross-section for large magnifications, in excess of a factor of 10. We find that the multiple-imaging cross-section can be enhanced significantly by an almost edge-on Milky Way disc compared with a singular isothermal sphere (SIS) in individual cases; however, when averaged over all disc inclinations, the cross-section is only increased by about 50 per cent. These results are consistent with other recent work. The presence of a disc, however, increases the inclination-averaged high-magnification cross-section by an order of magnitude compared with a SIS. This result has important implications for magnification bias in future lens surveys, particularly those in the submillimetre waveband, where dust extinction in the lensing galaxy has no effect on the brightness of the images.