Giant Arcs Research Articles

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.

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.

Giant stellar arcs in the Large Magellanic Cloud: a possible link with past activity of the Milky Way nucleus

Abstract The origin of the giant stellar arcs in the Large Magellanic Cloud (LMC) remains a controversial issue, one that has been discussed since 1966. No other star/cluster arc is so perfect a segment of a circle; moreover, there is another similar arc nearby. Many hypotheses were advanced to explain these arcs and all but one of these was disproved. It was proposed in 2004 that the origin of these arcs was a bow shock from the jet that is intermittently fired by the Milky Way nucleus; during its last episode of activity the jet was pointed toward the LMC. Quite recently, evidence for such a jet indeed appeared. We suggest that it was once energetic enough to trigger star formation in the LMC, and if the jet opening angle was about 2° then it could push out H i gas from a region of about 2 kpc in size, forming a cavity LMC4, but also squeeze two dense clouds that occurred in the same area, causing the formation of stars along their surfaces facing the core of the Milky Way. As a result, spherical segments of stellar shells might arise, visible now as the arcs named the Quadrant and Sextant, the apexes of which point towards the centre of the Milky Way. The orientation of both arcs could be the key to unlocking their origin. Here we give data that confirm the above hypothesis, amongst which are the radial velocities of stars inside and outside the larger of the LMC arcs. The probability is low that a jet from an active galactic nucleus (AGN) points towards a nearby galaxy and triggers star formation there, but a few other examples are now known or suspected.

The strongest gravitational lenses

For more than a decade now, it has been controversial whether or not the high rate of giant gravitational arcs and the largest observed Einstein radii are consistent with the standard cosmological model. Recent studies indicate that mergers provide an efficient mechanism to substantially increase the strong-lensing efficiency of individual clusters. Based on purely semi-analytic methods, we investigated the statistical impact of cluster mergers on the distribution of the largest Einstein radii and the optical depth for giant gravitational arcs of selected cluster samples. Analysing representative all-sky realizations of clusters at redshifts z < 1 and assuming a constant source redshift of z_s = 2.0, we find that mergers increase the number of Einstein radii above 10 arcsec (20 arcsec) by ~ 35 % (~ 55 %). Exploiting the tight correlation between Einstein radii and lensing cross sections, we infer that the optical depth for giant gravitational arcs with a length-to-width ratio > 7.5 of those clusters with Einstein radii above 10 arcsec (20 arcsec) increases by ~ 45 % (85 %). Our findings suggest that cluster mergers significantly influence in particular the statistical lensing properties of the strongest gravitational lenses. We conclude that semi-analytic studies must inevitably take these events into account before questioning the standard cosmological model on the basis of the largest observed Einstein radii and the statistics of giant gravitational arcs.

How baryonic processes affect strong lensing properties of simulated galaxy clusters

The observed abundance of giant arcs produced by galaxy cluster lenses and the measured Einstein radii have presented a source of tension for Λ cold dark matter (ΛCDM), particularly at low redshifts (z ∼ 0.2). Previous cosmological tests for high-redshift clusters (z > 0.5) have suffered from small number statistics in the simulated sample and the implementation of baryonic physics is likely to affect the outcome. We analyse zoomed-in simulations of a fairly large sample of cluster-sized objects, with Mvir > 3 × 1014 h−1 M⊙, identified at z = 0.25 and 0.5, for a concordance ΛCDM cosmology. These simulations have been carried out by incrementally increasing the physics considered. We start with dark-matter-only simulations and then add gas hydrodynamics, with different treatments of baryonic processes: non-radiative cooling, radiative cooling with star formation and galactic winds powered by supernova explosions, and finally including the effect of active galactic nucleus (AGN) feedback. Our analysis of strong lensing properties is based on the computation of the cross-section for the formation of giant arcs and of the Einstein radii. We find that the addition of gas in non-radiative simulations does not change the strong lensing predictions significantly, but gas cooling and star formation together significantly increase the number of expected giant arcs and the Einstein radii, particularly for lower redshift clusters and lower source redshifts. Further inclusion of AGN feedback reduces the predicted strong lensing efficiencies such that the lensing probability distributions become closer to those obtained for simulations including only dark matter. Our results indicate that the inclusion of baryonic physics in simulations will not solve the arc-statistics problem at low redshifts, when the physical processes included provide a realistic description of cooling in the central regions of galaxy clusters. As outcomes of our analysis, we encourage the adoption of Einstein radii as a robust measure of strong lensing efficiency, and provide the ΛCDM predictions to be used for future comparisons with high-redshift cluster samples.

THE A2667 GIANT ARC ATz= 1.03: EVIDENCE FOR LARGE-SCALE SHOCKS AT HIGH REDSHIFT

We present the spatially resolved emission line ratio properties of a ~10^10 M_sun star-forming galaxy at redshift z=1.03. This galaxy is gravitationally lensed as a triple-image giant arc behind the massive lensing cluster Abell 2667. The main image of the galaxy has magnification factors of 14+/-2.1 in flux and ~ 2 by 7 in area, yielding an intrinsic spatial resolution of 115-405 pc after AO correction with OSIRIS at KECK II. The HST morphology shows a clumpy structure and the H\alpha\ kinematics indicates a large velocity dispersion with V_{max} sin(i)/\sigma ~ 0.73, consistent with high redshift disk galaxies of similar masses. From the [NII]/H\alpha\ line ratios, we find that the central 350 parsec of the galaxy is dominated by star formation. The [NII]/H\alpha\ line ratios are higher in the outer-disk than in the central regions. Most noticeably, we find a blue-shifted region of strong [NII]/H\alpha\ emission in the outer disk. Applying our recent HII region and slow-shock models, we propose that this elevated [NII]/H\alpha\ ratio region is contaminated by a significant fraction of shock excitation due to galactic outflows. Our analysis suggests that shocked regions may mimic flat or inverted metallicity gradients at high redshift.

Intrinsic Edge Asymmetry in Narrow Zigzag Hexagonal Heteroatomic Nanoribbons Causes their Subtle Uniform Curvature

The atomic and electronic structure of narrow zigzag nanoribbons with finite length, consisting of graphene terminated by fluorine on one side, hexagonal (h) h-BN, and h-SiC were studied with density functional theory. It is found that the asymmetry of nanoribbon edges causes a uniform curvature of the ribbons due to structural stress in the aromatic ring plane. Narrow graphene nanoribbons terminated with fluorine on one side demonstrate a considerable out-of-plane bend, suggesting that the nanoribbon is a fraction of a conical surface. It is shown that the intrinsic curvature of the narrow nanoribbons destroys the periodicity and results in a systematic cancellation of the dipole moment. The in- and out-of-plane curvature of thin arcs allows their closure in nanorings or cone fragments of giant diameter. Using the fragment molecular orbital method, we optimized the structure of a planar giant arc and a closed ring of h-BN with a diameter of 105 nm.

SPATIALLY RESOLVEDHSTGRISM SPECTROSCOPY OF A LENSED EMISSION LINE GALAXY ATz∼ 1

We take advantage of gravitational lensing amplification by Abell 1689 (z=0.187) to undertake the first space-based census of emission line galaxies (ELGs) in the field of a massive lensing cluster. Forty-three ELGs are identified to a flux of i_775=27.3 via slitless grism spectroscopy. One ELG (at z=0.7895) is very bright owing to lensing magnification by a factor of ~4.5. Several Balmer emission lines detected from ground-based follow-up spectroscopy signal the onset of a major starburst for this low-mass galaxy (M_* = 2 x 10^9 solar masses) with a high specific star formation rate (~20 /Gyr). From the blue emission lines we measure a gas-phase oxygen abundance consistent with solar (12+log(O/H)=8.8 +/- 0.2). We break the continuous line-emitting region of this giant arc into seven ~1kpc bins (intrinsic size) and measure a variety of metallicity dependent line ratios. A weak trend of increasing metal fraction is seen toward the dynamical center of the galaxy. Interestingly, the metal line ratios in a region offset from the center by ~1kpc have a placement on the blue HII region excitation diagram with f([OIII])/f(Hbeta) and f([NeIII])/f(Hbeta) that can be fit by an AGN. This asymmetrical AGN-like behavior is interpreted as a product of shocks in the direction of the galaxy's extended tail, possibly instigated by a recent galaxy interaction.

IDCS J1426.5+3508: COSMOLOGICAL IMPLICATIONS OF A MASSIVE, STRONG LENSING CLUSTER ATz= 1.75

The galaxy cluster IDCS J1426.5+3508 at z = 1.75 is the most massive galaxy cluster yet discovered at z > 1.4 and the first cluster at this epoch for which the Sunyaev-Zel'Dovich effect has been observed. In this paper we report on the discovery with HST imaging of a giant arc associated with this cluster. The curvature of the arc suggests that the lensing mass is nearly coincident with the brightest cluster galaxy, and the color is consistent with the arc being a star-forming galaxy. We compare the constraint on M200 based upon strong lensing with Sunyaev-Zel'Dovich results, finding that the two are consistent if the redshift of the arc is z > 3. Finally, we explore the cosmological implications of this system, considering the likelihood of the existence of a strongly lensing galaxy cluster at this epoch in an LCDM universe. While the existence of the cluster itself can potentially be accomodated if one considers the entire volume covered at this redshift by all current high-redshift cluster surveys, the existence of this strongly lensed galaxy greatly exacerbates the long-standing giant arc problem. For standard LCDM structure formation and observed background field galaxy counts this lens system should not exist. Specifically, there should be no giant arcs in the entire sky as bright in F814W as the observed arc for clusters at z \geq 1.75, and only \sim 0.3 as bright in F160W as the observed arc. If we relax the redshift constraint to consider all clusters at z \geq 1.5, the expected number of giant arcs rises to \sim15 in F160W, but the number of giant arcs of this brightness in F814W remains zero. These arc statistic results are independent of the mass of IDCS J1426.5+3508. We consider possible explanations for this discrepancy.

THE CFHTLS-STRONG LENSING LEGACY SURVEY (SL2S): INVESTIGATING THE GROUP-SCALE LENSES WITH THE SARCS SAMPLE

We present the Strong Lensing Legacy Survey - ARCS (SARCS) sample compiled from the final T0006 data release of the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) covering a total non-overlapping area of 159 sq.deg. We adopt a semi-automatic method to find gravitational arcs in the survey that makes use of an arc-finding algorithm. The candidate list is pruned by visual inspection and ranking to form the SARCS sample. This list also includes some serendipitously discovered lens candidates. The SARCS sample consists of 127 lens candidates which span arc radii~2"-18" within the unmasked area of ~ 150 sq. deg. Within the sample, 54 systems are promising lenses amongst which, we find 12 giant arcs and 2 radial arc candidates. From our sample, we detect a systematic alignment of giant arcs with the ellipticity of the baryonic component of the lens in concordance with previous studies. The lens redshift distribution corresponding to both the giant arcs and all arcs, estimated from photometric catalogs, peaks at z~0.6. Owing to the large area and depth of the CFHTLS, we find the largest lens sample probing group-scales for the first time. We compare the observed image separation distribution (ISD) of our arcs with theoretical models. A two-component density profile for the lenses which accounts for both the central galaxy and dark matter component is required by the data to explain the observed ISD. Unfortunately, current levels of uncertainties and degeneracies accommodate models both with and without adiabatic contraction. We also show the effects of changing parameters of the model that predict the ISD and that a larger lens sample might constrain relations such as the concentration-mass relation, mass-luminosity relation and slope of the luminosity function. (abridged)

Constraints on cosmological models from strong gravitational lensing systems

Strong lensing has developed into an importantastrophysical tool for probing both cosmology and galaxies (theirstructure, formation, and evolution). Using the gravitationallensing theory and cluster mass distribution model, we try tocollect a relatively complete observational data concerning theHubble constant independent ratio between two angular diameterdistances Dds/Ds from various large systematic gravitationallens surveys and lensing by galaxy clusters combined with X-rayobservations, and check the possibility to use it in the future ascomplementary to other cosmological probes. On one hand, stronglygravitationally lensed quasar-galaxy systems create such a newopportunity by combining stellar kinematics (central velocitydispersion measurements) with lensing geometry (Einstein radiusdetermination from position of images). We apply such a method to acombined gravitational lens data set including 70 data points fromSloan Lens ACS (SLACS) and Lens Structure and Dynamics survey(LSD). On the other hand, a new sample of 10 lensing galaxy clusterswith redshifts ranging from 0.1 to 0.6 carefully selected fromstrong gravitational lensing systems with both X-ray satelliteobservations and optical giant luminous arcs, is also used toconstrain three dark energy models (ΛCDM, constant w andCPL) under a flat universe assumption. For the full sample (n = 80)and the restricted sample (n = 46) including 36 two-image lenses and10 strong lensing arcs, we obtain relatively good fitting values ofbasic cosmological parameters, which generally agree with theresults already known in the literature. This results encouragesfurther development of this method and its use on larger samplesobtained in the future.

SOURCE-PLANE RECONSTRUCTION OF THE BRIGHT LENSED GALAXY RCSGA 032727-132609

We present new HST/WFC3 imaging data of RCSGA 032727-132609, a bright lensed galaxy at z=1.7 that is magnified and stretched by the lensing cluster RCS2 032727-132623. Using this new high-resolution imaging, we modify our previous lens model (which was based on ground-based data) to fully understand the lensing geometry, and use it to reconstruct the lensed galaxy in the source plane. This giant arc represents a unique opportunity to peer into 100-pc scale structures in a high-redshift galaxy. This new source reconstruction will be crucial for a future analysis of the spatially-resolved rest-UV and rest-optical spectra of the brightest parts of the arc.

Combined strong and weak lensing analysis of 28 clusters from the Sloan Giant Arcs Survey★

We study the mass distribution of a sample of 28 galaxy clusters using strong and weak lensing observations. The clusters are selected via their strong lensing properties as part of the Sloan Giant Arcs Survey (SGAS) from the Sloan Digital Sky Survey (SDSS). Mass modelling of the strong lensing information from the giant arcs is combined with weak lensing measurements from deep Subaru/Suprime-cam images to primarily obtain robust constraints on the concentration parameter and the shape of the mass distribution. We find that the concentration c_vir is a steep function of the mass, c_vir \propto M_vir^-0.59\pm0.12, with the value roughly consistent with the lensing-bias-corrected theoretical expectation for high mass (10^15 h^-1 M_sun) clusters. However, the observationally inferred concentration parameters appear to be much higher at lower masses (10^14 h^-1 M_sun), possibly a consequence of the modification to the inner density profiles provided by baryon cooling. The steep mass-concentration relation is also supported from direct stacking analysis of the tangential shear profiles. In addition, we explore the two-dimensional shape of the projected mass distribution by stacking weak lensing shear maps of individual clusters with prior information on the position angle from strong lens modelling, and find significant evidence for a large mean ellipticity with the best-fit value of e = 0.47 \pm 0.06 for the mass distribution of the stacked sample. We find that the luminous cluster member galaxy distribution traces the overall mass distribution very well, although the distribution of fainter cluster galaxies appears to be more extended than the total mass.

BROADBAND PHOTOMETRY OF 105 GIANT ARCS: REDSHIFT CONSTRAINTS AND IMPLICATIONS FOR GIANT ARC STATISTICS

We measure the photometric properties of 105 giant arcs that were identified in systematic searches for galaxy-cluster-scale strong lenses in the Second Red-Sequence Cluster Survey (RCS-2) and the Sloan Digital Sky Survey (SDSS). The cluster lenses span 0.2 < z_lens < 1.2 in redshift, with a median z_lens = 0.58. Using broadband color criteria we sort the entire arc sample into redshift bins based on u-g and g-r colors, and also r-z colors for the ~90% of arcs that have z-band data. This analysis yields broad redshift constraints with 71 +5 -4 % of the arcs at z > 1.0, 64 +6 -4 % at z > 1.4, 56 +5 -4 % at z > 1.9, and 21 +4 -2 % at z > 2.7. The remaining 29 +3 -5 % have z < 1. The inferred median redshift is z_s = 2.0 +/- 0.1, in good agreement with a previous determination from a smaller sample of brighter arcs (g < 22.5). This agreement confirms that z_s = 2.0 +/- 0.1 is the typical redshift for giant arcs with g < 24 that are produced by cluster-scale strong lenses, and that there is no evidence for strong evolution in the redshift distribution of arcs over a wide range of g-band magnitudes (20 < g < 24). Establishing that half of all giant arcs are at z > 2 contributes significantly toward relieving the tension between the number of arcs observed and the number expected in a Lambda-CDM cosmology, but there is considerable evidence to suggest that a discrepancy persists. Additionally, this work confirms that forthcoming large samples of giant arcs will supply the observational community with many magnified galaxies at z > 2.

Structural sequence and geochronology of the Qomo Ri accretionary complex, Central Qiangtang, Tibet: Implications for the Late Triassic subduction of the Paleo-Tethys Ocean

The Late Paleozoic Qomo Ri Accretionary Complex (QRAC) in the Central Qiangtang region of Tibet lies at the southern margin of the Longmu Co–Shuanghu suture. QRAC is tectonically linked with the Nierong and Jitang metamorphic complexes in eastern Tibet and the Yunling and Lancang complexes in western Yunnan province, SW China. This metamorphic complex is mainly composed of Late Paleozoic passive continental marginal strata of the South Qiangtang basin, which was underthrust beneath North Qiangtang in the Late Triassic. At least three stages of deformation, D1, D2 and D3, with two corresponding metamorphic events, M1 and M2, were identified within the QRAC. D1 is characterized by a penetrative foliation, S1, bearing a dextral shear and a corresponding M1 mineral assemblage of phengite, garnet and quartz. This deformation was interpreted to be the result of the northwestward oblique subduction of the Paleo-Tethys Ocean and dated at 211–219Ma by phengite 40Ar/39Ar ages. D2, a subsequent compression deformation, followed D1 immediately and exhibits flexural folds and pervasive axial crenulation in foliation S2. Deformations from D1 to D2 indicate that an oblique oceanic subduction was immediately followed by a collision between the North and South Qiangtang blocks along the Longmu Co–Shuanghu suture. The D3, recorded by minor folds and divisional axial cleavage (S3), is related to a giant arc structure with an extension of ~50km.

Cluster lenses

Clusters of galaxies are the most recently assembled, massive, bound structures in the Universe. As predicted by General Relativity, given their masses, clusters strongly deform space-time in their vicinity. Clusters act as some of the most powerful gravitational lenses in the Universe. Light rays traversing through clusters from distant sources are hence deflected, and the resulting images of these distant objects therefore appear distorted and magnified. Lensing by clusters occurs in two regimes, each with unique observational signatures. The strong lensing regime is characterized by effects readily seen by eye, namely, the production of giant arcs, multiple-images, and arclets. The weak lensing regime is characterized by small deformations in the shapes of background galaxies only detectable statistically. Cluster lenses have been exploited successfully to address several important current questions in cosmology: (i) the study of the lens(es) - understanding cluster mass distributions and issues pertaining to cluster formation and evolution, as well as constraining the nature of dark matter; (ii) the study of the lensed objects - probing the properties of the background lensed galaxy population - which is statistically at higher redshifts and of lower intrinsic luminosity thus enabling the probing of galaxy formation at the earliest times right up to the Dark Ages; and (iii) the study of the geometry of the Universe - as the strength of lensing depends on the ratios of angular diameter distances between the lens, source and observer, lens deflections are sensitive to the value of cosmological parameters and offer a powerful geometric tool to probe Dark Energy. In this review, we present the basics of cluster lensing and provide a current status report of the field.

A PETAL OF THE SUNFLOWER: PHOTOMETRY OF THE STELLAR TIDAL STREAM IN THE HALO OF MESSIER 63 (NGC 5055)

We present surface photometry of a very faint, giant arc feature in the halo of the nearby spiral galaxy NGC 5055 (M63) that is consistent with being a part of a stellar stream resulting from the disruption of a dwarf satellite galaxy. This faint feature was first detected in early photographic studies by van der Kruit (1979); more recently by Mart\'inez-Delgado et al. (2010) and as presented in this work, the loop has been realized to be the result of a recent minor merger through evidence obtained by deep images taken with a telescope of only 0.16 m aperture. The stellar stream is confirmed in additional images taken with the 0.5 m of the BlackBird Remote Observatory and the 0.8 m of the McDonald Observatory. This low surface brightness structure around the disk of the galaxy extends ~29 kpc from its center, with a projected width of 3.3 kpc. The stream's morphology is consistent with that of the visible part of a "great-circle" stellar stream originating from the accretion of a ~10^8 M_sun dwarf satellite in the last few Gyr. The progenitor satellite's current position and fate are not conclusive from our data. The color of the stream's stars is consistent with Local Group dwarfs and is similar to the outer regions of M63's disk and stellar halo. We detect other low surface brightness "plumes"; some of these may be extended spiral features related to the galaxy's complex spiral structure and others may be tidal debris associated with the disruption of the galaxy's outer stellar disk as a result of the accretion event. We differentiate between features related to the tidal stream and faint, blue features in the outskirts of the galaxy's disk previously detected by the GALEX satellite. With its highly warped HI gaseous disk (~20 deg), M63 represents one of several examples of an isolated spiral galaxy with a warped disk showing strong evidence of an ongoing minor merger.

Lensing clusters of galaxies in the SDSS-III

We identify new strong lensing clusters of galaxies from the Sloan Digital Sky Survey III (SDSS DR8) by visually inspecting color images of a large sample of clusters of galaxies. We find 68 new clusters showing giant arcs in addition to 30 known lensing systems. Among 68 cases, 13 clusters are “almost certain" lensing systems with tangential giant arcs, 22 clusters are “probable" and 31 clusters are “possible" lensing systems. We also find two exotic systems with blue rings. The giant arcs have angular separations of 2.0″–25.7″ from the bright central galaxies. We note that the rich clusters are more likely to be lensing systems and the separations between the arcs and the central galaxies increase with cluster richness.

Combining optical and X-ray observations of galaxy clusters to constrain cosmological parameters

Galaxy clusters present unique advantages for cosmological study. Here we collect a new sample of 10 lensing galaxy clusters with X-ray observations to constrain cosmological parameters. The redshifts of the lensing clusters lie between 0.1 and 0.6, and the redshift range of their arcs is from 0.4 to 4.9. These clusters are selected carefully from strong gravitational lensing systems which have both X-ray satellite observations and optical giant luminous arcs with known redshifts. Giant arcs usually appear in the central region of clusters, where mass can be traced with luminosity quite well. Based on gravitational lensing theory and a cluster mass distribution model, we can derive a ratio using two angular diameter distances. One is the distance between lensing sources and the other is that between the deflector and the source. Since angular diameter distance relies heavily on cosmological geometry, we can use these ratios to constrain cosmological models. Moreover, X-ray gas fractions of galaxy clusters can also be a cosmological probe. Because there are a dozen parameters to be fitted, we introduce a new analytic algorithm, Powell's UOBYQA (Unconstrained Optimization By Quadratic Approximation), to accelerate our calculation. Our result demonstrates that this algorithm is an effective fitting method for such a continuous multi-parameter constraint. We find an interesting fact that these two approaches are separately sensitive to ΩΛ and ΩM. By combining them, we can get reasonable fitting values of basic cosmological parameters: ΩM = 0.26+0.04−0.04, and ΩΛ = 0.82+0.14−0.16.

The effects of primordial non-Gaussianity on giant-arc statistics

For over a decade, it has been debated whether the concordance Λ cold dark matter (ΛCDM) model is consistent with the observed abundance of giant arcs in clusters. While previous theoretical studies have focused on properties of the lens and source populations, as well as cosmological effects such as dark energy, the impact of initial conditions on the giant-arc abundance is relatively unexplored. Here, we quantify the impact of non-Gaussian initial conditions with the local bispectrum shape on the predicted frequency of giant arcs. Using a path-integral formulation of the excursion set formalism, we extend a semi-analytic model for calculating halo concentrations to the case of primordial non-Gaussianity, which may be useful for applications outside of this work. We find that massive haloes tend to collapse earlier in models with positive fNL, relative to the Gaussian case, leading to enhanced concentration parameters. The converse is true for fNL < 0. In addition to these effects, which change the lensing cross-sections, non-Gaussianity also modifies the abundance of supercritical clusters available for lensing. These combined effects work together to either enhance (fNL > 0) or suppress (fNL < 0) the probability of giant-arc formation. Using the best value and 95 per cent confidence levels currently available from the Wilkinson Microwave Anisotropy Probe, we find that the giant-arc optical depth for sources at zs∼ 2 is enhanced by ∼20 and ∼45 per cent for fNL= 32 and 74, respectively. In contrast, we calculate a suppression of ∼5 per cent for fNL=−10. These differences translate to similar relative changes in the predicted all-sky number of giant arcs.