Radial Arcs Research Articles

RXJ0437+00: constraining dark matter with exotic gravitational lenses

ABSTRACT We present the first strong-gravitational-lensing analysis of the galaxy cluster RX J0437.1+0043 (RXJ0437; z = 0.285). Newly obtained, deep MUSE observations, Keck/MOSFIRE near-infrared spectroscopy, and Hubble Space Telescope SNAPshot imaging reveal 13 multiply imaged background galaxies, three of them (at z = 1.98, 2.97, and 6.02, respectively) in hyperbolic umbilic (H–U) lensing configurations. The H–U images are located only 20–50 kpc from the cluster centre, i.e. at distances well inside the Einstein radius where images from other lens configurations are demagnified and often unobservable. Extremely rare (only one H–U lens was known previously) these systems are able to constrain the inner slope of the mass distribution – and unlike radial arcs, the presence of H–U configurations is not biased towards shallow cores. The galaxies lensed by RXJ0437 are magnified by factors ranging from 30 to 300 and (in the case of H–U systems) stretched nearly isotropically. Taking advantage of this extreme magnification, we demonstrate how the source galaxies in H–U systems can be used to probe for small-scale (∼109 M⊙) substructures, providing additional insight into the nature of dark matter.

Constraining the cross-section of dark matter with giant radial arcs in galaxy clusters

ABSTRACT We compare the statistics and morphology of giant arcs in galaxy clusters using N-body and non-radiative SPH simulations within the standard cold dark matter (CDM) model and simulations where dark matter (DM) has a non-negligible probability of interaction (parametrized by its cross-section), i.e self-interacting dark matter (SIDM). We use a ray-tracing technique to produce a statistically large number of arcs around six simulated galaxy clusters at different redshifts. Since DM is more likely to interact in colliding clusters than in relaxed clusters, and this probability of interaction is largest in denser regions, we focus our analysis on radial arcs (which trace the lensing potential in the central region better than tangential arcs) in galaxy clusters that underwent (or are undergoing) a major merger. We find that SIDM produces fewer radial arcs than standard CDM but they are on average more magnified. We also appreciate differences in the arc morphology that could be used to statistically favour one model versus the other.

Constraining the abundance of dark matter in the central region of the galaxy cluster MACS J1206.2−0847 with a free-form strong lensing analysis

We performed a free-form strong lensing analysis of the galaxy cluster MACS J1206.2−0847 in order to estimate and constrain its inner dark matter distribution. The free-form method estimates the cluster total mass distribution without using any prior information about the underlying mass. We used 97 multiple lensed images belonging to 27 background sources and derived several models, which are consistent with the data. Among these models, we focus on those that better reproduce the radial images that are closest to the centre of the cluster. These radial images are the best probes of the dark matter distribution in the central region and constrain the mass distribution down to distances ∼7 kpc from the centre. We find that the morphology of the innermost radial arcs is due to the elongated morphology of the dark matter halo. We estimate the stellar mass contribution of the brightest cluster galaxy and subtracted it from the total mass in order to quantify the amount of dark matter in the central region. We fitted the derived dark matter density profile with a gNFW, which is characterised byrs= 167 kpc,ρs= 6.7 × 106 M⊙kpc−3, andγgNFW= 0.70. These results are consistent with a dynamically relaxed cluster. This inner slope is smaller than the cannonicalγ = 1 predicted by standard CDM models. This slope does not favour self-interacting models for which a shallower slope would be expected.

Preliminary study of shaping the railway track geometry in terms of their maintenance costs and capacity

In Poland, due to the increase in investments made by railways in recent years, and thus the increase in the replacement value of transport infrastructure, the need for expenditure on infrastructure maintenance will increase in the next 30 years, or the development of the developed transport network will degrade. As part of the overall discipline of resource management, subdiscipline has emerged - infrastructure asset management. As part of the management of railway transport infrastructure, the demand for cheaper maintenance costs will grow. The cost reduction of infrastructure maintenance is possible through meticulous assessment of its condition, rational selection of locations and scope of repairs at the assumed risk level, as well as at the stage of preparation of new construction or modernization projects taking into account aspects of later maintenance. For some time, we have been observing the accumulation of knowledge (methods, programs, procedures) in the country and abroad enabling optimization of infrastructure condition assessment and programming of its maintenance. The implementation of these solutions may result in a more rational use of funds for infrastructure maintenance and not disturb its smooth functioning in operation. The article discusses aspects that should be considered in the design process of railway infrastructure. Particular attention was paid to the durability of steel components of the railway superstructure, maintenance costs as well as aspects related to the capacity of the track node. An example of dependence of selected values of radial arcs depending on their durability and maintenance costs was presented. It was proposed to change the track layout at the Warszawa Srodmiescie passenger stop planned for reconstruction. Calculations of kinematic parameters for various configurations of railway turnouts were performed. Also, calculations of the capacity for the existing track system solution as well as the proposed track system after reconstruction of the analysed Warszawa Srodmiescie railway station were also carried out.

Laser direct writing of complex radially varying single-mode polymer waveguide structures

Increasing board-to-board and chip-to-chip computational data rates beyond 12.5 Gbs will require the use of single-mode polymer waveguides (WGs) that have high bandwidths and are able to be wavelength division multiplexed. Laser direct writing (LDW) of polymer WGs provides a scalable and reconfigurable maskless procedure compared to common photolithography fabrication. LDW of straights and radial curves are readily achieved using predefined drive commands of the two-axis direct drive linear stage system. Using the laser direct write process for advanced WG structures requires stage-drive programming techniques that account for specified polymer material exposure durations. Creating advanced structures such as WG S-bends into single-mode polymer WG builds provides designers with the ability to affect pitch control, optical coupling, and reduce footprint requirements. Fabrication of single-mode polymer WG segmented radial arcs is achieved through a smooth radial arc user-programmed defined mathematical algorithm. Cosine and raised-sine S-bends are realized through a segmentation method where the optimal incremental step length and bend dimensions are controlled to achieve minimal structure loss. Laser direct written S-bends are compared with previously published photolithographic S-bend results using theoretical bend loss models. Fabrication results show that LDW is a viable method in the fabrication of advanced polymer WG structures.

Lensing effects in inhomogeneous cosmological models

Concepts developed in the gravitational lensing techniques such as shear, convergence, tangential, and radial arcs maybe used to see how tenable inhomogeneous models proposed to explain the acceleration of the universe models are. We study the widely discussed Lemaitre-Tolman-Bondi (LTB) cosmological models. It turns out that for the observer sitting at origin of a global LTB solution the shear vanishes as in the Friedmann-Robertson-Walker models, while the value of convergence is different, which may lead to observable cosmological effects. We also consider Swiss-cheese models proposed recently based on LTB with an observer sitting in the Friedmann-Robertson-Walker part. It turns out that they have different behavior as far as the formation of radial and tangential arcs are concerned.

Comparisons between Isothermal and NFW Mass Profiles for Strong‐Lensing Galaxy Clusters

While both isothermal and NFW-based mass models for galaxy clusters are widely adopted in strong-lensing studies, they cannot easily be distinguished based solely on observed positions of arcs and arclets. We compare the magnifications predicted for giant arcs obtained from isothermal and NFW profiles, taking axially symmetric and asymmetric mass distributions into account. We find that arc magnifications can differ strongly between the two types of density profile even if the image morphology is well reproduced. Magnifications by lenses with NFW density profiles are usually larger than those for lenses with singular or nearly singular isothermal density profiles, unless the latter have large cores. Asymmetries play an important role. We illustrate our results with the two well-studied clusters, MS 2137 and A370. We confirm earlier results showing that both isothermal and NFW mass models can very well reproduce the observed arcs, radial arcs, and other arclets. While the mass model for MS 2137 is not very well constrained, the two types of mass models produce strongly differing critical curves and caustics for A370. We find that the NFW mass profile is preferred for A370. We identify new arclet candidates in the field of A370. Redshift estimates allowed by the lens model are consistent with results in the literature, where available. Three newly found counterimages are suggested to arise from an active, dust-enshrouded star-forming galaxy at z approximate to 1.1.

A Systematic Search for Gravitationally Lensed Arcs in theHubble Space TelescopeWFPC2 Archive

We present the results of a systematic search for gravitationally lensed arcs in clusters of galaxies located in the Hubble Space Telescope Wide Field and Planetary Camera 2 data archive. By carefully examining the images of 128 clusters we have located 12 candidate radial arcs and 104 tangential arcs, each of whose length-to-width ratio exceeds 7. In addition, 24 other radial arc candidates were identified with a length-to-width ratio of less than 7. Keck spectroscopy of 17 candidate radial arcs suggests that contamination of the radial arc sample from nonlensed objects is ~30%-50%. With our catalog, we explore the practicality of using the number ratio of radial to tangential arcs as a statistical measure of the slope β of the dark matter distribution in cluster cores (where ρDM r-β at small radii). Despite the heterogeneous nature of the cluster sample, we demonstrate that this abundance ratio is fairly constant across various cluster subsamples partitioned according to X-ray luminosity and optical survey depth. We develop the necessary formalism to interpret this ratio in the context of two-component mass models for cluster cores. Although the arc statistics in our survey are consistent with a range of density profiles—β 1.6 depending on various assumptions—we show that one of the prime limiting factors is the distribution of stellar masses for the brightest cluster galaxies. We discuss the prospects for improving the observational constraints and thereby providing a reliable statistical constraint on cluster dark matter profiles on 100 kpc scales.

Strong Lensing Analysis of A1689 from Deep ACS Images

ACS observations of massive lensing clusters permit an order of magnitude increase in the numbers of multiply-lensed background galaxies identified behind a given cluster. We have developed a code to take the pixels belonging to any given image and generate counter-images with full resolution, so that multiple systems are convincingly and exhaustively identified. Over 130 images of 35 multiply lensed galaxies are found behind A1689, including many radial arcs and also tiny counter-images projected on the center of mass. The derived mass profile is found to flatten steadily towards the center, like and NFW profile, with a mean slope $d{\log{\Sigma}}/d{\log{r}}\approx-0.55\pm0.1$ , over the range $r kpc/h, which is somewhat steeper than predicted for such a massive halo. We also clearly see the expected geometric increase of bend angles with redshift, however, given the low redshift of A1689, $z=0.18$ , the dependence on cosmological parameters is weak, but using higher redshift clusters from our GTO program we may derive a more competitive constraint. To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

Lensing & Dynamics in the Galaxy Cluster MS2137-23

We present a new model of the lensing cluster of galaxies MS2137-23. By incorporating strong and weak lensing data in a fully elliptical lens modeling, we show that the total density profile must be close to the predictions of numerical simulations with an inner slope well consistent with a NFW profile. The model that best fits the lensing constraints is used to infer to line-of-sight velocity distribution (LOSVD) of stars in the central cD galaxy. This distribution is found to be far from Maxwellian. The important non-Gaussian tails produce a significant low-bias when measuring the velocity dispersion by assuming Gaussian absorption lines. In the case of MS2137, most of the information comes from multiples arcs. Internal kinematics of stars only help modeling the innermost kiloparsecs. However, in clusters with fewer constraints (no radial arcs for instance), a detailed modeling of both strong lensing and internal kinematics is crucial.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

The impact of cluster mergers on arc statistics

We study the impact of merger events on the strong lensing properties of galaxy clusters. Previous lensing simulations were not able to resolve dynamical time scales of cluster lenses, which arise on time scales which are of order a Gyr. In this case study, we first describe qualitatively with an analytic model how some of the lensing properties of clusters are expected to change during merging events. We then analyse a numerically simulated lens model for the variation in its efficiency for producing both tangentia l and radial arcs while a massive substructure falls onto the main cluster body. We find that: ( 1) during the merger, the shape of the critical lines and caustics changes substantially; (2) the lensing cross sections for long and thin arcs can grow by one order of magnitude and reach their maxima when the extent of the critical curves is largest; (3) the cross section for radial arcs also grows, but the cluster can efficiently produce this kind of arcs only while the merging substructure crosses the main cluster centre; (4) while the arc cross sections pass through their m axima as the merger proceeds, the cluster’s X-ray emission increases by a factor of ∼ 5. Thus, we conclude that accounting for these dynamical processes is very important for arc statist ics studies. In particular, they may provide a possible explanation for the arc statistics probl em.

The Dark Matter Distribution in the Central Regions of Galaxy Clusters: Implications for Cold Dark Matter

We have undertaken a spectroscopic survey of gravitational arcs in a carefully chosen sample of six clusters each containing a dominant brightest cluster galaxy. We use these systems to study the relative distributions of dark and baryonic material in the central regions. Three clusters present both radial and tangential arcs and provide particularly strong constraints on the mass profiles, whereas the other three display only tangential arcs and act as a control set. We analyze stellar velocity dispersion data for the brightest cluster galaxies in conjunction with the arc redshifts and lens models to constrain the dark and baryonic mass profiles jointly. For the systems containing radial arcs we find that the inner dark matter density profile is consistent with a 3-D distribution, rho_{DM} propto r^-beta, with logarithmic slope <beta>=0.52^{+0.05}_{-0.05} (68% CL). Similarly, we find that the tangential arc sample gives an upper limit, beta<0.57 (99% CL). Taking the 6 clusters together, the mean dark matter distribution is quite inconsistent with the standard Navarro, Frenk & White (1997) value, beta=1.0, at >99% confidence. In addition, we find considerable cosmic scatter in the beta (Delta beta ~0.3) values of the radial arc sample. We find no evidence that systems with radial arcs preferentially yield flatter dark matter profiles as might be expected if they were a biased subset. We discuss the validity of our 1-D mass reconstruction method and verify its conclusions by comparing with results of a more rigorous ray-tracing lensing code. Our results extend and strengthen the earlier conclusions presented by Sand et al. (2002) and suggest the relationship between dark and visible matter in the cores of clusters is more complex than anticipated from recent simulations. (abridged)

The dark matter halos of spheroidal galaxies and clusters of galaxies

We describe the first results from two observational projects aimed at measuring the amount and spatial distribution of dark matter in distant early-type galaxies (E/S0s) and clusters of galaxies. At the galaxy scale, the Lenses Structure and Dynamics (LSD) Survey is gathering kinematic data for distant (up to z ⋐ 1) E/S0s that are gravitational lenses. A joint lensing and dynamical analysis constrains the fraction of dark matter within the Einstein radius, the mass-to-light ratio of the stellar component, and the total slope of the mass density profile. These properties and their evolution with redshift are briefly discussed in terms of the formation and evolution of E/S0 galaxies and measurement of the Hubble Constant from gravitational time delay systems. At the cluster scale – after careful removal of the stellar component with a joint lensing and dynamical analysis – systems with giant radial arcs can be used to measure precisely the inner slope of the dark matter halo. An HST search for radial arcs and the analysis of a first sample are briefly discussed in terms of the universal dark matter halos predicted by CDM simulations.

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.

The Dark Matter Density Profile of the Lensing Cluster MS 2137−23: A Test of the Cold Dark Matter Paradigm

We present new spectroscopic observations of the gravitational arcs and the brightest cluster galaxy (BCG) in the cluster MS 2137-23 (z = 0.313) obtained with the Echelle Spectrograph and Imager on the Keck II telescope. We find that the tangential and radial arcs arise from sources at almost identical redshifts (z = 1.501, 1.502). We combine the measured stellar velocity dispersion profile of the BCG with a lensing analysis to constrain the distribution of dark and stellar matter in the central 100 kpc of the cluster. Our data indicate a remarkably flat inner slope for the dark matter profile, ?d r-?, with ? < 0.9 at a 99% CL. Steep inner slopes obtained in cold dark matter cosmological simulations?such as Navarro, Frenk, & White (? = 1) or Moore (1.5) universal dark matter profiles?are ruled out at better than 99% CL. As baryon collapse is likely to have steepened the dark matter profile from its original form, our data provide a powerful test of the cold dark matter paradigm at the cluster mass scale.

Systematic Effects on Tangential and Radial Arc Statistics: The Finite Source Size and Ellipticities of the Lens and Source

It has been recognized that the arc statistics of gravitational lensing are a useful probe of the density profile of clusters of galaxies. We examine several systematic effects that are important in predicting the number of arcs, with particular attention to the difference between tangential and radial arcs. First, we derive an analytic expression for the cross section for radial arcs taking account of the source size and find that a moderate source size enhances the cross section for radial arcs, while a larger source size (≳1'' in our example) suppresses the number of radial arcs. On the other hand, tangential arcs are much less sensitive to the source size. Next, we numerically calculate the cross section for arcs considering the lens and source ellipticities. We find that the numbers of both tangential and radial arcs are highly enhanced by both ellipticities, by 1 or 2 orders of magnitude. The number ratio of radial to tangential arcs is, however, not so affected if the threshold axis ratio of arcs is large (≳7). The number ratio therefore still remains a good statistic for probing the density profile of lens objects if the source-size effect is correctly taken into account.

Source Ellipticity and the Statistics of Lensed Arcs

The statistics of gravitationally lensed arcs, which can be used for a variety of cosmological tests, are sensitive to the intrinsic shapes of the source galaxies. I present an analytic formalism that makes it simple to include elliptical sources in analytic calculations of lens statistics. For cuspy lens models, sources with an axis ratio of 2:1 enhance the total number of arcs longer than 10:1 by a factor of order 2, while modestly decreasing the number ratio of radial arcs to tangential arcs. Source ellipticity is therefore an important systematic effect in detailed quantitative studies, but it should not hinder cosmological applications such as attempts to constrain cluster dark matter profiles with arc statistics.

Probing the Core Structure of Dark Halos with Tangential and Radial Arc Statistics

We study the arc statistics of gravitational lensing generated by dark matter halos in order to probe their density profile. We characterize the halo profile by two parameters, the inner slope of the central cusp α and the median amplitude of the concentration parameter, cnorm, for a halo of mass 1014 h-1 M☉ at z = 0 and compute the numbers of tangential and radial arcs produced by gravitational lensing of galaxy clusters. We find that the number of arcs divided by the number of halos is a good statistic that is sensitive to both cnorm and α with very weak dependence on the cosmological parameters. If arc samples with well-defined selection criteria for the clusters become available, one can strongly constrain both cnorm and α. While our tentative comparison with the existing observational data indicates that the inner density profile of dark halos is indeed as steep as predicted by recent simulations (α ~ 1.5), homogeneous samples of tangential and radial arcs are required for more quantitative discussions.

Radial Arc Statistics: A Powerful New Probe of the Central Density Profile of Galaxy Clusters

We show that the number ratio of radial arcs to tangential arcs in a cluster of galaxies depends sensitively on the central density profile of galaxy clusters but depends little on the lensing parameter and the threshold ellipticity of the lensed images. Based on these results, we propose a method to constrain the central density profile of clusters using radial arc statistics. A tentative comparison with the observations shows that radial arc statistics can be a powerful tool for constraining the cluster central density profile. Our results show that a systematic survey of radial and tangential arcs for an unbiased uniform cluster sample can be a promising test of the fundamental characteristics of dark matter.

Giant cluster arcs as a constraint on the scattering cross-section of dark matter

We carry out ray tracing through five high resolution simulations of a galaxy cluster to study how its ability to produce giant gravitationally lensed arcs is influenced by the collision cross-section of its dark matter. In three cases typical dark matter particles in the cluster core undergo between 1 and 100 collisions per Hubble time; two more explore the long (``collisionless'') and short (``fluid'') mean free path limits. We study the size and shape distributions of arcs and compute the cross-section for producing ``extreme'' arcs of various sizes. Even a few collisions per particle modify the core structure enough to destroy the cluster's ability to produce long, thin arcs. For larger collision frequencies the cluster must be scaled up to unrealistically large masses before it regains the ability to produce giant arcs. None of our models with self-interacting dark matter (except the ``fluid'' limit) is able to produce radial arcs; even the case with the smallest scattering cross-section must be scaled to the upper limit of observed cluster masses before it produces radial arcs. Apparently the elastic collision cross-section of dark matter in clusters must be very small, below 0.1 cm^2 g^-1, to be compatible with the observed ability of clusters to produce both radial arcs and giant arcs.