A Remark on Using Gravitational Lensing Probability as a Probe of the Central Regions of CDM Halos

We calculate the gravitational lensing probabilities by cold dark matter (CDM) halos with different density profiles, and compare them with current observations from the Cosmic Lens All-Sky Survey (CLASS) and the Jodrell-Bank VLA Astrometric Survey (JVAS). We find that the lensing probability is dramatically sensitive to the clumping of the dark matter, or quantitatively, the concentration parameter. We also find that our predicted lensing probabilities in most cases show inconsistency with the observations. It is argued that high lensing probability may not be an effective tool for probing the statistical properties of inner structures of dark matter halos.     

重子物质对暗物质晕形状和角动量的影响

利用高精度大样本的冷暗物质($\Lambda$ cold dark matter, $\Lambda$CDM)宇宙学数值模拟的数据, 对重子物质如何影响暗物质晕的形状和角动量进行了研究.使用了3种数值模拟数据, 纯暗物质模拟、含辐射冷却、恒星形成和动力学超新星反馈的模拟, 包含活动星系核反馈效应的恒星形成模拟. 对这3种模拟, 还进行了不同红移处的比较. 主要结果如下.重子物理过程会改变暗物质晕的质量分布, 特别是有活动星系核反馈机制的情况下.比如, 活动星系核反馈会减少大质量暗物质晕的形成.随着宇宙的演化, 暗物质晕的空间形态逐渐由扁变圆. 重子物质的存在会加速暗物质晕形状的变化过程, 而且会使暗物质晕形状变得更圆. 但是活动星系核的反馈会对这一加速效应产生抑制.重子物质对暗物质晕的影响与暗物质晕的质量和半径都存在一定的依赖性.暗物质晕的质量越大, 它会呈现更扁的形态. 同时, 重子物质对任意质量的暗物质晕或暗物质晕在任意半径处的变圆均有一定的促进作用,尽管活动星系核反馈会抑制这一促进作用.特别是对于暗物质晕在0.2--0.6倍维里半径处的形状, 重子物质的影响尤为明显.此外, 重子物质的存在会对暗物质晕的角动量产生显著影响, 它会增大暗物质的角动量. 暗物质晕的自旋参数与质量无相关性, 但是与暗物质晕的半径存在一定的相关性.     

Galaxy density profiles and shapes – II. Selection biases in strong lensing surveys

Many current and future astronomical surveys will rely on samples of strong gravitational lens systems to draw conclusions about galaxy mass distributions. We use a new strong lensing pipeline (presented in Paper I of this series) to explore selection biases that may cause the population of strong lensing systems to differ from the general galaxy population. Our focus is on point-source lensing by early-type galaxies with two mass components (stellar and dark matter) that have a variety of density profiles and shapes motivated by observational and theoretical studies of galaxy properties. We seek not only to quantify but also to understand the physics behind selection biases related to: galaxy mass, orientation and shape; dark matter profile parameters such as inner slope and concentration; and adiabatic contraction. We study how all of these properties affect the lensing Einstein radius, total cross-section, quad/double ratio and image separation distribution, with a flexible treatment of magnification bias to mimic different survey strategies. We present our results for two families of density profiles: cusped and deprojected Sérsic models. While we use fixed lens and source redshifts for most of the analysis, we show that the results are applicable to other redshift combinations, and we also explore the physics of how our results change for very different redshifts. We find significant (factors of several) selection biases with mass; orientation, for a given galaxy shape at fixed mass; cusped dark matter profile inner slope and concentration; concentration of the stellar and dark matter deprojected Sérsic models. Interestingly, the intrinsic shape of a galaxy does not strongly influence its lensing cross-section when we average over viewing angles. Our results are an important first step towards understanding how strong lens systems relate to the general galaxy population.     

A comparison of different cluster mass estimates: consistency or discrepancy?

Rich and massive clusters of galaxies at intermediate redshift are capable of magnifying and distorting the images of background galaxies. A comparison of different mass estimators among these clusters can provide useful information about the distribution and composition of cluster matter and its dynamical evolution. Using the hitherto largest sample of lensing clusters drawn from the literature, we compare the gravitating masses of clusters derived from the strong/weak gravitational lensing phenomena, from the X-ray measurements based on the assumption of hydrostatic equilibrium, and from the conventional isothermal sphere model for the dark matter profile characterized by the velocity dispersion and core radius of galaxy distributions in clusters. While there is excellent agreement between the weak lensing, X-ray and isothermal sphere model-determined cluster masses, these methods are likely to underestimate the gravitating masses enclosed within the central cores of clusters by a factor of 2–4 as compared with the strong lensing results. Such a mass discrepancy has probably arisen from the inappropriate applications of the weak lensing technique and the hydrostatic equilibrium hypothesis to the central regions of clusters, as well as from assuming an unreasonably large core radius for both luminous and dark matter profiles. Nevertheless, it is pointed out that these cluster mass estimators may be safely applied on scales greater than the core sizes. Namely, the overall clusters of galaxies at intermediate redshift can still be regarded as the dynamically relaxed systems, in which the velocity dispersion of galaxies and the temperature of X-ray emitting gas are good indicators of the underlying gravitational potentials of clusters.     

Galaxy density profiles and shapes – I. Simulation pipeline for lensing by realistic galaxy models

Studies of strong gravitational lensing in current and upcoming wide and deep photometric surveys, and of stellar kinematics from (integral-field) spectroscopy at increasing redshifts, promise to provide valuable constraints on galaxy density profiles and shapes. However, both methods are affected by various selection and modelling biases, which we aim to investigate in a consistent way. In this first paper in a series, we develop a flexible but efficient pipeline to simulate lensing by realistic galaxy models. These galaxy models have separate stellar and dark matter components, each with a range of density profiles and shapes representative of early-type, central galaxies without significant contributions from other nearby galaxies. We use Fourier methods to calculate the lensing properties of galaxies with arbitrary surface density distributions, and Monte Carlo methods to compute lensing statistics such as point-source lensing cross-sections. Incorporating a variety of magnification bias modes lets us examine different survey limitations in image resolution and flux. We rigorously test the numerical methods for systematic errors and sensitivity to basic assumptions. We also determine the minimum number of viewing angles that must be sampled in order to recover accurate orientation-averaged lensing quantities. We find that for a range of non-isothermal stellar and dark matter density profiles typical of elliptical galaxies, the combined density profile and corresponding lensing properties are surprisingly close to isothermal around the Einstein radius. The converse implication is that constraints from strong lensing and/or stellar kinematics, which are indeed consistent with isothermal models near the Einstein radius, cannot trivially be extrapolated to smaller and larger radii.     

The dark matter environment of the Abell 901/902 supercluster: a weak lensing analysis of the HST STAGES survey

We present a high-resolution dark matter reconstruction of the   z = 0.165  Abell 901/902 supercluster from a weak lensing analysis of the Hubble Space Telescope STAGES survey. We detect the four main structures of the supercluster at high significance, resolving substructure within and between the clusters. We find that the distribution of dark matter is well traced by the cluster galaxies, with the brightest cluster galaxies marking out the strongest peaks in the dark matter distribution. We also find a significant extension of the dark matter distribution of Abell 901a in the direction of an infalling X-ray group Abell 901α. We present mass, mass-to-light and mass-to-stellar mass ratio measurements of the structures and substructures that we detect. We find no evidence for variation of the mass-to-light and mass-to-stellar mass ratio between the different clusters. We compare our space-based lensing analysis with an earlier ground-based lensing analysis of the supercluster to demonstrate the importance of space-based imaging for future weak lensing dark matter 'observations'.     

Using weak lensing to find halo masses

Since the strength of weak gravitational lensing is proportional to the mass along the line of sight, it might be possible to use lensing data to find the masses of individual dark matter clusters. Unfortunately, the effect on the lensing field of other matter along the line of sight is substantial. We investigate to what extent we can correct for these projection effects if we have additional information about the most massive halos along the line of sight from deep optical data. We do this by calculating the contributions of these line-of-sight halos to the lensing field and then subtracting off this effect. Three different approaches are used to calculate these contributions: the first approach uses the exact mass distribution of the line-of-sight halos, the second assumes the masses are known and uses the NFW model and the third approach uses richness as an estimator for mass and then also assumes the NFW model. We find that, whichever approach we take, unless we know the masses and positions of line-of-sight halos down to a very low mass, we can only correct for a small part of the line-of-sight projection. We conclude that if we try to use lensing data to find individual cluster masses, there is an error of about 15–20% due to line-of-sight projection that cannot be corrected for.     

Strong lensing optical depths in a ΛCDM 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.     

Gravitational lenses in the dark Universe

We discuss how different cosmological models of the Universe affect the probability that a background source has multiple images related by an angular distance, i.e., the optical depth of gravitational lensing. We examine some cosmological models for different values of the density parameter Ω _i : (i) the cold dark matter model, (ii) the ΛCDM model, (iii) the Bose-Einstein condensate dark matter model, (iv) the Chaplygin gas model, (v) the viscous fluid cosmological model and (vi) the holographic dark energy model by using the singular isothermal sphere (SIS) model for the halos of dark matter. We note that the dependence of the energy-matter content of the universe profoundly modifies the frequency of multiple quasar images.     

The dynamical state of RX J1347.5−1145 from a combined strong lensing and X-ray analysis

We perform a combined X-ray and strong lensing analysis of RX J1347.5−1145, one of the most luminous galaxy clusters at X-ray wavelengths. We show that evidence from strong lensing alone, based on published Very Large Telescope (VLT) and new Hubble Space Telescope ( HST ) data, strongly argues in favour of a complex structure. The analysis takes into account arc positions, shapes and orientations, and is done thoroughly in the image plane. The cluster inner regions are well fitted by a bimodal mass distribution, with a total projected mass of   M _tot= (9.9 ± 0.3) × 10¹⁴ M_⊙  h ⁻¹  within a radius of 360 kpc  h ⁻¹ (1.5 arcmin). Such a complex structure could be a signature of a recent major merger as further supported by X-ray data. A temperature map of the cluster, based on deep Chandra observations, reveals a hot front located between the first main component and an X-ray emitting south-eastern subclump. The map also unveils a filament of cold gas in the innermost regions of the cluster, most probably a cooling wake caused by the motion of the cD inside the cool core region. A merger scenario in the plane of the sky between two dark matter subclumps is consistent with both our lensing and X-ray analyses, and can explain previous discrepancies with mass estimates based on the virial theorem.     

Rotation in gravitational lenses

Gravitational lensing deflects light. A single lens deflector can only shear images, but cannot induce rotations. Multiple lens planes can induce rotations. Such rotations can be observed in quadruply imaged sources, and can be used to distinguish between two proposed solutions of the flux anomaly problem: substructures in lensing galaxies versus large-scale structure. We predict the expected amount of rotation due to large-scale structure in strong lensing systems, and show how this effect can be measured using ∼mas very long baseline interferometry astrometry of quadruple lenses with extended source structures. The magnitude of rotation is around 1°. The biggest theoretical uncertainty is the power spectrum of dark matter on very small scales. This procedure can potentially be turned around to measure the dark matter power spectrum on very small scales. We list the predicted rms rotation angles for several quadruple lenses with known lens and source redshifts.     

Low‐temperature primordial gas in merging halos

The thermal regime of the baryons behind shock waves arising in the process of virialization of dark matter halos is governed at certain conditions by radiation of HD lines. A small fraction of the shocked gas can cool down to the temperature of the cosmic microwave background (CMB). We estimate an upper limit for this fraction: at z = 10 it increases sharply from about q_T ∼ 10^–3 for dark halos of M = 5 × 10⁷ M_⊙ to ∼ 0.1 for halos with M = 10⁸ M_⊙. Further increase of the halo mass does not lead however to a significant growth of q_T – the asymptotic value for M ≫ 10⁸ M_⊙ is 0.3. We estimate the star formation rate associated with such shock waves, and show that they can provide a small but not negligible fraction of the star formation. We argue that extremely metal‐poor low‐mass stars in the Milky Way may have been formed from primordial gas behind such shocks. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Separation of the visible and dark matter in the Einstein ring LBG J213512.73−010143

We model the mass distribution in the recently discovered Einstein ring LBG J213512.73−010143 (the 'Cosmic Eye') using archival Hubble Space Telescope imaging. We reconstruct the mass density profile of the z = 0.73 lens and the surface brightness distribution of the z = 3.07 source and find that the observed ring is best fitted with a dual-component lens model consisting of a baryonic Sersic component nested within a dark matter halo. The dark matter halo has an inner slope of 1.42^+0.24_−0.22, consistent with cold dark matter simulations after allowing for baryon contraction. The baryonic component has a mass-to-light ratio of  1.71^+0.28_−0.38 M_⊙/L _{B ⊙}  which when evolved to the present day is in agreement with local ellipticals. Within the Einstein radius of 0.77 arcsec (5.6 kpc), the baryons account for 46 ± 11 per cent of the projected lens mass. External shear from a nearby foreground cluster is accurately predicted by the model. The reconstructed surface brightness distribution in the source plane clearly shows two peaks. Through a generalization of our lens inversion method, we conclude that the redshifts of both peaks are consistent with each other, suggesting that we are seeing structure within a single galaxy.     

Dark matter halo structure in CDM hydrodynamical simulations

We have carried out a comparative analysis of the properties of dark matter haloes in N -body and hydrodynamical simulations. We analyse their density profiles, shapes and kinematical properties with the aim of assessing the effects that hydrodynamical processes might produce on the evolution of the dark matter component. The simulations performed allow us to reproduce dark matter haloes with high resolution, although the range of circular velocities is limited. We find that for haloes with circular velocities of [150–200] km s⁻¹ at the virial radius, the presence of baryons affects the evolution of the dark matter component in the central region, modifying the density profiles, shapes and velocity dispersions. We also analyse the rotation velocity curves of disc-like structures and compare them with observational results.     

Non-parametric strong lens inversion of Cl 0024+1654: illustrating the monopole degeneracy

The cluster lens Cl 0024+1654 is undoubtedly one of the most beautiful examples of strong gravitational lensing, providing five large images of a single source with well-resolved substructure. Using the information contained in the positions and the shapes of the images, combined with the null space information, a non-parametric technique is used to infer the strong lensing mass map of the central region of this cluster. This yields a strong lensing mass of  1.60 × 10¹⁴ M_⊙  within a 0.5  arcmin radius around the cluster centre. This mass distribution is then used as a case study of the monopole degeneracy, which may be one of the most important degeneracies in gravitational lensing studies and which is extremely hard to break. We illustrate the monopole degeneracy by adding circularly symmetric density distributions with zero total mass to the original mass map of Cl 0024+1654. These redistribute mass in certain areas of the mass map without affecting the observed images in any way. We show that the monopole degeneracy and the mass-sheet degeneracy together lie at the heart of the discrepancies between different gravitational lens reconstructions that can be found in the literature for a given object, and that many images/sources, with an overall high image density in the lens plane, are required to construct an accurate, high-resolution mass map based on strong lensing data.     

Does the Fornax dwarf spheroidal have a central cusp or core?

The dark matter dominated Fornax dwarf spheroidal has five globular clusters orbiting at ∼1 kpc from its centre. In a cuspy cold dark matter halo the globulars would sink to the centre from their current positions within a few Gyr, presenting a puzzle as to why they survive undigested at the present epoch. We show that a solution to this timing problem is to adopt a cored dark matter halo. We use numerical simulations and analytic calculations to show that, under these conditions, the sinking time becomes many Hubble times; the globulars effectively stall at the dark matter core radius. We conclude that the Fornax dwarf spheroidal has a shallow inner density profile with a core radius constrained by the observed positions of its globular clusters. If the phase space density of the core is primordial then it implies a warm dark matter particle and gives an upper limit to its mass of ∼0.5 keV, consistent with that required to significantly alleviate the substructure problem.     

General polytropic spheres as gravitational lenses

We propose hydrostatic polytropic spheres governed by the Lane-Emden equation (LEE) of index $n$ as a novel set of physical models for axially averaged gravitational lenses anywhere in the Universe, alternative to the familiar singular isothermal sphere (SIS) and the Navarro–Frenk–White (NFW) profile, as such general polytropic spheres are conceptually simple, versatile in representing a series of equations of state, and able to address both the inner core and cusp features. As LEE is nonlinear, there exist several distinct classes of LEE solutions to serve as physical lens models. With a few scaling parameters, the complete problem can be readily reconstructed with full physical dimensions. A given mass density profile satisfying LEE produces lensing effects that are solely determined by a dimensionless parameter $q$ which contains geometric and kinematic information about the source-lens-observer system. The lens mapping and tangential shear or distortion profile are derived, first analytically for special cases and then asymptotically at the outskirts or near the edge of the lens. Numerical procedures for calculating full lensing profiles of a general lens are developed. Our results include the analytical “singular polytropic sphere” (SPS) profile which generalizes the SIS model and may outperform the latter in modeling dark matter halos among others. We further point out that dynamic models of general polytropic spheres in self-similar evolution can serve as several broad classes of gravitational lenses and produce time-dependent lensing effects slow or fast depending on the pertinent time scales. Astrophysical sources that can be lensed include electromagnetic wave sources in the entire frequency band, gravitational wave sources in the entire frequency band, gravitons even possibly with finite masses, neutrino sources of three different types, neutron sources, and ultra high energy cosmic rays (UHECRs) of electrically charged particles which can also interact with magnetic fields. We discuss and elabrate applications to dark matter halos, hypermassive black holes and supermassive black holes in the entire Universe including the early Universe, magnetized supermassive stars, static and dynamically evolving spherical and cylindrical lenses in contexts of astrophysics and cosmology.     

Precision of diffuse 21-cm lensing

We study the limits of accuracy for weak lensing maps of dark matter using diffuse 21-cm radiation from the pre-reionization epoch using simulations. We improve on previous 'optimal' quadratic lensing estimators by using shear and convergence instead of deflection angles. This is a generalization of the deflection estimator, and is more optimal for non-Gaussian sources. The cross-power spectrum of shear and convergence is an unbiased estimator of lensing power spectrum which does not require knowledge of the source four-point function. We find that non-Gaussianity provides a limit to the accuracy of weak lensing reconstruction, even if instrumental noise is reduced to zero. The best reconstruction result is equivalent to Gaussian sources with effective independent cell of side length  2.0  h ⁻¹ Mpc  . Using a source full map from z = 10 to 20, this limiting sensitivity allows mapping of dark matter at a signal-to-noise ratio greater than 1 out to l ≲ 6000, which is better than any other proposed technique for large-area weak lensing mapping.     

MOND plus classical neutrinos are not enough for cluster lensing

Clusters of galaxies offer a robust test bed for probing the nature of dark matter that is insensitive to the assumption of the gravity theories. Both Modified Newtonian Dynamics (MOND) and General Relativity (GR) would require similar amounts of non-baryonic matter in clusters as MOND boosts the gravity only mildly on cluster scales. Gravitational lensing allows us to estimate the enclosed mass in clusters on small (∼20–50 kpc) and large (∼several 100 kpc) scales independent of the assumptions of equilibrium. Here, we show for the first time that a combination of strong and weak gravitational lensing effects can set interesting limits on the phase-space density of dark matter in the centres of clusters. The phase-space densities derived from lensing observations are inconsistent with neutrino masses ranging from 2–7 eV, and hence do not support the 2 eV-range particles required by MOND. To survive, the most plausible modification for MOND may be an additional degree of dynamical freedom in a covariant incarnation.