Dark matter subhaloes in numerical simulations

We use cosmological Λ cold dark matter (CDM) numerical simulations to model the evolution of the substructure population in 16 dark matter haloes with resolutions of up to seven million particles within the virial radius. The combined substructure circular velocity distribution function (VDF) for hosts of 10¹¹ to  10¹⁴ M_⊙  at redshifts from zero to two or higher has a self-similar shape, is independent of host halo mass and redshift, and follows the relation  d n /d v = (1/8)( v _cmax/ v _cmax,host)⁻⁴  . Halo to halo variance in the VDF is a factor of roughly 2 to 4. At high redshifts, we find preliminary evidence for fewer large substructure haloes (subhaloes). Specific angular momenta are significantly lower for subhaloes nearer the host halo centre where tidal stripping is more effective. The radial distribution of subhaloes is marginally consistent with the mass profile for   r ≳ 0.3 r _vir  , where the possibility of artificial numerical disruption of subhaloes can be most reliably excluded by our convergence study, although a subhalo distribution that is shallower than the mass profile is favoured. Subhalo masses but not circular velocities decrease towards the host centre. Subhalo velocity dispersions hint at a positive velocity bias at small radii. There is a weak bias towards more circular orbits at lower redshift, especially at small radii. We additionally model a cluster in several power-law cosmologies of   P ∝ kⁿ   , and demonstrate that a steeper spectral index, n , results in significantly less substructure.     

Analytical approach to subhalo population in dark matter haloes

In the standard model of cosmic structure formation, dark matter haloes form by gravitational instability. The process is hierarchical: smaller systems collapse earlier, and later merge to form larger haloes. The galaxy clusters, hosted by the largest dark matter haloes, are at the top of this hierarchy and representing the largest as well as the last structures formed in the Universe, while the smaller and first haloes are those Earth-sized dark subhaloes that have been both predicted by theoretical considerations and found in numerical simulations, though there do not exist any observational hints of their existence. The probability that a halo of mass m at redshift z will be part of a larger halo of mass M at the present time can be described in the frame of the extended Press & Schecter theory making use of the progenitor (conditional) mass function. Using the progenitor mass function, we calculate analytically, at redshift zero, the distribution of subhaloes in mass, formation epoch and rarity of the peak of the density field at the formation epoch. That is done for a Milky Way size system, assuming both a spherical and an ellipsoidal collapse model. Our calculation assumes that small progenitors do not lose mass due to dynamical processes after entering the parent halo, and that they do not interact with other subhaloes. For a Λ cold dark matter power spectrum, we obtain a subhalo mass function  d n /d m   proportional to   m ^−α  with a model-independent  α∼ 2  . Assuming that the dark matter is a weakly interacting massive particle, the inferred distributions are used to test the feasibility of an indirect detection in the γ-ray energy band of such a population of subhaloes with a Gamma-ray Large Area Space Telescope like satellite.     

Halo masses for optically selected and for radio-loud AGN from clustering and galaxy–galaxy lensing

We compute two-point correlation functions and measure the shear signal due to galaxy–galaxy lensing for 80 000 optically identified and 5700 radio-loud active galactic nuclei (AGN) from Data Release 4 of the Sloan Digital Sky Survey. Halo occupation models are used to estimate halo masses and satellite fractions for these two types of AGN. The large sample size allows us to separate AGN according to the stellar mass of their host galaxies. We study how the halo masses of optical and radio AGN differ from those of the parent population at fixed   M _*  . Halo masses deduced from clustering and from lensing agree satisfactorily. Radio AGN are found in more massive haloes than optical AGN: in our samples, their mean halo masses are  1.6 × 10¹³  and  8 × 10¹¹  h ⁻¹ M_⊙  , respectively. Optical AGN follow the same relation between stellar mass and halo mass as galaxies selected without regard to nuclear properties, but radio-loud AGN deviate significantly from this relation. The dark matter haloes of radio-loud AGN are about twice as massive as those of control galaxies of the same stellar mass. This boost is independent of radio luminosity, and persists even when our analysis is restricted to field galaxies. The large-scale gaseous environment of the galaxy clearly plays a crucial role in producing observable radio emission. The dark matter halo masses that we derive for the AGN in our two samples are in good agreement with recent models in which feedback from radio AGN becomes dominant in haloes where gas cools quasi-statically.     

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.     

Expectation for the X—ray Galactic Halo

1 INTRODUCTION In the hierarchical clustering model, massive objects form by gravitational aggregation oflower-mass objects, and the disks in spiral galaxies like our Galaxy form by a late accretionof gas from an extended reservoir around the galactic halos. According to this scenario, spiralgalaxies are still growing at present. At the virial temperature of galactic halos, T r.-' io5 ?i06 K, the dominant cooling mech-anism is X-ray bremsstrahlung. If the cooling rate is significant, the…     

Weak gravitational flexion

Flexion is the significant third-order weak gravitational lensing effect responsible for the weakly skewed and arc-like appearance of lensed galaxies. Here we demonstrate how flexion measurements can be used to measure galaxy halo density profiles and large-scale structure on non-linear scales, via galaxy–galaxy lensing, dark matter mapping and cosmic flexion correlation functions. We describe the origin of gravitational flexion, and discuss its four components, two of which are first described here. We also introduce an efficient complex formalism for all orders of lensing distortion. We proceed to examine the flexion predictions for galaxy–galaxy lensing, examining isothermal sphere and Navarro–Frenk–White (NFW) profiles and both circularly symmetric and elliptical cases. We show that in combination with shear we can precisely measure galaxy masses and NFW halo concentrations. We also show how flexion measurements can be used to reconstruct mass maps in two-dimensional projection on the sky, and in three dimensions in combination with redshift data. Finally, we examine the predictions for cosmic flexion, including convergence–flexion cross-correlations, and we find that the signal is an effective probe of structure on non-linear scales.     

The fate of substructures in cold dark matter haloes

We use the Millennium Simulation, a large, high-resolution N -body simulation of the evolution of structure in a Λ cold dark matter cosmology, to study the properties and fate of substructures within a large sample of dark matter haloes. We find that the subhalo mass function departs significantly from a power law at the high-mass end. We also find that the radial and angular distributions of substructures depend on subhalo mass. In particular, high-mass subhaloes tend to be less radially concentrated and to have angular distributions closer to the direction perpendicular to the spin of the host halo than their less massive counterparts. We find that mergers between subhaloes occur. These tend to be between substructures that were already dynamically associated before accretion into the main halo. For subhaloes larger than 0.001 times the mass of the host halo, it is more likely that the subhalo will merge with the central or main subhalo than with another subhalo larger than itself. For lower masses, subhalo–subhalo mergers become equally likely to mergers with the main subhalo. Our results have implications for the variation of galaxy properties with environment and for the treatment of mergers in galaxy formation models.     

On Einstein clusters as galactic dark matter haloes

We consider global and gravitational lensing properties of the recently suggested Einstein clusters of weakly interacting massive particles (WIMPs) as galactic dark matter haloes. Being tangential pressure dominated, Einstein clusters are strongly anisotropic systems which can describe any galactic rotation curve by specifying the anisotropy. Due to this property, Einstein clusters may be considered as dark matter candidates. We analyse the stability of the Einstein clusters against both radial and non-radial pulsations, and we show that the Einstein clusters are dynamically stable. With the use of the Buchdahl type inequalities for anisotropic bodies, we derive upper limits on the velocity of the particles defining the cluster. These limits are consistent with those obtained from stability considerations. The study of light deflection shows that the gravitational lensing effect is slightly smaller for the Einstein clusters as compared to the singular isothermal density sphere model for dark matter. Therefore, lensing observations may discriminate, at least, in principle, between Einstein cluster and the other dark matter models.     

Galaxy–dark matter correlations applied to galaxy–galaxy lensing: predictions from the semi-analytic galaxy formation models

We use semi-analytic models of galaxy formation combined with high-resolution N -body simulations to make predictions for galaxy–dark matter correlations and apply them to galaxy–galaxy lensing. We analyse cross-power spectra between the dark matter and different galaxy samples selected by luminosity, colour or star formation rate. We compare the predictions with the recent detection by the Sloan Digital Sky Survey (SDSS). We show that the correlation amplitude and the mean tangential shear depend strongly on the luminosity of the sample on scales below 1  h ⁻¹ Mpc, reflecting the correlation between the galaxy luminosity and the halo mass. The cross-correlation cannot, however, be used to infer the halo profile directly because different halo masses dominate on different scales and because not all galaxies are at the centres of the corresponding haloes. We compute the redshift evolution of the cross-correlation amplitude and compare it with those of galaxies and dark matter. We also compute the galaxy–dark matter correlation coefficient and show that it is close to unity on scales above 1  h ⁻¹ Mpc for all considered galaxy types. This would allow one to extract the bias and the dark matter power spectrum on large scales from the galaxy and galaxy–dark matter correlations.     

The distribution of ejected subhaloes and its implication for halo assembly bias

Using a high-resolution cosmological N -body simulation, we identify the ejected population of subhaloes, which are haloes at redshift   z = 0  but were once contained in more massive 'host' haloes at high redshifts. The fraction of the ejected subhaloes in the total halo population of the same mass ranges from 9 to 4 per cent for halo masses from  ∼10¹¹  to  ∼10¹²  h ⁻¹ M_⊙  . Most of the ejected subhaloes are distributed within four times the virial radius of their hosts. These ejected subhaloes have distinct velocity distribution around their hosts in comparison to normal haloes. The number of subhaloes ejected from a host of given mass increases with the assembly redshift of the host. Ejected subhaloes in general reside in high-density regions, and have a much higher bias parameter than normal haloes of the same mass. They also have earlier assembly times, so that they contribute to the assembly bias of dark matter haloes seen in cosmological simulations. However, the assembly bias is not dominated by the ejected population, indicating that large-scale environmental effects on normal haloes are the main source for the assembly bias.     

The image separation distribution of strong lenses: halo versus subhalo populations

We present a halo model prediction of the image separation distribution of strong lenses. Our model takes into account the subhalo population, which has been ignored in previous studies, as well as the conventional halo population. Haloes and subhaloes are linked to central and satellite galaxies by adopting a universal scaling relation between masses of (sub)haloes and luminosities of galaxies. Our model predicts that 10–20 per cent of lenses should be caused by the subhalo population. The fraction of lensing by satellite galaxies (subhaloes) peaks at ∼1 arcsec and decreases rapidly with increasing image separations. We compute fractions of lenses which lie in groups and clusters and find them to be ∼14 and ∼4 per cent, respectively; nearly half of such lenses are expected to be produced by satellite galaxies, rather than central parts of haloes. We also study mass distributions of lensing haloes and find that, even at image separations of ∼3 arcsec, the deviation of lens mass distributions from isothermal profiles is large; at or beyond ∼3 arcsec, image separations are enhanced significantly by surrounding haloes. Our model prediction agrees reasonably well with observed image separation distributions from galaxy to cluster scales.     

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.     

The clustering and host haloes of galaxy mergers at high redshift

High-resolution simulations of cosmological structure formation indicate that dark matter substructure in dense environments, such as groups and clusters, may survive for a long time. These dark matter subhaloes are the likely hosts of galaxies. We examine the small-scale spatial clustering of subhalo major mergers at high redshift using high-resolution N -body simulations of cosmological volumes. Recently merged, massive subhaloes exhibit enhanced clustering on scales  ∼100–300  h ⁻¹ kpc  , relative to all subhaloes of the same infall mass, for a short time after a major merger (<500 Myr). The small-scale clustering enhancement is smaller for lower mass subhaloes, which also show a deficit on scales just beyond the excess. Haloes hosting recent subhalo mergers tend to have more subhaloes; for massive subhaloes, the excess is stronger and it tends to increase for the most massive host haloes. The subhalo merger fraction is independent of halo mass for the scales we probe. In terms of satellite and central subhaloes, the merger increase in small-scale clustering for massive subhaloes arises from recently merged massive central subhaloes having an enhanced satellite population. Our mergers are defined via their parent infall mass ratios. Subhaloes experiencing major mass gains also exhibit a small-scale clustering enhancement, but these correspond to two-body interactions leading to two final subhaloes, rather than subhalo coalescence.     

Inferring dark halo structure from observed scaling laws of late-type galaxies and LSBs

We re-examine the Fall & Efstathiou scenario for galaxy formation, including the dark halo gravitational reaction to the formation of the baryon disc, as well as continuous variations in the intrinsic halo density profile. The recently published rotation curves of low surface brightness (LSB) and dwarf galaxies together with previously known scaling relations provide sufficient information on the present-day structure of late-type disc galaxies to invert the problem. By requiring that the models reproduce all the observational restrictions we can fully constrain the initial conditions of galaxy formation, with a minimum of assumptions, in particular without the need to specify a cold dark matter (CDM) halo profile. This allows one to solve for all the initial conditions, in terms of the halo density profile, the baryon fraction and the total angular momentum. We find that a unique initial halo shape is sufficient to accurately reproduce the rotation curves of both LSB and normal late-type spiral galaxies. This unique halo profile differs substantially from that found in standard CDM models. A galactic baryon fraction of 0.065 is found. The initial value of the dimensionless angular momentum is seen to be the principal discriminator between the galaxy classes we examine. The present-day scalings between structural parameters are seen to originate in the initial conditions.     

The edge-on spiral gravitational lens B1600+434

We present new observations of the gravitational lens (GL) system B1600+434, strongly suggesting that the lens is an edge-on spiral galaxy. These observations are used to constrain the mass model of the system, in particular the oblateness and velocity dispersion of the dark matter halo around the lensing galaxy. From an analytical model we find a lower limit on the halo oblateness q _halo=( c/a )_ρ≳0.4; more detailed numerical models give a lower limit of q _halo≳0.5. We determine an average halo velocity dispersion of σ_halo=190±15 km s⁻¹ over all non-singular isothermal elliptical (NIE) halo models. Constraining the models to larger and more massive discs decreases this average by only 10 km s⁻¹. A lower limit of σ_halo≳150 km s⁻¹ is found, even for disc masses larger than the mass inside the Einstein radius. This lower limit indicates the need for a massive dark matter halo, contributing at least half of the mass inside the Einstein radius. Time-delay calculations give (54±3)/ h ₅₀ d for the NIE halo model and (70±4)/ h ₅₀ d for the modified Hubble profile (MHP) halo model. Although the time delay for both NIE and MHP halo models is well constrained on our parameter grid, it strongly depends on the halo surface density profile. We furthermore find that the presence of a flat luminous mass distribution can severely alter the statistical properties of the lens.     

The role of luminous substructure in the gravitational lens system MG 2016+112

MG 2016+112 is a quadruply imaged lens system with two complete images A and B and a pair of merging partial images in region C as seen in the radio. The merging images are found to violate the expected mirror symmetry. This indicates an astrometric anomaly which could only be of gravitational origin and could arise due to substructure in the environment or line of sight of the lens galaxy. We present new high-resolution multifrequency very long baseline interferometry (VLBI) observations at 1.7, 5 and 8.4 GHz. Three new components are detected in the new VLBI imaging of both the lensed images A and B. The expected opposite parity of the lensed images A and B was confirmed due to the detection of non-collinear components. Furthermore, the observed properties of the newly detected components are inconsistent with the predictions of previous mass models. We present new scenarios for the background quasar which are consistent with the new observations. We also investigate the role of the satellite galaxy situated at the same redshift as the main lensing galaxy. Our new mass models demonstrate quantitatively that the satellite galaxy is the primary cause of the astrometric anomaly found in region C. The detected satellite is consistent with the abundance of subhaloes expected in the halo from cold dark matter (CDM) simulations. However, the fraction of the total halo mass in the satellite as computed from lens modelling is found to be higher than that predicted by CDM simulations.     

On non-baryonic dark objects in galactic haloes

Taking into account that a hierarchical pattern of clustering appears in cold dark matter scenarios, the existence of cold dark matter substructure in galactic haloes is explored. For this purpose, well-known dynamical constraints are imposed on non-baryonic objects, at solar Galactocentric distance. In this paper, aggregates of axions, aggregates of fermions and clusters of these aggregates have been considered, and ranges for their masses and radii have been estimated. Non-baryonic objects with radii and masses different from those allowed must have been disrupted by dynamical effects, so that their components must be orbiting freely within the Galactic halo. Upper limits for the ratio between the mass (per volume unit) that remains bound to dark objects and the cold dark matter total mass (per volume unit) in the Galactic halo have also been estimated.     

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.     

Do the Unidentified Egret Sources Trace Annihilating Dark Matter in the Local Group?

In a cold dark matter (CDM) framework of structure formation, the dark matter haloes around galaxies assemble through successive mergers with smaller haloes. This merging process is not completely efficient, and hundreds of surviving halo cores, or subhaloes, are expected to remain in orbit within the halo of a galaxy like the Milky Way. While the dozen visible satellites of the Milky Way may trace some of these subhaloes, the majority are currently undetected. A large number of high-velocity clouds (HVCs) of neutral hydrogen are observed around the Milky Way, and it is plausible that some of the HVCs may trace subhaloes undetected in the optical. Confirming the existence of concentrations of dark matter associated with even a few of the HVCs would represent a dramatic step forward in our attempts to understand the nature of dark matter. Supersymmetric (SUSY) extensions of the Standard Model of particle physics currently suggest neutralinos as a natural well-motivated candidate for the non-baryonic dark matter of the universe. If this is indeed the case, then it may be possible to detect dark matter indirectly as it annihilates into neutrinos, photons or positrons. In particular, the centres of subhaloes might show up as point sources in gamma-ray observations. In this work, we consider the possibility that some of the unidentified EGRET γ-ray sources trace annihilating neutralino dark matter in the dark substructure of the Local Group. We compare the observed positions and fluxes of both the unidentified EGRET sources and the HVCs with the positions and fluxes predicted by a model of halo substructure, to determine up to what extent any of these three populations could be associated.     

Deflection of jets induced by jet–cloud and jet–galaxy interactions

The model first introduced by Raga & Cantó in which astrophysical jets are deflected on passing through an isothermal high‐density region is generalized by taking into account gravitational effects on the motion of the jet as it crosses the high‐density cloud. The problem is also generalized for relativistic jets in which gravitational effects induced by the cloud are neglected. Two further cases, classical and relativistic, are discussed for the cases in which the jet is deflected on passing through the interstellar gas of a galaxy in which a dark matter halo dominates the gravitational potential. The criteria for the stability of jets due to the formation of internal shocks are also discussed.