Measuring the 3D distribution of mass on galaxy cluster scales is a crucial test of the LCDM model, providing constraints on the behaviour of dark matter. Recent work investigating mass distributions of individual galaxy clusters (e.g. Abell 1689) using weak and strong gravitational lensing has revealed potential inconsistencies between the predictions of structure formation models relating halo mass to concentration and those relationships as measured in massive clusters. However, such analyses employ simple spherical halo models while a growing body of work indicates that triaxial 3D halo structure is both common and important in parameter estimates. The very strong assumptions about the symmetry of the lensing halo implied with circular or perturbative elliptical NFW models are not physically motivated and lead to incorrect parameter estimates with significantly underestimated error bars. We here introduce a Markov Chain Monte Carlo (MCMC) method to fit fully triaxial models to weak lensing data that gives parameter and error estimates that fully incorporate the true uncertainty present in nature. Applying the MCMC triaxial fitting method to a population of NFW triaxial lenses drawn from the shape distribution of structure formation simulations, we find that including triaxiality cannot explain a population of massive, highly concentrated clusters within the framework of LCDM, but easily explains rare cases of apparently massive, highly concentrated, very efficient lensing clusters. Our MCMC triaxial NFW fitting method is easily expandable to include constraints from additional data types, and its application returns model parameters and errors that more accurately capture the true (and limited) extent of our knowledge of the structure of galaxy cluster lenses. (abridged)
We present a technique for constructing equilibrium triaxial N-body haloes with nearly arbitrary density profiles, axial ratios and spin parameters. The method is based on the way in which structures form in hierarchical cosmological simulations, where prolate and oblate haloes form via mergers with low and high angular momentum, respectively. We show that major mergers between equilibrium spherical cuspy haloes produce similarly cuspy triaxial remnants and higher angular-momentum mergers produce systems with lower concentrations. Triaxial haloes orbiting within deeper potentials become more s…
We have constructed realistic, self-consistent models of triaxial elliptical galaxies embedded in triaxial dark matter haloes. We examined three different models for the shape of the dark matter halo: (i) the same axis ratios as the luminous matter (0.7:0.86:1); (ii) a more prolate shape (0.5:0.66:1); (iii) a more oblate shape (0.7:0.93:1). The models were obtained by means of the standard orbital superposition technique introduced by Schwarzschild. Self-consistent solutions were found in each of the three cases. Chaotic orbits were found to be important in all of the models,and their presence…
(Abridged) We develop the halo model of large-scale structure to include triaxial dark matter haloes and their intrinsic alignments. As a direct application we derive general expressions for the power spectrum. This we calculate for two different triaxial density profiles. The first is a toy-model that allows us to isolate the dependence of clustering on halo shape alone and the second is the more realistic model of Jing & Suto (2002). In both cases, we find that the effects of triaxiality are manifest as a suppression of power at the level of ~5% on scales k~1-10 h/Mpc. When considered by mas…
We study the stability of trajectories near the disk plane of galaxy models with a triaxial dark matter halo component. We also examine the effect of weak discreteness noise, rapidly rotating bar perturbations and weak dissipation on these trajectories. If the matter distribution is triaxial and has a constant density core, dissipation leads to inflow of material inside the core radius to the centre. This leads to the formation of central masses which in turn destabilise the trajectories of any stars formed in these regions. In particular, even if the gas settles by dissipation into a flat dis…
This paper presents the properties of a family of scale-free triaxial haloes. We adduce arguments to suggest that the velocity ellipsoids of such models are aligned in conical coordinates. We provide an algorithm to find the set of conically aligned velocity second moments that support a given density against the gravity field of the halo. The case of the logarithmic ellipsoidal model -- the simplest triaxial generalisation of the familiar isothermal sphere -- is examined in detail. The velocity dispersions required to hold up the self-consistent model are analytic. The velocity distribution o…
The cold dark matter (CDM) scenario generically predicts the existence of triaxial dark matter haloes which contain notable amounts of substructure. However, analytical halo models with smooth, spherically symmetric density profiles are routinely adopted in the modelling of light propagation effects through such objects. In this paper, we address the biases introduced by this procedure by comparing the surface mass densities of actual N-body haloes against the widely used analytical model suggested by Navarro, Frenk and White (1996) (NFW). We conduct our analysis in the redshift range of 0.0 -…
The masses of supermassive black holes (SBHs) show correlations with bulge properties in disk and elliptical galaxies. We study the formation of galactic structure within flat-core triaxial haloes and show that these correlations can be understood within the framework of a baryonic component modifying the orbital structure in the underlying potential. In particular, we find that terminal properties of bulges and their central SBHs are constrained by the destruction of box orbits in the harmonic cores of dark haloes and the emergence of progressively less eccentric loop orbits there. SBH masses…
We present an efficient method for building equilibrium multi-component galaxies with non-spherical haloes and bulges. The gist of our approach is to tailor the velocity ellipsoid directly to the geometry of the mass distribution. Thus we avoid computing the anisotropic velocity dispersions which leads to large savings in the cpu budget. The computational time of the algorithm for triaxial equilibria scales linearly with the number of particles, N. The approximate solution to the velocity field causes structural relaxation: tests with N = 50,000 show that fluctuations of the inertia tensor (no…
Using eight dark matter haloes extracted from fully-self consistent cosmological N-body simulations, we perform microlensing experiments. A hypothetical observer is placed at a distance of 8.5 kpc from the centre of the halo measuring optical depths, event durations and event rates towards the direction of the Large Magellanic Cloud. We simulate 1600 microlensing experiments for each halo. Assuming that the whole halo consists of MACHOs, f = 1.0, and a single MACHO mass is m_M = 1.0 Msun, the simulations yield mean values of tau = 4.7^{+5.0}_{-2.2} 10^{-7} and Gamma = 1.6^{+1.3}_{-0.6} 10^{-6}…
The Hubble constant can be constrained using the time delays between multiple images of gravitationally lensed sources. In some notable cases, typical lensing analyses assuming isothermal galaxy density profiles produce low values for the Hubble constant, inconsistent with the result of the HST Key Project (72 +- 8 km/s/Mpc). Possible systematics in the values of the Hubble constant derived from galaxy lensing systems can result from a number of factors, e.g. neglect of environmental effects, assumption of isothermality, or contamination by line-of-sight structures. One additional potentially …
We study the three-dimensional and projected shapes of galaxy groups in the Sloan Digital Sky Survey Data Release 4, and examine the alignment between the orientation of the central galaxy and the spatial distribution of satellite galaxies. The projected ellipticity of a group is measured using the moments of the discrete distribution of its member galaxies. We infer the three-dimensional and projected axis ratios of their dark matter haloes by comparing the measured ellipticity distributions with those obtained from Monte Carlo simulations of projected, triaxial dark matter haloes with differ…
Cosmological simulations suggest that dark matter haloes are not spherical, but typically moderately to strongly triaxial systems. We investigate methods to convert spherical potential-density pairs into axisymmetric ones, in which the basic characteristics of the density profile (such as the slope at small and large radii) are retained. We achieve this goal by replacing the spherical radius r by an oblate radius m in the expression of the gravitational potential. We extend and formalize the approach pioneered by Miyamoto & Nagai (1975) to be applicable to arbitrary potential-density pairs. Un…
We use the recently completed one billion particle Via Lactea II LambdaCDM simulation to investigate local properties like density, mean velocity, velocity dispersion, anisotropy, orientation and shape of the velocity dispersion ellipsoid, as well as structure in velocity space of dark matter haloes. We show that at the same radial distance from the halo centre, these properties can deviate by orders of magnitude from the canonical, spherically averaged values, a variation that can only be partly explained by triaxiality and the presence of subhaloes. The mass density appears smooth in the cen…
We study the properties of the 3-dimensional and projected shapes of haloes using high resolution numerical simulations and observational data where the latter comes from the 2PIGG (Eke et al. 2004) and SDSS-DR3GC group catalogues (Merchan & Zandivarez 2005). We investigate the dependence of halo shape on characteristics such as mass and number of members. In the 3-dimensional case, we find a significant correlation between the mass and halo shape; massive systems are more prolate than small haloes. We detect a source of strong systematics in estimates of the triaxiality of a halo, which is fo…
In hierarchical models, the time derivative of the halo mass function may be thought of as the difference of two terms - a creation term, which describes the increase in the number of haloes of mass m from mergers of less massive objects, and a destruction term, which describes the decrease in the number of m-haloes as these merge with other haloes, creating more massive haloes as a result. In models where haloes form from a spherical collapse, the distribution of halo creation times can be estimated from the same formalism which is used to estimate halo abundances: the constant-barrier excurs…
Measuring the 3D distribution of mass on galaxy cluster scales is a crucial test of the LCDM model, providing constraints on the nature of dark matter. Recent work investigating mass distributions of individual galaxy clusters (e.g. Abell 1689) using weak and strong gravitational lensing has revealed potential inconsistencies between the predictions of structure formation models relating halo mass to concentration and those relationships as measured in massive clusters. However, such analyses employ simple spherical halo models while a growing body of work indicates that triaxial 3D halo struc…
(Abridged) We study predictions for galaxy cluster observables that can test the statistics of dark matter halo shapes expected in a flat LCDM universe. We present a simple analytical model for the prediction of cluster-scale X-ray observations, approximating clusters as isothermal systems in hydrostatic equilibrium, and dark matter haloes as ellipsoids with uniform axial ratios. We test the model against high-resolution, hydrodynamic cluster simulations to gauge its reliability. We find that this simple prescription does a good job of predicting the distribution of cluster X-ray ellipticities…
(Abridged) We use the triaxial halo model of Smith & Watts to investigate the impact of dark matter halo shapes on the bispectrum. Analytic expressions are derived and evaluated through numerical integration. Two models for the ellipsoidal halo profiles are considered: a toy model designed to isolate the effects of halo shape on the clustering alone; and the realistic model of Jing & Suto. For equilateral k-space triangles, we show that the predictions of the triaxial model are suppressed, relative to the spherical model, by roughly ~7% and ~4% for the two profiles respectively. The reduced bi…
Ultra-high energy cosmic rays (UHECRs) may originate from the decay of massive relic particles in the dark halo of the Galaxy, or they may be produced by supermassive black holes in the nuclei of nearby galaxies. The anisotropy in the arrival directions is studied in four dark halo models (cusped, isothermal, triaxial and tilted) and in four galaxy samples (galaxies intrinsically brighter than Centaurus A within 50 and 100 Mpc, and brighter than M32 within 50 and 100 Mpc). In decaying dark matter models, the amplitude of the anisotropy is controlled by the size of the Galactic halo, while the …
There is strong evidence that the mass in the Universe is dominated by dark matter, which exerts gravitational attraction but whose exact nature is unknown. In particular, all galaxies are believed to be embedded in massive haloes of dark matter. This view has recently been challenged by surprisingly low random stellar velocities in the outskirts of ordinary elliptical galaxies, which were interpreted as indicating a lack of dark matter (Mendez et al. 2001; Romanowsky et al. 2003). Here we show that the low velocities are in fact compatible with galaxy formation in dark-matter haloes. Using nu…
The formulation of the tensor virial equations is generalized to unrelaxed configurations, where virial equilibrium does not coincide with dynamical (or hydrostatic) equilibrium. Further investigation is devoted to special classes of homeoidally striated ellipsoids, defined as homeoidally striated, Jacobi ellipsoids. In particular, virial equilibrium configurations with constant anisotropy parameters are studied with more detail, including both flattened and elongated, triaxial configurations, and the determination of the related bifurcation points. The explicit expression of different rotatio…
Isolated barred galaxies evolve by redistributing their internal angular momentum, which is emitted mainly at the inner disc resonances and absorbed mainly at the resonances in the outer disc and the halo. This causes the bar to grow stronger and its pattern speed to decrease with time. A massive, responsive halo enhances this process. I show correlations and trends between the angular momentum absorbed by the halo and the bar strength, pattern speed and morphology. It is thus possible to explain why some disc galaxies are strongly barred, while others have no bar, or only a short bar or an ov…
N-body simulations argue that the inner haloes of barred galaxies should not be spherical, nor even axisymmetric, but triaxial. The departure from sphericity is strongest near the centre and decreases outwards; typical axial ratios for the innermost parts are of the order of 0.8. The halo shape is prolate-like in the inner parts up to a certain radius and then turns to oblate-like. I call this inner halo structure the `halo bar' and analyse here in depth its structure and kinematics in a representative model. It is always considerably shorter than the disc bar. It lags the disc bar by only a f…
The distribution of mass on galaxy cluster scales is an important test of structure formation scenarios, providing constraints on the nature of dark matter itself. Several techniques have been used to probe the mass distributions of clusters, sometimes yielding results which are discrepant, or at odds with clusters formed in simulations - for example giving NFW concentration parameters much higher than expected in the standard CDM model. In addition, the velocity fields of some well studied galaxy clusters reveal the presence of several structures close to the line-of-sight, often not dynamica…
We perform controlled N-Body/SPH simulations of disk galaxy formation by cooling a rotating gaseous mass distribution inside equilibrium cuspy spherical and triaxial dark matter halos. We systematically study the angular momentum transport and the disk morphology as we increase the number of dark matter and gas particles from 10^4 to 10^6, and decrease the gravitational softening from 2 kpc to 50 parsecs. The angular momentum transport, disk morphology and radial profiles depend sensitively on force and mass resolution. At low resolution, similar to that used in most current cosmological simul…
