Triaxial Halo Research Articles

Loss of halo triaxiality due to bar formation

Cosmological N-body simulations indicate that the dark matter haloes of galaxies should be generally triaxial. Yet, the presence of a baryonic disc is believed to alter the shape of the haloes. Here we aim to study how bar formation is affected by halo triaxiality and how, in turn, the presence of the bar influences the shape of the halo. We perform a set of collisionless N-body simulations of disc galaxies with triaxial dark matter haloes, using elliptical discs as initial conditions. We study models of different halo triaxialities and, to investigate the behaviour of the halo shape in the absence of bar formation, we run models with different disc masses, halo concentrations, disc velocity dispersions and also models where the disc shape is kept artificially axisymmetric. We find that the introduction of a massive disc causes the halo triaxiality to be partially diluted. Once the disc is fully grown, a strong stellar bar develops within the halo that is still non-axisymmetric, causing it to lose its remaining non-axisymmetry. In triaxial haloes in which the initial conditions are such that a bar does not form, the halo is able to remain triaxial and the circularisation of its shape on the plane of the disc is limited to the period of disc growth. We conclude that part of the circularisation of the halo is due to disc growth, but part must be attributed to the formation of a bar. We find that initially circular discs respond excessively to the triaxial potential and become highly elongated. They also lose more angular momentum than the initially elliptical discs and thus form stronger bars. Because of that, the circularisation that their bars induce on their haloes is also more rapid. We also analyse halo vertical shapes and observe that their vertical flattenings remain considerable, meaning that the haloes become approximately oblate by the end of the simulations. [abridged]

SUZAKUOBSERVATION OF A1689: ANISOTROPIC TEMPERATURE AND ENTROPY DISTRIBUTIONS ASSOCIATED WITH THE LARGE-SCALE STRUCTURE

(Abridged) We present results of Suzaku observations of the intracluster medium (ICM) in Abell 1689, combined with complementary analysis of the SDSS data and weak and strong lensing analysis of Subaru/Suprime-Cam and HST/ACS observations. Faint X-ray emission from the ICM around the virial radius is detected at 4.0 sigma significance. We find anisotropic gas temperature and entropy distributions in cluster outskirts correlated with large-scale structure of galaxies. The high temperature and entropy region in the northeastern (NE) outskirts is connected to an overdense filamentary structure. The outskirt regions in contact with low density void environments have low gas temperatures and entropies, deviating from hydrostatic equilibrium. These results suggest that thermalization of the ICM occurs faster along the filamentary structures than the void regions. A joint X-ray and lensing analysis shows that the hydrostatic mass is $\sim60-90%$ of spherical lensing one but comparable to a triaxial halo mass within errors in $0.6r_{2500} \simlt r \simlt 0.8r_{500}$, and that it is significantly biased as low as $\simlt60%$ within $0.4r_{2500}$, irrespective of mass models. The thermal gas pressure within $r_{500}$ is, at most, $\sim50$--60% of the total pressure to balance fully the gravity of the spherical lensing mass, and $\sim30$--40% around the virial radius. Although these constitute lower limits when one considers the possible halo triaxiality, these small relative contributions of thermal pressure would require additional sources of pressure, such as bulk and/or turbulent motions.

THE SAGITTARIUS DWARF GALAXY: A MODEL FOR EVOLUTION IN A TRIAXIAL MILKY WAY HALO

We present a new N-body model for the tidal disruption of the Sagittarius (Sgr) dwarf that is capable of simultaneously satisfying the majority of angular position, distance, and radial velocity constraints imposed by current wide-field surveys of its dynamically young (< 3 Gyr) tidal debris streams. In particular, this model resolves the conflicting angular position and radial velocity constraints on the Sgr leading tidal stream that have been highlighted in recent years. While the model does not reproduce the apparent bifurcation observed in the leading debris stream, recent observational data suggest that this bifurcation may represent a constraint on the internal properties of the Sgr dwarf rather than the details of its orbit. The key element in the success of this model is the introduction of a non-axisymmetric component to the Galactic gravitational potential which can be described in terms of a triaxial dark matter halo whose minor/major axis ratio (c/a)_Phi = 0.72 and intermediate/major axis ratio (b/a)_Phi = 0.99 at radii 20 < r < 60 kpc. The minor/intermediate/major axes of this halo lie along the directions (l, b) = (7, 0), (0, 90), and (97, 0) respectively, corresponding to a nearly-oblate ellipsoid whose minor axis is contained within the Galactic disk plane. We demonstrate that with simple assumptions about the star formation history of Sgr, tidal stripping models naturally give rise to gradients in the metallicity distribution function (MDF) along the stellar debris streams similar to those observed in recent studies. (Abridged).

UNVEILING THE THREE-DIMENSIONAL STRUCTURE OF GALAXY CLUSTERS: RESOLVING THE DISCREPANCY BETWEEN X-RAY AND LENSING MASSES

[Abridged] We present the first determination of the intrinsic three-dimensional shapes and the physical parameters of both dark matter (DM) and intra-cluster medium (ICM) in a triaxial galaxy cluster. While most previous studies rely on the standard spherical modeling, our approach allows to infer the properties of the non-spherical intra-cluster gas distribution sitting in hydrostatic equilibrium within triaxial DM halos by combining X-ray, weak and strong lensing observations. We present an application of our method to the galaxy cluster MACS J1423.8+2404. This source is an example of a well relaxed object with a unimodal mass distribution and we infer shape and physical properties of the ICM and the DM for this source. We found that this is a triaxial galaxy cluster with DM halo axial ratios 1.53+/-0.15 and 1.44+/-0.07 on the plane of the sky and along the line of sight, respectively. We show that accounting for the three-dimensional geometry allows to solve the long-standing discrepancy between galaxy cluster masses determined from X-ray and gravitational lensing observations. We focus also on the determination of the inner slope of the DM density profile alpha, since the cuspiness of dark-matter density profiles is one of the critical tests of the cold dark matter (CDM) paradigm for structure formation: we measure alpha=0.94+/-0.09 by accounting explicitly for the 3D structure for this cluster, a value which is close to the CDM predictions, while the standard spherical modeling leads to the biased value alpha=1.24+/-0.07. Our findings provide further evidences that support the CDM scenario and open a new window in recovering the intrinsic shapes and physical parameters of galaxy clusters in a bias-free way. This has important consequences in using galaxy clusters as cosmological probes.

The orbital evolution induced by baryonic condensation in triaxial haloes

Using spectral methods, we analyse the orbital structure of prolate/triaxial dark matter (DM) halos in N-body simulations to understand the processes that drive the evolution of shapes of DM halos and elliptical galaxies in which central masses are grown. A longstanding issue is whether the change in the shapes of DM halos is the result of chaotic scattering of box orbits, or whether they change shape adiabatically in response to the evolving galactic potential. We use orbital frequencies to classify orbits, to quantify orbital shapes, and to identify resonant orbits and chaotic orbits. The frequency-based method overcomes the limitations of Lyapunov exponents which are sensitive to numerical discreteness effects. Regardless of the distribution of the baryonic component, the shape of a DM halo changes primarily due to changes in the shapes of individual orbits within a given family. Orbits with small pericentric radii are more likely to change both their orbital type and shape than orbits with large pericentric radii. Whether the evolution is regular (and reversible) or chaotic (and irreversible), depends primarily on the radial distribution of the baryonic component. The growth of an extended baryonic component of any shape results in a regular rather than chaotic change in orbital populations. In contrast the growth of a massive and compact central component results in chaotic scattering of a significant fraction of both box and long-axis tube orbits. The growth of a disk causes a significant fraction of halo particles to become trapped by major global orbital resonances. Despite the fact that shape of a DM halo is always quite oblate following the growth of a central baryonic component, a significant fraction of its orbit population has characteristics of its triaxial or prolate progenitor (ABRIDGED).

On the overconcentration problem of strong lensing clusters

Λ cold dark matter paradigm predicts that galaxy clusters follow a universal mass density profile and fit a well-defined mass–concentration relation, with lensing clusters being preferentially triaxial haloes elongated along the line of sight. Oddly, recent strong and weak lensing analyses of clusters with a large Einstein radius suggested those haloes to be highly overconcentrated. Here, we investigate what intrinsic shape and orientation a halo should have to account for both theoretical predictions and observations. We considered a sample of 10 strong lensing clusters. We first measured their elongation assuming a given mass–concentration relation. Then, for each cluster, we found the intrinsic shape and orientation which are compatible with the inferred elongation and the measured projected ellipticity. We distinguished two groups. The first one (nearly one-half) seems to be composed of outliers of the mass–concentration relation, which they would fit only if they were characterized by a filamentary structure extremely elongated along the line of sight, that is not plausible considering standard scenarios of structure formations. The second sample supports expectations of N-body simulations which prefer mildly triaxial lensing clusters with a strong orientation bias.

Tidal disruption of globular clusters in dwarf galaxies with triaxial dark matter haloes

We use N-body simulations to study the tidal evolution of globular clusters (GCs) in dwarf spheroidal (dSph) galaxies. Our models adopt a cosmologically motivated scenario in which the dSph is approximated by a static NFW halo with a triaxial shape. We apply our models to five GCs spanning three orders of magnitude in stellar density and two in mass, chosen to represent the properties exhibited by the five GCs of the Fornax dSph. We show that only the object representing Fornax's least dense GC (F1) can be fully disrupted by Fornax's internal tidal field--the four denser clusters survive even if their orbits decay to the centre of Fornax. For a large set of orbits and projection angles we examine the spatial and velocity distribution of stellar debris deposited during the complete disruption of an F1-like GC. Our simulations show that such debris appears as shells, isolated clumps and elongated over-densities at low surface brightness (>26 mag/arcsec^2), reminiscent of substructure observed in several MW dSphs. Such features arise from the triaxiality of the galaxy potential and do not dissolve in time. The kinematics of the debris depends strongly on the progenitor's orbit. Debris associated with box and resonant orbits does not display stream motions and may appear "colder"/"hotter" than the dSph's field population if the viewing angle is perpendicular/parallel to progenitor's orbital plane. In contrast, debris associated with loop orbits shows a rotational velocity that may be detectable out to few kpc from the galaxy centre. Chemical tagging that can distinguish GC debris from field stars may reveal whether the merger of GCs contributed to the formation of multiple stellar components observed in dSphs.

Cosmology with the cluster mass function: mass estimators and shape systematics in large weak lensing surveys

Accurate measurement of the cluster mass function is a crucial element in efforts to constrain structure formation models, the normalisation of the matter power spectrum and the cosmological matter density, and the nature and evolution of dark energy. Large weak lensing surveys of ~20,000 galaxy clusters and groups will be key tools in the observational pursuit of that goal. These weak lensing studies often proceed by stacking the lensing signals of many clusters and groups binned by mass-correlated observables such as richness and luminosity; typically such analyses ignore the triaxial structure of dark matter halos on the assumption that the averaging of many shear signals within each mass bin makes its effects (as large as factors of two in mass model parameter estimates from individual clusters) negligible. We test this assumption and find that triaxiality can bias 3D virial mass estimates compared to those for a spherical population by a few percent if suboptimal mass estimators are used. This bias affects not only direct lensing constraints on the mass function but can also affect the scatter and normalization of the mass-observable relations derived from lensing that are so crucial to constraining the cluster mass function with large samples. However, we demonstrate that a careful choice of mass estimator can remove the bias very effectively if the lensing signals from a sufficient number of triaxial halos are averaged together, and further quantify that sufficient number for adequate shape averaging. We thus show that by choosing observable bins to contain an adequate number of halos and by utilizing a carefully chosen 3D mass estimator stacked weak-lensing analyses can give unbiased constraints on the triaxial mass function.

GALACTIC WARPS IN TRIAXIAL HALOS

We study the behaviors of galactic disks in triaxial halos both numerically and analytically to see if warps can be excited and sustained in triaxial potentials. We consider the following two scenarios: 1) galactic disks that are initially tilted relative to the equatorial plane of the halo (for a pedagogical purpose), and 2) tilted infall of dark matter relative to the equatorial plane of the disk and the halo. With numerical simulations of 100,000 disk particles in a fixed halo potential, we find that in triaxial halos, warps can be excited and sustained just as in spherical or axisymmetric halos but they show some oscillatory behaviors and even can be transformed to a polar-ring system if the halo has a prolate-like triaxiality. The non-axisymmetric component of the halo causes the disk to nutate, and the differential nutation between the inner and outer parts of the disk generally makes the magnitude of the warp slightly diminish and fluctuate. We also find that warps are relatively weaker in oblate and oblate-like triaxial halos, and since these halos are the halo configurations of disk galaxies inferred by cosmological simulations, our results are consistent with the fact that most of the observed warps are quite weak. We derive approximate formulae for the torques exerted on the disk by the triaxial halo and the dark matter torus, and with these formulae we successfully describe the behaviors of the disks in our simulations. The techniques used in deriving these formulae could be applied for realistic halos with more complex structures.

What is the largest Einstein radius in the universe?

The Einstein radius plays a central role in lens studies as it characterises the strength of gravitational lensing. The distribution of Einstein radii near the upper cutoff should probe the largest mass concentrations in the universe. Adopting a triaxial halo model, we compute expected distributions of large Einstein radii. To assess the cosmic variance, we generate a number of all-sky Monte-Carlo realisations. We find that the expected largest Einstein radius in the universe is sensitive to the cosmological model: for a source redshift z=1, they are 42^{+9}_{-7}, 35^{+8}_{-6}, and 54^{+12}_{-7} arcseconds, assuming best-fit parameters of the WMAP5, WMAP3 and WMAP1 data, respectively. These values are broadly consistent with current observations given their incompleteness. For the same source redshift, we expect in all-sky 35 (WMAP5), 15 (WMAP3), and 150 (WMAP1) clusters that have Einstein radii larger than 20". Whilst the values of the largest Einstein radii are almost unaffected by the primordial non-Gaussianity currently of interest, the abundance of large lens clusters should probe non-Gaussianity competitively with CMB, but only if other cosmological parameters are well-measured. We also find that these "superlens" clusters constitute a highly biased population. For instance, a substantial fraction of these superlens clusters have major axes preferentially aligned with the line-of-sight. As a consequence, the projected mass distributions of the clusters are rounder by an ellipticity of 0.2 and have 40%-60% larger concentrations compared with typical clusters with similar redshifts and masses. We argue that the large concentration measured in A1689 is consistent with our model prediction at the 1.2\sigma level. (Abridged)

A new look at massive clusters: weak lensing constraints on the triaxial dark matter haloes of A1689, A1835 and A2204

Measuring the three-dimensional (3D) distribution of mass on galaxy cluster scales is a crucial test of thecold dark matter (� CDM) model, providing constraints on the nature of dark mat- ter. 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 spher- ical halo models while a growing body of work indicates that triaxial 3D halo structure is both common and important in parameter estimates. We recently introduced a Markov Chain Monte Carlo method to fit fully triaxial models to weak lensing data that gives parameter and error estimates that fully incorporate the true shape uncertainty present in nature. In this paper we apply that method to weak lensing data obtained with the ESO/MPG Wide Field Imager for galaxy clusters A1689, A1835 and A2204, under a range of Bayesian priors derived from theory and from independent X-ray and strong lensing observations. For Abell 1689, using a simple strong lensing prior we find marginalized mean parameter values M200 = (0.83 ± 0.16) × 10 15 h −1 Mand C = 12.2 ± 6.7, which are marginally consistent with the mass- concentration relation predicted inCDM. With the same strong lensing prior we find for Abell 1835 M200 = (0.67 ± 0.22) × 10 15 h −1 Mand C = 7.1 +10.6

An MCMC fitting method for triaxial dark matter haloes

Measuring the 3D distribution of mass on galaxy cluster scales is a crucial test of the Λ cold dark matter (ΛCDM) 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. Though lensing is sensitive only to 2D projected structure and is thus incapable of independently constraining 3D models, the very strong assumptions about the symmetry of the lensing halo implied with circular or perturbative elliptical Navarro, Frenk & White (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. Using weak lensing data alone, the fits are sensitive to the Bayesian priors on axis ratio; we explore the impact of various general and physically motivated priors, and emphasize the need for future work combining lensing data with other data types to fully constrain the 3D structure of galaxy clusters. 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 ΛCDM, 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.

The Causes of Halo Shape Changes Induced by Cooling Baryons: Disks versus Substructures

Cold dark matter cosmogony predicts triaxial dark matter halos, whereas observations find quite round halos. This is most likely due to the condensation of baryons leading to rounder halos. We examine the halo phase space distribution basis for such shape changes. Triaxial halos are supported by box orbits, which pass arbitrarily close to the density center. The decrease in triaxiality caused by baryons is thought to be due to the scattering of these orbits. We test this hypothesis with simulations of disks grown inside triaxial halos. After the disks are grown we check whether the phase space structure has changed by evaporating the disks and comparing the initial and final states. While the halos are substantially rounder when the disk is at full mass, their final shape after the disk is evaporated is not much different from the initial. Likewise, the halo becomes (more) radially anisotropic when the disk is grown, but the final anisotropy is consistent with the initial. Only if the baryons are unreasonably compact or massive does the halo change irreversibly. We show that the character of individual orbits is not generally changed by the growing mass. Thus, the central condensation of baryons does not destroy enough box orbits to cause the shape change. Rather, box orbits merely become rounder along with the global potential. However, if angular momentum is transferred to the halo, either via satellites or via bars, a large irreversible change in the halo distribution occurs. The ability of satellites to alter the phase space distribution of the halo is of particular concern to galaxy formation simulations since halo triaxiality can profoundly influence the evolution of disks.

The Hubble constant from galaxy lenses: impacts of triaxiality and model degeneracies

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 important factor is the triaxial structure of the lensing galaxy halo; most lens models account for halo shape simply by perturbing the projected spherical lensing potential, an approximation that is often necessary but that is inadequate at the levels of triaxiality predicted in the CDM paradigm. To quantify the potential error introduced by this assumption in estimates of the Hubble parameter, we strongly lens a distant galaxy through a sample of triaxial softened isothermal halos and use an MCMC method to constrain the lensing halo profile and the Hubble parameter from the resulting multiple image systems. We explore the major degeneracies between the Hubble parameter and several parameters of the lensing model, finding that without a way to accurately break these degeneracies accurate estimates of the Hubble parameter are not possible. Crucially, we find that triaxiality does not significantly bias estimates of the Hubble constant, and offer an analytic explanation for this behaviour in the case of isothermal profiles. Neglected triaxial halo shape cannot contribute to the low Hubble constant values derived in a number of galaxy lens systems.

Infall Caustics in Dark Matter Halos?

We show that most particle and subhalo orbits in simulated cosmological cold dark matter halos are surprisingly regular and periodic: the phase-space structure of the outer halo regions shares some of the properties of the classical self-similar secondary infall model. Some of the outer branches are clearly visible in the radial velocity-radius plane at certain epochs. However, they are severely broadened in realistic, triaxial halos with nonradial, clumpy, mass accretion. This prevents the formation of high-density caustics: even in the best cases there are only broad, very small (<10%) enhancements in the spherical density profile. Larger fluctuations in ρ (r) caused by massive satellites are common. Infall caustics are therefore too weak to affect lensing or dark matter annihilation experiments. Their detection is extremely challenging, as it requires a large number of accurate tracer positions and radial velocities in the outer halo. The stellar halo of the Milky Way is probably the only target where this could become feasible in the future.

Probing the intrinsic shape and alignment of dark matter haloes using SDSS galaxy groups

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 different axis ratios. We find that the halo shape has a strong dependence on the halo mass. While the haloes of low-mass groups are nearly spherical, those of massive groups tend to be prolate. For groups containing at least four members, the statistical distribution of their measured ellipticities does not have a strong dependence on the colours of their central galaxies. Our analysis further shows that the average three-dimensional axis ratio for haloes with 12 < log[M/(h −1 M� )] � 15 is about 1 : 0.46 : 0.46, resulting in a projected axis ratio of ∼0.77. Our results for the alignment between the orientation of the central galaxy of a group and the distribution of their satellite galaxies are in broad agreement with those obtained by Yang et al. The distribution of satellite galaxies preferentially aligns with the major axis of the central galaxy, with a clear dependence on both halo mass and galaxy colours. In particular, the alignment is stronger in more massive groups, and the strongest alignment is seen between red centrals and the distribution of red satellites. For groups with blue centrals, no significant alignment is detected. Finally, we examine how the observed alignment can be reproduced with the information about the halo axis ratios. The observed alignment signal can be reproduced if the angle between the major axis of the central galaxy and the projected major axis of the host halo has a Gaussian distribution with a mean of 0 ◦ and a dispersion of ∼23 ◦ .

Weak Elliptical Distortion of the Milky Way Potential traced by Open Clusters

From photometric observations and star counts, the existence of a bar in the central few kpc of the Galaxy is suggested. It is generally thought that our Galaxy is surrounded by a massive invisible halo. The gravitational potential of the Galaxy is therefore made non-axisymmetric generated by the central triaxial bar, by the outer triaxial halo, and/or by the spiral structures. Selecting nearly 300 open clusters with complete spatial velocity measurements and ages, we were able to construct the rotation curve of the Milky Way within a range of 3 kpc of the Sun. Using a dynamic model for an assumed elliptical disk, a clear weak elliptical potential of the disk with ellipticity of (R0) = 0.060±0.012 is detected, the Sun is found to be near the minor axis, displaced by 30°±3°. The motion of the clusters is suggested to be on an oval orbit rather than on a circular one.

An analytical model of surface mass densities of cold dark matter haloes - with an application to MACHO microlensing optical depths

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 routine ly 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 - 1.5. In cluster sized haloes, we find that triaxiality can cause sc atter in the surface mass density of the haloes up to �+ = +60% and � = 70%, where the 1-� limits are relative to the analytical NFW model given value. Subhaloes can increase this scatter to �+ = +70% and � = 80%. In galaxy sized haloes, the triaxial scatter can be as high a s �+ = +80% and � = 70%, and with subhaloes the values can change to �+ = +40% and � = 80%. We present an analytical model for the surface mass density scatter as a function of distance to the halo centre, halo redshift and halo mass. The analytical description enables one to investigate the reliability of results obtained with sim plified halo models. Additionally, it provides the means to add simulated surface density scatter to analytical density profiles. As an example, we discuss the impact of our results on the calculation of microlensing optical depths for MACHOs in CDM haloes.

A statistical study of weak lensing by triaxial dark matter haloes: consequences for parameter estimation

Measuring the distribution of mass on galaxy cluster scales is a crucial test of the cold dark matter (CDM) model, providing constraints on the nature of dark matter. Recent work investigating mass distributions of individual galaxy clusters using gravitational lensing has illuminated 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 typically employ only simple spherical halo models with canonical Navarro, Frenk & White (NFW) slopes, while the haloes formed in simulations show a range of more complex features. Here we investigate the impact of such expected deviations from the canonical NFW halo profile on mass and parameter estimation using weak gravitational lensing on massive cluster scales. Changes from the canonical NFW profile slopes are found to affect parameter estimation. However, the most important deviation is halo triaxiality because it is impossible even with fiducial weak lensing data to fully resolve the 3D structure of the halo due to lensing's sensitivity only to projected mass. Significant elongation of the halo along the line of sight can cause the mass and concentration to be overestimated by as much as 50 per cent and by a factor of 2, respectively, while foreshortening has the opposite effect. Additionally, triaxial haloes in certain orientations are much better lenses than their spherical counterparts of the same mass, indicating that clusters chosen for study because of evident lensing are likely to be drawn from the high-triaxiality end of the halo shape distribution; cluster samples chosen with no shear bias return correct average parameter values. While the effects of triaxiality alone may not be enough to fully explain the very high concentrations reported for some clusters, such as Abell 1689, they go a long way in easing the tensions between observations and the predictions of the CDM paradigm.

Kinematics of hypervelocity stars in the triaxial halo of the Milky Way

Hypervelocity stars (HVSs) ejected by the massive black hole at the Galactic center have unique kinematic properties compared to other halo stars. Their trajectories will deviate from being exactly radial because of the asymmetry of the Milky Way potential produced by the flattened disk and the triaxial dark matter halo, causing a change of angular momentum that can be much larger than the initial small value at injection. We study the kinematics of HVSs and propose an estimator of dark halo triaxiality that is determined only by instantaneous position and velocity vectors of HVSs at large Galactocentric distances (r>~50kpc). We show that, in the case of a substantially triaxial halo, the distribution of deflection angles (the angle between the stellar position and velocity vector) for HVSs on bound orbits is spread uniformly over the range 10--180deg. Future astrometric and deep wide-field surveys should measure the positions and velocities of a significant number of HVSs, and provide useful constraints on the shape of the Galactic dark matter halo.