The Shapes of Galaxies and Their Dark Halos

PREFACE.

CONTENTS.

We discuss the factors leading to spatial correlations in the observed shapes of galaxies and their implications for weak lensing measurements. Focusing on a model where the intrinsic correlations arise from angular momentum correlations, we examine the predicted shape correlations and how they may be distinguished from weak lensing.

A new technique is proposed to measure the flattening of dark matter halos using weak gravitational lensing. The shape parameters of the mass distribution of foreground galaxies can be measured from the two-dimensional shear field derived from background galaxies using an extension of the standard galaxy-galaxy lensing scheme. Modeling galaxies using an elliptical, isothermal profile, it is demonstrated that measuring the flatness is feasible with data from the on-going Sloan Digital Sky Survey (SDSS).

It has recently been argued that the observed ellipticities of galaxies may be determined at least in part by the primordial tidal gravitational field in which the galaxy formed. Long-range correlations in the tidal field could thus lead to an ellipticity-ellipticity correlation for widely separated galaxies. I present results of a calculation of the angular power spectrum of intrinsic galaxy shape correlations using a new model relating ellipticity to angular momentum. I show that for low redshift galaxy surveys, the model predicts that intrinsic correlations will dominate correlations induced by weak lensing, in good agreement with previous theoretical work and observations. The model also produces 'E-mode' correlations enhanced by a factor of 3.5 over 'B-modes' on small scales, making it harder to disentangle intrinsic correlations from weak lensing.

Gravitational lensing causes background galaxy images to become aligned, and the statistical characteristics of the image alignments can then be used to constrain the power spectrum of mass fluctuations. Analyses of gravitational lensing assume that intrinsic galaxy alignments are negligible, but if this assumption does not hold, then the interpretation of image alignments will be in error. As gravitational lensing experiments become more ambitious and seek to measure very low-level alignments arising from lensing by large-scale structure, it becomes more important to estimate the level of intrinsic alignment in the galaxy population. In this article, I review the cluster of independent theoretical studies of this issue, as well as the current observational status. Theoretically, the calculation of intrinsic alignments is by no means straightforward, but some consensus has emerged from the existing works, despite each making very different assumptions. This consensus is that a) intrinsic alignments are a small but non-negligible (≲ 10%) contaminant of the lensing ellipticity correlation function, for samples with a median redshift ; b) intrinsic alignments dominate the signal for low-redshift samples , as expected in the SuperCOSMOS lensing survey and the Sloan Digital Sky Survey.

We present a new approach to measure the shapes of galaxies, a fundamental task in observational astronomy. This approach is based on the decomposition of a galaxy image into a series of orthogonal basis functions, or 'shapelets'. Our choice of basis functions, namely the Gauss-Hermite series, has a number of remarkable properties under distortions, convolutions and noise, which makes them particularly well suited for astrophysical applications. In particular, we describe how they can be used to measure the shear induced by weak gravitational lensing, with the precision required for upcoming surveys. We also show how shapelets can be used to reconstruct images from interferometric observations. Other application of shapelets, such as image compression, PSF deconvolution, de-projection and the study of galaxy morphology, are also briefly discussed.

The accurate measurement of galaxy ellipticities is vital for weak lensing studies, in particular cosmic shear. We describe a Bayesian approach to this problem in which galaxies are parameterized as sums of Gaussians, convolved with a PSF which is also a sum of Gaussians, following Kuijken (1999). We calculate the uncertainties in the output parameters using a Markov Chain Monte Carlo approach. We show that for a simple simulation, the ellipticity estimates do not give a biased result when averaged by statistical weight. It is shown that the uncertainties in the ellipticities are not increased by allowing freedom in the galaxy radial profile, or by allowing the photon shot noise level to be a free parameter. Finally we confirm the result of Kuijken (1999) that on changing the ellipticity of two point spread function Gaussian components, the reconstructed galaxy ellipticity is unbiased.

Realistic self-consistent models of galaxies can be obtained by specifying the velocity field and solving the Euler equation semi-analytically. The velocity potential Ψ is introduced as the main hydrodynamic function which determines the physical quantities such as the velocity , the density ρ, the vorticity , and the pressure p. The hydrodynamic equation is expressed in terms of the velocity potential Ψ, in order to study self gravitating equilibrium configurations parameterized by suitable velocity fields.

Gravitational Lensing is a unique tool to constrain the mass distribution of collapsed structures, this is particularly true for galaxies, either on a case by case basis using multiple images of background sources (such as quasars), or statistically using the so called galaxy-galaxy lensing technique. First, I will present the lensing theory, and then discuss the various methods applied to current observations. Finally, I will review the bright future prospects of galaxy lensing that will benefit of the development of high resolution, large, wide and deep (lensing) surveys.

We present measurements of the extended dark halo profiles of bright early-type galaxies at redshifts 0.1 < z < 0.9 obtained via galaxy-galaxy lensing analysis of images taken at the CFHT using the UH8K CCD mosaic camera. Six 0.5 × 0.5 degree fields were observed for a total of 2 hours each in I and V, resulting in catalogs containing ~ 20000 galaxies per field. We used V - I color and I magnitude to select bright early-type galaxies as the lens galaxies, yielding a sample of massive lenses with fairly well determined redshifts and absolute magnitudes M ~ M_* ± 1. We paired these with faint galaxies lying at angular distances 20″ < θ < 60″, corresponding to physical radii of 26 < r < 77h^-1 kpc (z = 0.1) and 105 < r < 315h^-1 kpc (z = 0.9), and computed the mean tangential shear γ_T(θ) of the faint galaxies. The shear falls off with radius roughly as γ_T ∝ 1/θ as expected for flat rotation curve halos. The shear values were weighted in proportion to the square root of the luminosity of the lens galaxy. Our results give a value for the average mean rotation velocity of an L_⋆ galaxy halo at r ~ 50 - 200h^-1 kpc of for a flat lambda (Ω_m0 = 0.3, Ω_λ0 = 0.7) cosmology ( for Einstein-de Sitter), and with little evidence for evolution with redshift. We find a mass-to-light ratio of M/L_B ≃ 121 ± 28h(r/100h^-1 kpc) (for L_⋆ galaxies) and these halos constitute Ω ≃ 0.04 ± 0.01(r/100h^-1 kpc) of closure density.

We use comparisons between the shapes of gravitational lens galaxies and models for their mass distributions to derive statistical constraints on the alignment of the mass distribution relative to the observed lens galaxy and on the strength of tidal shear perturbations. The mass distributions are aligned with the luminous galaxies, with a 〈Δθ²〉^1/2 < 10° upper limit on the dispersion in the angle between the major axes. Statistical constraints, such as our bound on the misalignment between mass and light, are an important new approach to reducing the uncertainties in individual lens models, particularly for lenses used to estimate the Hubble constant.

We describe weak lensing measurements of galaxy halos. Early SDSS data are used to measure the galaxy-mass correlation function (GMCF). This GMCF is a direct measure of the massive halos which luminous galaxies occupy. To make these measurements we use a sample of ~35,000 lens galaxies and 3.6×10⁶ background 'source' galaxies. Every lens galaxy has a spectroscopic redshift and highly accurate five color photometry. As a result our determination of the mass and size scales of the GMCF are very robust. Detailed information about all lens objects also allows us to study the relationship between the luminous properties of galaxies (luminosity, morphology, local density) and the dark matter halos which surround them. To make this comparison we define an aperture mass M₂₆₀, which characterizes the normalization of the GMCF. While M₂₆₀ is essentially independent of the u′ luminosity of a galaxy, we find that it is linearly dependent on luminosity in red bands. This suggests that the current rate of star formation in a galaxy (reflected by the u′ light) is poorly correlated with its dark matter environment. The light in redder bands however, which reflects the integrated star formation history of the lenses, is closely coupled to the dark matter halos in which the galaxies form.

Here we present results from a maximum likelihood analysis of galaxy-galaxy weak lensing effects as measured in a 12.5′ × 12.5′ field obtained at the Nordic Optical Telescope, on La Palma, Spain. The analysis incorporates photometric redshifts and gives circular velocities consistent with previous weak lensing work.

We study gravitational lensing by groups of galaxies in both the strong and weak lensing regime. As the abundance of groups is high, gravitational lensing by groups is likely to be important observationally. Here, we examine the shear, magnification, image geometries and time delays produced by compact groups and discuss how these observables depend on the details of the mass distribution in the group. We find that in the weak lensing regime a tangential shear signal of order 3 per cent is to be expected and that it depends measurably on the mass distribution in the group. In the strong lensing regime we show that a group's potential may have a significant effect on the measured image geometries, magnification ratios and time delays for individual multiple-image systems. We also find that some statistical lensing properties, like the distribution of time delays, depend on the details of the groups mass distribution.

We summarize the observed properties and lens modeling results of the unique JVAS system B2114+022. We argue that the observational and modeling results are most consistent with a two-plane lensing hypothesis, particularly for the widest separated and observationally similar radio components A and D. We point out the potential power of this system for constraining galactic mass models and hence deriving the relations between the light and mass distributions.

The systematic weak lensing of background galaxies by foreground galaxies has been detected by a number of different investigations. This effect is known as "galaxy–galaxy lensing" and it promises to provide strong constraints on the physical parameters of the dark matter halos which surround galaxies (such as their typical physical extents, total masses, and projected shapes). Here we use detailed Monte Carlo simulations to investigate galaxy–galaxy lensing by non–spherical dark matter halos and we estimate the area of a deep, ground–based imaging survey which would be required to detect the effects of flattened halos (〈∊〉 ~ 0.3) on the galaxy–galaxy lensing signal.

We introduce the octopole moment measurement of the light distribution in galaxies as a probe of the weak lensing shear field. While traditional ellipticity estimates of local shear have traditionally been limited by the width of the background intrinsic ellipticity distribution, the dispersion in the intrinsic octopole distribution is expected to be quite small, meaning that the signal is ultimately limited by measurement noise, not by intrinsic scatter. In a series of estimates, we show that current observations are at the regime where the octopole estimates will be able to contribute to the overall accuracy of the estimates of local shear fields.

In this contribution, we illustrate that by combining lensing and X-ray surface brightness data the elongation of clusters along the line-of-sight can be estimated. The distribution of three dimensional shapes of the mass in clusters of galaxies could potentially place constraints on Ω and provide clues to the nature of dark matter. With the abundance of multi-wavelength data the prospects for mapping the three-dimensional shapes are promising.

I present an analysis of the shapes of dark matter halos in ΛCDM and ΛWDM cosmologies. The main results are derived from a statistical sample of galaxy-mass halos drawn from a high resolution ΛCDM N-body simulation. Halo shapes show significant trends with mass and redshift: low-mass halos are rounder than high mass halos, and, for a fixed mass, halos are rounder at low z. Contrary to previous expectations, which were based on cluster-mass halos and non-COBE normalized simulations, ΛCDM galaxy-mass halos at z = 0 are not strongly flattened, with short to long axis ratios of s = 0.70 ± 0.17. I go on to study how the shapes of individual halos change when going from a ΛCDM simulation to a simulation with a warm dark matter power spectrum (ΛWDM). Four halos were compared, and, on average, the WDM halos are more spherical than their CDM counterparts (s ≃ 0.77 compared to s ≃ 0.71). A larger sample of objects will be needed to test whether the trend is significant.

Numerical simulations have revealed the presence of long-lived substructure in Cold Dark Matter (CDM) halos. These surviving cores of past merger and accretion events vastly outnumber the known satellites of the Milky Way. This finding has prompted suggestions that substructure in cold dark matter (CDM) halos may be incompatible with observation and in conflict with the presence of thin, dynamically fragile stellar disks. N-body simulations of a disk/bulge/halo model of the Milky Way that includes several hundred dark matter satellites with masses, densities and orbits derived from high-resolution cosmological CDM simulations indicate that substructure plays only a minor dynamical role in the heating of the disk. This is because the orbits of satellites seldom take them near the disk, where their tidal effects are greatest. We conclude that substructure might not preclude virialized CDM halos from being acceptable hosts of thin stellar disks like that of the Milky Way.

Spherical density profiles and specific angular momentum profiles of Dark Matter halos found in cosmological N–body simulations have been measured extensively. The distribution of the total angular momentum of dark matter halos is also used routinely in semi–analytic modeling of the formation of disk galaxies. However, it is unclear whether the initial (i.e. at the time the halo is assembled) angular momentum distributions of baryons is related to the dark matter at all. Theoretical models for ellipticities in weak lensing studies often rely on an assumed correlation of the angular momentum vectors of dark matter and gas in galaxies. Both of these assumptions are shown to be in reasonable agreement with high resolution cosmological smoothed particle hydrodynamical simulations that follow the dark matter as long as only adiabatic gas physics is included. However, we argue that in more realistic models of galaxy formation one expects pressure forces to play a significant role at "turn–around". Consequently the torquing force on DM and baryons will be uncorrelated and their respective angular momenta are not expected to align. An SPH simulation with ad-hoc feedback is presented that illustrates these effects. Massive low redshift elliptical galaxies may be a notable exception where "light may trace mass".

I give a very brief review of aspects of internal dynamics that affect the global shape of a galaxy, focusing on triaxiality, bars and warps. There is general agreement that large central masses can destroy triaxial shapes, but recent simulations of this process seem to suffer from numerical difficulties. Central black holes alone are probably not massive enough to destroy global triaxiality, but when augmented by star and gas concentrations in barred galaxies, the global shape may be affected. Even though we do not understand the origin of bars in galaxies, they are very useful as probes of the dark matter density of the inner halo. Finally, I note that dynamical friction acts to reduce a misalignment between the spin axes of the disk and halo, producing a nice warp in the outer disk which has many of the properties of observed galactic warps.

Elliptical galaxies formed in a major merger have a tendency to become more nearly spherical with time, thanks to the gravitational effect of their central black hole (or black holes). Observational results indicate that elliptical galaxies with older stellar populations (t > 7.5 Gyr) have rounder central isophotes than ellipticals with younger stellar populations. In addition, the older ellipticals tend to have core profiles, while the younger ellipticals have power-law profiles. Numerical simulations of galaxy mergers indicate that if one or both of the progenitors have a central black hole with mass ~ 0.2% of the stellar mass, then the effect of the black hole(s) is to make the central regions of the remnant rounder, with a characteristic time scale of a few gigayears.

This paper reviews some recent work on the properties of the outer halos of galaxies. I particularly focus on recent and upcoming advances made with the study of globular clusters. Globular clusters can be observed out to ~ 100 kpc from the centers of galaxies, allowing the study of galactic halos well beyond the regions probed by many other techniques such as observations of the integrated light of galaxies. In the few well-studied cases to date, the study of globular cluster systems has provided dynamical evidence for dark matter halos around elliptical galaxies, and demonstrated kinematic differences between different globular cluster populations that shed light on the formation history of their host galaxies.

We examine the claim by Oppenheimer et al. (2001) that the local halo density of white dwarfs is an order of magnitude higher than previously thought. As it stands, the observational data support the presence of a kinematically distinct population of halo white dwarfs at the >99% confidence level. A maximum-likelihood analysis gives a radial velocity dispersion of and an asymmetric drift of , for a Schwarzschild velocity distribution function with σ_U:σ_V:σ_W = 1:2/3:1/2. Halo white dwarfs have a local number density of , which amounts to per cent of the nominal local dark-matter halo density and is times (90% C.L.) higher and thus only marginally in agreement with previous estimates. We discuss several direct consequences of this white-dwarf population (e.g. microlensing) and postulate a potential mechanism to eject young white dwarfs from the disc to the halo, through the orbital instabilities in triple or multiple stellar systems.

Keck spectroscopy is presented for four dwarf elliptical galaxies in the Virgo Cluster. At this distance, the mean velocity and velocity dispersion are well resolved as a function of radius between 100 to 1000 pc, allowing a clear separation between nuclear and surrounding galaxy light. We find a variety of dispersion profiles for the inner regions of these objects, and show that none of these galaxies is rotationally flattened.

We present an investigation of the halo dynamics of M31 using planetary nebulae (PNe) velocities. We describe our current velocity data, and imaging to enable spectroscopy to be performed deeper into the galaxy halo (~ 20 kpc). In the future we will measure the total mass, mass distribution and velocity anisotropy as a function of radius. We plan to compare kinematics of the globular cluster and PNe populations to test if both trace similar stellar populations.

I present results from an ongoing Keck spectroscopic survey of red giant stars in the halo of the Andromeda spiral galaxy (M31) and its dwarf spheroidal satellites. The observed shape of M31's stellar halo, roughly 2:1 in projection, is consistent with rotational flattening: its rotation speed and line-of-sight velocity dispersion are measured to be ν_rot ≈ σ_ν ≈ 150 km s^-1. The M31 stellar halo appears to be denser and/or larger than our Galaxy's halo. Yet, the best estimate of the mass of M31's dark halo, using the most extensive set of dynamical tracers available, suggests that the galaxy is likely to be less massive than our own. A small group of metal-rich stars is seen at a common velocity indicative of substructure in M31's halo or a disk that is very extended and/or warped. The unusual properties of the M31 satellite LGS3, classified as a transition type object between dwarf spheroidals and dwarf irregulars, may be related to its being on a highly eccentric orbit around the parent galaxy. The brightest of the M31 dwarf spheroidal satellites, Cas dSph (or And VII), has an internal velocity dispersion of about 9 km s^-1, which is indicative of a dark matter content consistent with the extrapolation of the properties of other Local Group dwarf spheroidal satellites.

This paper reviews the constraints that can be placed on the shapes of disk galaxies' dark halos using the distribution and kinematics of atomic hydrogen. These data indicate that dark halos are close to axisymmetric, with their axes of symmetry co-aligned with their disk axes. They also appear to be oblate, with shortest-to-longest axis ratios displaying quite a broad range of values from ~ 0.2 to ~ 0.8. These results are consistent with the predicted shapes of halos in cold dark matter scenarios, but rule out some of the more exotic dark matter candidates. However, the total number of measurements is still depressingly small, and more data are required if halo shape is to become a powerful diagnostic for theories of galaxy formation and evolution.

A polar ring galaxy has a ring or disk of dust, gas and stars orbiting almost over the pole of a central early-type galaxy. Measuring orbital speeds in the ring and the central object thus probes two roughly perpendicular planes. This can give a sensitive indication of how flattened the galactic mass distribution, which includes the unseen halo, must be. If the dark halos of polar ring systems are typical, the dark halos of galaxies range from nearly round, to being so flat that they approach the boundary of dynamical stability.

Rotation curves place important constraints on the radial mass distribution of dark matter halos, ρ(r). At large radii, rotation curves tend to become asymptotically flat. For ρ(r) ∝ r^α, this implies α ≈ -2, which persists as far out as can be measured. At small radii, the data strongly prefer dark matter halos with constant density cores (α ≈ 0) over the cuspy halos (α ≤ -1) predicted by cosmological simulations. As better data have been obtained, this cusp-core problem has become more severe.

If a satellite in orbit around the Milky Way is losing mass due to tidal forces the debris will spread in leading/trailing streamers along its orbit. These streamers are dynamically cold and (if in an orbit at sufficient distance from the Galaxy) can maintain coherence for a Hubble time. Such unique properties make them particularly sensitive probes of the mass distribution in the Milky Way. In this contribution I will briefly outline the properties of tidal debris and evidence for its existence around the Milky Way. I will then review methods for recovering the global mass distribution in the Milky Way using such stellar distributions. Finally, I will describe an approach to using tidal debris as a constraint on the degree of dark matter substructure around the Milky Way.

Stars and their kinematics provide one of the tools available for studies of the shapes of galaxies and their halos. In this review I focus on two specific applications: the shape of the Milky Way dark halo and the shape of the LMC disk. The former is constrained by a variety of observations, but an accurate determination of the axial ratio q_DH remains elusive. A very flattened Milky Way dark halo with q_DH ≤ 0.4 is ruled out, and values q_DH ≥ 0.7 appear most consistent with the data. Near-IR surveys have revealed that the LMC disk is not approximately circular, as long believed, but instead has an axial ratio of 0.7 in the disk plane. The elongation is perpendicular to the Magellanic Stream, indicating that it is most likely due to the tidal force of the Milky Way. Equilibrium dynamical modeling of galaxies is important for many applications. At the same time, detailed studies of tidal effects and tidal streams have the potential to improve our understanding of both the Milky Way dark halo and the structure of satellite galaxies such as the LMC.

We present results from our survey of RR Lyrae stars in the halo of the Milky Way. Since these stars are standard candles, the survey is capable of finding spatial structures in the halo, such as streams of debris left by the destruction of small satellites by the tidal forces of the Milky Way. We have found a large clump of stars at 50 kpc from the galactic center which is likely related to a tidal tail of the Sagittarius dwarf spheroidal galaxy. Several other over-densities were found in different regions. The halo of the Milky Way does not seem to have a uniform distribution of stars far from the galactic center.

We are exploring the extended stellar distributions of Galactic satellite galaxies and globular clusters. For seven objects studied thus far, the observed profile departs from a King function at large r, revealing a "break population" of stars. In our sample, the relative density of the "break" correlates to the inferred M/L of these objects. We discuss opposing hypotheses for this trend: (1) Higher M/L objects harbor more extended dark matter halos that support secondary, bound, stellar "halos". (2) The extended populations around dwarf spheroidals (and some clusters) consist of unbound, extratidal debris from their parent objects, which are undergoing various degrees of tidal disruption. In this scenario, higher M/L ratios reflect higher degrees of virial non-equilibrium in the parent objects, thus invalidating a precept underlying the use of core radial velocities to obtain masses.

Surface photometry of the M31 satellites M32 and NGC 205 is compared to numerical simulations of satellite destruction to constrain orbital parameters and the interaction history of the M31 subgroup. Our analysis reveals the following preliminary results: (1) Generic features of tidal disruption in the simulations include an extended "extra-tidal" excess region and an inner depletion zone, both of which are observed in M32 and NGC 205; (2) M32 is likely to be on a highly eccentric orbit well away from pericenter; (3) Surface brightness and luminosity evolution estimates for M32, the prototypical compact elliptical galaxy, imply that it is not simply the residual core of a tidally-stripped normal elliptical galaxy, but was instead formed in a truncated state.

High resolution N-body simulations show a high abundance of galaxy satellites, which is not seen observationally. It appears that too many subhalos survive in simulated galaxy halos. One likely cause for this is that dynamical friction is not properly simulated yet, not even for the highest resolution simulations to date, resulting in an "undermerging" problem. Another issue that can be resolved by properly simulating dynamical friction is the cuspiness of N-body halos. The orbital energy loss suffered by satellites causes their parent halo to heat up. This heating up can transform a central cusp into a core, especially if this heating is actually most efficient in the center. The orbital decay of a sufficient number of galaxy satellites can therefore, when properly simulated, resolve both issues.

I investigate some characteristics of dark matter in the Local Group and the nearby Sculptor Group. I find that there is no evidence for an extended dark matter halo around the Local Group. In addition, the angular momentum of the visible matter in the Sculptor Group is consistent with having been produced by tidal interaction among the galaxies, which indicates that the dark matter and luminous matter angular momenta are aligned.

We present preliminary constraints on the shape of the dark matter halo in the elliptical galaxy NGC 720 obtained from new Chandra imaging data. We also review X-ray constraints on dark matter shapes in galaxy clusters obtained with ROSAT and present some preliminary Chandra results.

Chandra's high angular resolution allows the detailed study of X-ray emission from elliptical galaxies. Chandra images show the interactions of radio plasmas with the hot interstellar medium, populations of galactic sources, structure in X-ray jets and the presence of AGN. Chandra spectroscopy allows the various emission mechanisms to be determined. This paper discusses the ellipticals Cen A and M84 as well as fossil groups.

We have used STIS aboard HST to search for Lyα absorption in the outer regions of nine nearby (cz < 6000 km s^-1) galaxies using background QSOs and AGN as probes. The foreground galaxies are intercepted between 26 and 199 h^–1 kpc from their centers, and in all cases we detect Lyα within ±500 km s^-1 of the galaxies' systemic velocities. The intervening galaxies have a wide range of luminosities, from M_B = -17.1 to -20.0, and reside in various environments: half the galaxies are relatively isolated, the remainder form parts of groups or clusters of varying richness. The equivalent widths of the Lyα lines range from 0.08 – 0.68 Å and, with the notable exception of absorption from one pair, correlate with sightline separation in a way consistent with previously published data, though the column densities derived from the lines do not. The lack of correlation between line strength and galaxy luminosity or, in particular, the environment of the galaxy suggests that the absorption is not related to any individual galaxy, but arises in gas which follows the same dark-matter structures that the galaxies inhabit.

No abstract received.