Anisotropy and rotation in homeoidally striated Jacobi ellipsoids

In this paper a unified theory of systematically rotating and peculiar motions is developed for homeoidally striated Jacobi ellipsoids, where both real and imaginary rotations are considered. The effect of positive or negative residual motion excess along the equatorial plane is considered to be equivalent either to an additional real or an imaginary rotation, respectively. The principle results consist of (i) the discovery that homeoidally striated Jacobi ellipsoids always admit an adjoint configuration i.e. a classical Jacobi ellipsoid of equal mass and axes; (ii) the establishment of further constraints on the amount of residual velocity anisotropy along the principal axes for triaxial configurations; (iii) the finding that bifurcation points from axisymmetric to triaxial configurations occur as in classical Jacobi ellipsoids, contrary to earlier findings. An interpretation of recent results from numerical simulations on stability is provided in the light of the model. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dwarf galaxy rotation curves and the core problem of dark matter haloes

The standard cold dark matter (CDM) model has recently been challenged by the claim that dwarf galaxies have dark matter haloes with constant-density cores, whereas CDM predicts haloes with steeply cusped density distributions. Consequently, numerous alternative dark matter candidates have recently been proposed. In this paper we scrutinize the observational evidence for the incongruity between dwarf galaxies and the CDM model. To this end, we analyse the rotation curves of 20 late-type dwarf galaxies studied by Swaters. Taking the effects of beam smearing and adiabatic contraction into account, we fit mass models to these rotation curves with dark matter haloes with different cusp slopes, ranging from constant-density cores to r ⁻² cusps. Even though the effects of beam smearing are small for these data, the uncertainties in the stellar mass-to-light ratio and the limited spatial sampling of the halo's density distribution hamper a unique mass decomposition. Consequently, the rotation curves in our sample cannot be used to discriminate between dark haloes with constant-density cores and r ⁻¹ cusps. We show that the dwarf galaxies analysed here are consistent with CDM haloes in a ΛCDM cosmology, and that there is thus no need to abandon the idea that dark matter is cold and collisionless. However, the data are also consistent with any alternative dark matter model that produces dark matter haloes with central cusps less steep than r ^−1.5. In fact, we argue that based on existing H  i rotation curves alone, at best weak limits can be obtained on cosmological parameters and/or the nature of the dark matter. In order to make progress, rotation curves with higher spatial resolution and independent measurements of the mass-to-light ratio of the disc are required.     

An alternative method of finding bifurcation points in pseudo-barotropes

Starting from the equations of hydrodynamics, which include both collisional and collisionless ideal fluids, the special case of pseudo-arotropes with anisotropic pressure distribution along tangential or vertical direction (in respect to a “vertical” rotation axis) is considered. We find that vertical motions are equivalent to an imaginary rotation, and call “pseudo-otation” the combination of rotation and real or imaginary peculiar circular motions. By use of a necessary condition for equilibrium, i.e. the coincidence of the boundary with an isopotential (gravitational + rotational centrifugal + real peculiar or imaginary peculiar centrifugal) surface, a new method of finding bifurcation points from axisymmetric to triaxial pseudo-arotropic sequences – discussed in an earlier paper – is dealt with for the systems under discussion. A simple application to the special case where the isopycnic surfaces are spheroidal discloses that, on one hand, steadily pseudo-otating, heterogeneous spheroids, cannot be equilibrium configurations and, on the other hand, the same results obtained by use of the virial technique hold when the current method can work. Then the coincidence of the boundary with an isopotential surface and the validity of the virial equations of the second order make two independent (necessary) conditions for equilibrium and both must be satisfied. Under the further assumptions of steady rotation and homeoidally or focaloidally striated distribution of matter, the configurations for which a bifurcation point must necessarily occurr, are determined. In the former alternative a connection is also established, between local (on the boundary) and global anisotropy of pressure distribution; in particular, it is found that local isotropy (on the boundary) involves global isotropy and vice versa. In both cases, the right amount of of anisotropy turns out to yield violation of a treshold for stability, ϵ_rot = −E_rot/E_pot ⩽ 0.14, conjectured by Ostriker and Peebles (1973). This result gives additional support to a conclusion established in an earlier paper: it seems more germane to speak about Ostriker-eebles conjecture for stability in connection with visible bodies of galaxies, instead of Ostriker-eebles criterion for stability in connection with self-ravitating fluids.     

Mass distribution in nearby Abell clusters

We study the mass distribution in six nearby  ( z < 0.06)  relaxed Abell clusters of galaxies A0262, A0496, A1060, A2199, A3158 and A3558. Given the dominance of dark matter in galaxy clusters, we approximate their total density distribution by the Navarro, Frenk & White (NFW) formula characterized by virial mass and concentration. We also assume that the anisotropy of galactic orbits is reasonably well described by a constant and that galaxy distribution traces that of the total density. Using the velocity and position data for 120–420 galaxies per cluster we calculate, after removal of interlopers, the profiles of the lowest order even velocity moments, dispersion and kurtosis. We then reproduce the velocity moments by jointly fitting the moments to the solutions of the Jeans equations. Including the kurtosis in the analysis allows us to break the degeneracy between the mass distribution and anisotropy and constrain the anisotropy as well as the virial mass and concentration. The method is tested in detail on mock data extracted from the N -body simulations of dark matter haloes. We find that the best-fitting Galactic orbits are remarkably close to isotropic in most clusters. Using the fitted pairs of mass and concentration parameters for the six clusters, we conclude that the trend of decreasing concentration for higher masses found in the cosmological N -body simulations is consistent with the data. By scaling the individual cluster data by mass, we combine them to create a composite cluster with 1465 galaxies and perform a similar analysis on such sample. The estimated concentration parameter then lies in the range  1.5 < c < 14  and the anisotropy parameter in the range  −1.1 < β < 0.5  at the 95 per cent confidence level.     

Dissipationless mergers of elliptical galaxies and the evolution of the fundamental plane

We carry out numerical simulations of dissipationless major mergers of elliptical galaxies using initial galaxy models that consist of a dark matter haloes and a stellar bulge with properties consistent with the observed fundamental plane. By varying the density profile of the dark matter haloes [standard Navarro, Frenk & White (NFW) profile versus adiabatically contracted NFW profile], the global stellar to dark matter mass ratio and the orbit of the merging galaxies, we are able to assess the impact of each of these factors on the structure of the merger remnant. Our results indicate that the properties of the remnant bulge depend primarily on the angular momentum and energy of the orbit; for a cosmologically motivated orbit, the effective radius and velocity dispersion of the remnant bulge remain approximately on the fundamental plane. This indicates that the observed properties of elliptical galaxies are consistent with significant growth via late dissipationless mergers. We also find that the dark matter fraction within the effective radius of our remnants increases after the merger, consistent with the hypothesis that the tilt of the fundamental plane from the virial theorem is due to a varying dark matter fraction as a function of galaxy mass.     

Dynamical friction and galaxy merging time-scales

The time-scale for galaxies within merging dark matter haloes to merge with each other is an important ingredient in galaxy formation models. Accurate estimates of merging time-scales are required for predictions of astrophysical quantities such as black hole binary merger rates, the build-up of stellar mass in central galaxies and the statistical properties of satellite galaxies within dark matter haloes. In this paper, we study the merging time-scales of extended dark matter haloes using N -body simulations. We compare these results to standard estimates based on the Chandrasekhar theory of dynamical friction. We find that these standard predictions for merging time-scales, which are often used in semi-analytic galaxy formation models, are systematically shorter than those found in simulations. The discrepancy is approximately a factor of 1.7 for M _sat/ M _host≈ 0.1 and becomes larger for more disparate satellite-to-host mass ratios, reaching a factor of ∼3.3 for M _sat/ M _host≈ 0.01. Based on our simulations, we propose a new, easily implementable fitting formula that accurately predicts the time-scale for an extended satellite to sink from the virial radius of a host halo down to the halo's centre for a wide range of M _sat/ M _host and orbits. Including a central bulge in each galaxy changes the merging time-scale by ≲10 per cent. To highlight one concrete application of our results, we show that merging time-scales often used in the literature overestimate the growth of stellar mass by satellite accretion by ≈40 per cent, with the extra mass gained in low mass ratio mergers.     

Dark matter halo structure in CDM hydrodynamical simulations

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

The universal rotation curve of spiral galaxies – II. The dark matter distribution out to the virial radius

In the current ΛCDM cosmological scenario, N -body simulations provide us with a universal mass profile, and consequently a universal equilibrium circular velocity of the virialized objects, as galaxies. In this paper we obtain, by combining kinematical data of their inner regions with global observational properties, the universal rotation curve of disc galaxies and the corresponding mass distribution out to their virial radius. This curve extends the results of Paper I, concerning the inner luminous regions of Sb–Im spirals, out to the edge of the galaxy haloes.     

Constraints on dark matter physics from dwarf galaxies through galaxy cluster haloes

One of the predictions of the standard cold dark matter model is that dark haloes have centrally divergent density profiles. An extensive body of rotation curve observations of dwarf and low surface brightness galaxies shows the dark haloes of those systems to be characterized by soft constant-density central cores. Several physical processes have been proposed to produce soft cores in dark haloes, each one with different scaling properties. With the aim of discriminating among them we have examined the rotation curves of dark-matter-dominated dwarf and low surface brightness galaxies and the inner mass profiles of two clusters of galaxies lacking a central cD galaxy and with evidence of soft cores in the centre. The core radii and central densities of these haloes scale in a well-defined manner with the depth of their potential wells, as measured through the maximum circular velocity. As a result of our analysis we identify self-interacting cold dark matter as a viable solution to the core problem, where a non-singular isothermal core is formed in the halo centre surrounded by a Navarro, Frenk & White profile in the outer parts. We show that this particular physical situation predicts core radii in agreement with observations. Furthermore, using the observed scalings, we derive an expression for the minimum cross-section ( σ ) which has an explicit dependence with the halo dispersion velocity ( v ). If m _x is the mass of the dark matter particle: σ m _x ≈4×10⁻²⁵ (100 km s⁻¹  v ⁻¹) cm² GeV⁻¹.     

Dark haloes of spiral galaxies: ISO photometry

We exclude hydrogen-burning stars, of any mass above the hydrogen-burning limit and any metallicity, as significant contributors to the massive haloes deduced from rotation curves to dominate the outer parts of spiral galaxies. We present and analyse images of four nearly edge-on bulgeless spiral galaxies (UGC 711, NGC 2915, UGC 12426, UGC 1459) obtained with ISOCAM (The CAMera instrument on board the Infrared Space Observatory ) at 14.5 and 6.75 μm. Our sensitivity limit for detection of any diffuse infrared emission associated with the dark haloes in these galaxies is a few tens of μJy per 6 × 6 arcsec² pixel, with this limit currently set by remaining difficulties in modelling the non-linear behaviour of the detectors. All four galaxies show zero detected signal from extended non-disc emission, consistent with zero halo-like luminosity density distribution. The 95 per cent upper limit on any emission, for NGC 2915 in particular, allows us to exclude very low mass main-sequence stars ( M  > 0.08 M⊙) and young brown dwarfs (≲1 Gyr) as significant contributors to dark matter in galactic haloes. Combining our results with those of the Galactic microlensing surveys, which exclude objects with M  < 0.01 M⊙, excludes almost the entire possible mass range of compact baryonic objects from contributing to Galactic dark matter.     

The oscillations and the stability of rotating masses with magnetic fields

Using first variations of the integral properties of equilibrium second-order virial relations, the existence of the point of bifurcation of rotating gaseous masses with magnetic fields is substantiated. With the presence of a magnetic field component along the axis of rotation, it is shown that the point of bifurcation, where the Jacobi ellipsoids branch off from the Maclaurin spheroids, is altered, and in fact shifts to higher values of eccentricity compared to the one (namely,e=0.81267) obtained when there is no magnetic field.     

Andromeda IV,a solitary gas‐rich dwarf galaxy

Observations are presented of the isolated dwarf irregular galaxy And IV made with the Hubble Space Telescope Advanced Camera for Surveys and the Giant Metrewave Radio Telescope in the 21 cm HI line. We determine the galaxy distance of 7.17 ± 0.31 Mpc using the Tip of Red Giant Branch method. The galaxy has a total blue absolute magnitude of –12.81 mag, linear Holmberg diameter of 1.88 kpc, and an HI ‐disk extending to 8.4 times the optical Holmberg radius. The HI massto‐blue luminosity ratio for And IV amounts 12.9 M_⊙/L_⊙. From the GMRT data we derive the rotation curve for the HI and fit it with different mass models. We find that the data are significantly better fit with an iso‐thermal dark matter halo, than by an NFW halo. We also find that MOND rotation curve provides a very poor fit to the data. The fact that the isothermal dark matter halo provides the best fit to the data supports models in which star formation feedback results in the formation of a dark matter core in dwarf galaxies. The total mass‐to‐blue luminosity ratio of 162 M_⊙/L_⊙ makes And IV among the darkest dIrr galaxies known. However, its baryonic‐to‐dark mass ratio (M_gas + M *)/M_T = 0.11 is close to the average cosmic baryon fraction of 0.15. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the physical connections between galaxies of different types

Galaxies can be classified in two broad sequences which are likely to reflect their formation mechanism. The 'main sequence', consisting of spirals, irregulars and all dwarf galaxies, is probably produced by gas settling within dark matter haloes. We show that the sizes and surface densities along this sequence are primarily determined by the distributions of the angular momentum and formation time of dark haloes. They are well reproduced by current cosmogonies provided that galaxies form late, at z  ≲ 2. In this scenario, dwarf ellipticals were small 'discs' at z  ∼ 1 and become 'ellipticals' after they fall into cluster environments. The strong clustering of dwarf ellipticals is then a natural by-product of the merging and transformation process. The number of dwarf galaxies predicted in a cluster such as Virgo is in good agreement with the observed number. On the other hand, the 'giant branch', consisting of giant ellipticals and bulges, is probably produced by the merging of disc galaxies. Based on the observed phase-space densities of galaxies, we show that the main bodies of all giant ellipticals can be produced by dissipationless mergers of high-redshift discs. However, high-redshift discs, although denser than present-day ones, are still not compact enough to produce the high central phase-space density of some low-luminosity ellipticals. Dissipation must have occurred in the central parts of these galaxies during the merger which formed them.     

The post-collapse equilibrium structure of cosmological haloes in a low-density universe

An analytical model is presented for the post-collapse equilibrium structure of virialized objects that condense out of a low-density cosmological background universe, either matter-dominated or flat with a cosmological constant. This generalizes the model we derived previously for an Einstein–de Sitter (EdS) universe. The model is based upon the assumption that cosmological haloes form from the collapse and virialization of 'top-hat' density perturbations, and are spherical, isotropic and isothermal. This leads to the prediction of a unique, non-singular, truncated isothermal sphere (TIS), a particular solution of the Lane–Emden equation (suitably modified when Λ≠0) . The size and virial temperature are unique functions of the mass and redshift of formation of the object for a given background universe. The central density is roughly proportional to the critical density of the universe at the epoch of collapse. This TIS model is in good agreement with observations of the internal structure of dark-matter-dominated haloes on scales ranging from dwarf galaxies to X-ray clusters. It also reproduces many of the average properties of haloes in simulations of the cold dark matter (CDM) model to good accuracy, suggesting that it is a useful analytical approximation for haloes that form from realistic initial conditions. Our TIS model matches the density profiles of haloes in CDM N -body simulations outside the innermost region, while avoiding the steep central cusp of the latter which is in apparent conflict with observations. The TIS model may also be relevant to non-standard CDM models, such as that for self-interacting dark matter, recently proposed to resolve this conflict.     

Dynamical friction in dwarf galaxies

We present a simplified analytic approach to the problem of the spiralling of a massive body orbiting within the dark halo of a dwarf galaxy. This dark halo is treated as the core region of a King distribution of dark matter particles, in consistency with the observational result of dwarf galaxies having solid-body rotation curves. Thus we derive a simple formula which provides a reliable and general first-order solution to the problem, totally analogous to the one corresponding to the dynamical friction problem in an isothermal halo. This analytic approach allows a clear handling and a transparent understanding of the physics and the scaling of the problem. A comparison with the isothermal case shows that in the core regions of a King sphere, dynamical friction proceeds at a different rate, and is sensitive to the total core radius. Thus, in principle, observable consequences may result. In order to illustrate the possible effects, we apply this formula to the spiralling of globular cluster orbits in dwarf galaxies, and show how present-day globular cluster systems could, in principle, be used to derive better limits on the structure of dark haloes around dwarf galaxies, when the observational situation improves. As a second application, we study the way a massive black hole population forming a fraction of these dark haloes would gradually concentrate towards the centre, with a consequent deformation of an originally solid-body rotation curve. This effect allows us to set limits on the fraction/mass of any massive black hole minority component of the dark haloes of dwarf galaxies. In essence, we take advantage of the way the global matter distribution fixes the local distribution function for the dark matter particles, which in turn determines the dynamical friction problem.     

Measuring the distribution of galaxies between haloes

We develop a method to measure the probability, P ( N;   M ), of finding N galaxies in a dark matter halo of mass M from the theoretically determined clustering properties of dark matter haloes and the observationally measured clustering properties of galaxies. Knowledge of this function and the distribution of the dark matter completely specifies all clustering properties of galaxies on scales larger than the size of dark matter haloes. Furthermore, P ( N;   M ) provides strong constraints on models of galaxy formation, since it depends upon the merger history of dark matter haloes and the galaxy–galaxy merger rate within haloes. We show that measurements from a combination of the Two Micron All Sky Survey and Sloan Digital Sky Survey or Two-degree Field Galaxy Redshift Survey data sets will allow P ( N;   M ) averaged over haloes occupied by bright galaxies to be accurately measured for N =0–2 .     

The dark matter distribution in disc galaxies

We use high-quality optical rotation curves of nine low-luminosity disc galaxies to obtain the velocity profiles of the surrounding dark matter haloes. We find that they increase linearly with radius at least out to the edge of the stellar disc, implying that, over the entire stellar region, the density of the dark halo is about constant.
The properties of the mass structure of these haloes are similar to those found for a number of dwarf and low surface brightness galaxies, but provide a more substantial evidence of the discrepancy between the halo mass distribution predicted in the cold dark matter scenario and those actually detected around galaxies. We find that the density law proposed by Burkert reproduces the halo rotation curves, with halo central densities ( ρ ₀∼1–4×10⁻²⁴ g cm⁻³) and core radii ( r ₀∼5–15 kpc) scaling as ρ ₀∝ r ₀^−2/3.     

Lyman-break galaxies: high mass or low?

We reassess the hypothesis that Lyman-break galaxies (LBGs) at redshifts   z ∼ 3  mark the centres of the most massive dark matter haloes at that epoch. First we reanalyse the kinematic measurements of Pettini et al. and Erb et al. of the rest-frame optical emission lines of LBGs. We compare the distribution of the ratio of the rotation velocity to the central line width, against the expected distribution for galaxies with random inclination angles, modelled as singular isothermal spheres. The model fits the data well. On this basis we argue that the central line width provides a predictor of the circular velocity at a radius of several kpc. Assembling a larger sample of LBGs with measured line widths, we compare these results against the theoretical ΛCDM rotation curves of Mo, Mao & White, under the hypothesis that LBGs mark the centres of the most massive dark matter haloes. We find that the circular velocities are overpredicted by a substantial factor, which we estimate conservatively as  1.8 ± 0.4  . This indicates that the model is probably incorrect. The model of LBGs as relatively low-mass starburst systems, of Somerville, Primack & Faber, provides a good fit to the data.     

GHASP: an Hα kinematic survey of spiral and irregular galaxies – V. Dark matter distribution in 36 nearby spiral galaxies

The results obtained from a study of the mass distribution of 36 spiral galaxies are presented. The galaxies were observed using Fabry–Perot interferometry as part of the GHASP survey. The main aim of obtaining high-resolution Hα 2D velocity fields is to define more accurately the rising part of the rotation curves which should allow to better constrain the parameters of the mass distribution. The Hα velocities were combined with low resolution H  i data from the literature, when available. Combining the kinematical data with photometric data, mass models were derived from these rotation curves using two different functional forms for the halo: an isothermal sphere (ISO) and a Navarro–Frenk–White (NFW) profile. For the galaxies already modelled by other authors, the results tend to agree. Our results point at the existence of a constant density core in the centre of the dark matter haloes rather than a cuspy core, whatever the type of the galaxy from Sab to Im. This extends to all types the result already obtained by other authors studying dwarf and low surface brightness galaxies but would necessitate a larger sample of galaxies to conclude more strongly. Whatever model is used (ISO or NFW), small core radius haloes have higher central densities, again for all morphological types. We confirm different halo scaling laws, such as the correlations between the core radius and the central density of the halo with the absolute magnitude of a galaxy: low-luminosity galaxies have small core radius and high central density. We find that the product of the central density with the core radius of the dark matter halo is nearly constant, whatever the model and whatever the absolute magnitude of the galaxy. This suggests that the halo surface density is independent from the galaxy type.     

Constraining the Mass Distribution of Cluster Galaxies by Weak Lensing

Analysing the weak lensing distortions of the images of faint background galaxies provides a means to constrain the average mass distribution of cluster galaxies and potentially to test the extent of their dark matter haloes as a function of the density of their environment. The observable image distortions are a consequence of the interplay between the effects of a global cluster mass distribution and the perturbations resulting from individual cluster galaxies. Starting from a reconstruction of the cluster mass distribution with conventional techniques, we apply a maximum likelihood method to infer the average properties of an ensemble of cluster galaxies. From simulations this approach is found to be reliable as long as the galaxies including their dark matter haloes only contribute a small fraction to the total mass of the system. If their haloes are extended, the galaxies contain a substantial mass fraction. In this case our method is still applicable in the outer regions of clusters, where the surface mass density is low, but yields biased estimates of the parameters describing the mass profiles of the cluster galaxies in the central part of the cluster. In that case it will be necessary to resort to more sophisticated strategies by modelling cluster galaxies and an underlying global mass distribution simultaneously. We conclude that galaxy–galaxy lensing in clusters provides a unique means to probe the presence and extent of dark haloes of cluster galaxies.