Dynamical effects of an extended cloud of dark matter on dwarf spheroidals

If the dwarf spheroidals are embedded in an extended cloud of dark matter then their density profiles can be reproduced by assuming a Maxwellian distribution of velocities for the constituent stars. The observed luminosity profiles of dwarf spheroidals imply densities for the dark matter in the range 10^-26 to 10^-25 g cm^-3, and mass-to-luminosity ratios which are typically an order of magnitude greater than those of globular clusters. Neutrinos of mass ∼ 10 eV and (v) ∼ 1000 km s^-1 can provide this requisite density for the background.     

Dark matter distribution in dwarf spheroidal galaxies

We study the distribution of dark matter in dwarf spheroidal galaxies by modelling the moments of their line-of-sight velocity distributions. We discuss different dark matter density profiles, both cuspy and possessing flat density cores. The predictions are made in the framework of standard dynamical theory of two-component (stars and dark matter) spherical systems with different velocity distributions. We compare the predicted velocity dispersion profiles to observations in the case of Fornax and Draco dwarfs. For isotropic models the dark haloes with cores are found to fit the data better than those with cusps. Anisotropic models are studied by fitting two parameters, dark mass and velocity anisotropy, to the data. In this case all profiles yield good fits, but the steeper the cusp of the profile, the more tangential is the velocity distribution required to fit the data. To resolve this well-known degeneracy of density profile versus velocity anisotropy, we obtain predictions for the kurtosis of the line-of-sight velocity distribution for models found to provide best fits to the velocity dispersion profiles. It turns out that profiles with cores typically yield higher values of kurtosis which decrease more steeply with distance than the cuspy profiles, which will allow us to discriminate between the profiles once the kurtosis measurements become available. We also show that with present quality of the data the alternative explanation of velocity dispersions in terms of Modified Newtonian Dynamics cannot yet be ruled out.     

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.     

Dark matter halo response to the disc growth

We consider the sensitivity of the circular-orbit adiabatic contraction approximation to the baryon condensation rate and the orbital structure of dark matter haloes in the Λ cold dark matter (ΛCDM) paradigm. Using one-dimensional hydrodynamic simulations including the dark matter halo mass accretion history and gas cooling, we demonstrate that the adiabatic approximation is approximately valid even though haloes and discs may assemble simultaneously. We further demonstrate the validity of the simple approximation for ΛCDM haloes with isotropic velocity distributions using three-dimensional N -body simulations. This result is easily understood: an isotropic velocity distribution in a cuspy halo requires more circular orbits than radial orbits. Conversely, the approximation is poor in the extreme case of a radial orbit halo. It overestimates the response of a core dark matter halo, where radial orbit fraction is larger. Because no astronomically relevant models are dominated by low angular momentum orbits in the vicinity of the disc and the growth time-scale is never shorter than a dynamical time, we conclude that the adiabatic contraction approximation is useful in modelling the response of dark matter haloes to the growth of a disc.     

Dark matter subhaloes in numerical simulations

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

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.     

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 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.     

Nature and distribution of dark matter: 2. binaries,groups and clusters

We study the mass-radius relationship for aggregates of galaxies, viz. binaries, small groups and clusters. The data are subjected to a simple best-fit analysis similar to the one carried out earlier for individual field galaxies. The analysis shows that: (i) The data on binary galaxies are consistent with the assumption that binaries are just two galaxies, each with an individual isothermal (M ∫R) dark matter halo, moving under the mutual gravitational attraction, (ii) The data on the groups of galaxies are too scattered to obey a single power-law relation of the formM = kR ⁿ with any degree of reliability, (iii) The data on groups and clusters fit better with a law of the formM = AR ³ +BR. This form suggests the existence of two components in dark matter—one which is clustered around the galaxies (M ∫R) and another which is distributed smoothly (M ∫R ³ ). The smooth distributions becomes significant only at scales ≥ 1 Mpc and hence does not affect binaries significantly. We briefly discuss the theoretical implications of this analysis     

Dark matter haloes within clusters

We examine the properties of dark matter haloes within a rich galaxy cluster using a high-resolution simulation that captures the cosmological context of a cold dark matter universe. The mass and force resolution permit the resolution of 150 haloes with circular velocities larger than 80 km s⁻¹ within the cluster virial radius of 2 Mpc (with Hubble constant H ₀ = 50 km s⁻¹ Mpc⁻¹). This enables an unprecedented study of the statistical properties of a large sample of dark matter haloes evolving in a dense environment. The cumulative fraction of mass attached to these haloes varies from close to zero per cent at 200 kpc to 13 per cent at the virial radius. Even at this resolution the overmerging problem persists; haloes that pass within 100–200 kpc of the cluster centre are tidally disrupted. Additional substructure is lost at earlier epochs within the massive progenitor haloes. The median ratio of apocentric to pericentric radii is 6:1, so that the orbital distribution is close to isotropic, circular orbits are rare and radial orbits are common. The orbits of haloes are unbiased with respect to both position within the cluster and the orbits of the smooth dark matter background, and no velocity bias is detected. The tidal radii of surviving haloes are generally well-fitted using the simple analytic prediction applied to their orbital pericentres. Haloes within clusters have higher concentrations than those in the field. Within the cluster, halo density profiles can be modified by tidal forces and individual encounters with other haloes that cause significant mass loss —'galaxy harassment'. Mergers between haloes do not occur inside the cluster virial radius.     

Dark matter halo profiles in scale-free cosmologies

We explore the dependence of the central logarithmic slope of dark matter halo density profiles α on the spectral index n of the linear matter power spectrum P ( k ) using cosmological N -body simulations of scale-free models [i.e. P ( k ) ∝ k ⁿ ]. These simulations are based on a set of clear, reproducible and physically motivated criteria that fix the appropriate starting and stopping times for runs, and allow one to compare haloes across models with different spectral indices and mass resolutions. For each of our simulations we identify samples of well-resolved haloes in dynamical equilibrium and we analyse their mass profiles. By parametrizing the mass profile using a 'generalized' Navarro, Frenk & White profile in which the central logarithmic slope α is allowed to vary while preserving the r ⁻³ asymptotic form at large radii, we obtain preferred central slopes for haloes in each of our models. There is a strong correlation between α and n , such that α becomes shallower as n becomes steeper. However, if we normalize our mass profiles by r ₋₂, the radius at which the logarithmic slope of the density profile is −2, we find that these differences are no longer present. This is apparent if we plot the maximum slope     as a function of r / r ₋₂– we find that the profiles are similar for haloes forming in different n models. This reflects the importance of concentration, and reveals that the concentrations of haloes forming in steep- n cosmologies tend to be smaller than those of haloes forming in shallow- n cosmologies. We conclude that there is no evidence for convergence to a unique central asymptotic slope, at least on the scales that we can resolve.     

Dark matter halo creation in moving barrier models

In hierarchical models of structure formation, the time derivative of the halo mass function may be thought of as the difference of two terms – a creation term, which describes the increase in the number of haloes of mass m from mergers of less massive objects, and a destruction term, which describes the decrease in the number of m -haloes as these merge with other haloes, creating more massive haloes as a result. The first part of this paper focuses on estimating the distribution of times when these creation events take place. In models where haloes form from a spherical collapse, this distribution can be estimated from the same formalism which is used to estimate halo abundances: the constant-barrier excursion-set approach. In the excursion-set approach, moving rather than constant barriers are necessary for estimating halo abundances when the collapse is triaxial. First, we generalize the excursion-set estimate of the creation time distribution by incorporating ellipsoidal collapse. Then, we show that these moving barrier based predictions are in better agreement with measurements in numerical simulations than are the corresponding predictions of the spherical collapse model. In the second part of the paper, we link the creation time distribution to the creation term mentioned above. For this quantity, the improvement provided by the ellipsoidal collapse model is more evident. These results should be useful for studies of merger-driven star formation rates and active galactic nucleus activity. We also present a similar study of the creation of haloes conditioned on belonging to an object of a certain mass today, and reach similar conclusions – the moving barrier based estimates are in substantially better agreement with the simulations. This part of the study may be useful for understanding the tendency for the oldest stars to exist in the most massive objects, and for star formation to only occur in lower mass objects at late times.     

Gravitational Mesoscopic Constraints in Cosmological Dark Matter Halos

We present an analysis of the behaviour of the ‘coarse-grained’ (‘mesoscopic’) rank partitioning of the mean energy of collections of particles composing virialized dark matter halos in a Λ-CDM cosmological simulation. We find evidence that rank preservation depends on halo mass, in the sense that more massive halos show more rank preservation than less massive ones. We find that the most massive halos obey Arnold’s theorem (on the ordering of the characteristic frequencies of the system) more frequently than less massive halos. This method may be useful to evaluate the coarse-graining level (minimum number of particles per energy cell) necessary to reasonably measure signatures of ‘mesoscopic’ rank orderings in a gravitational system.     

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

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

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.