A new model of dark matter distribution in galaxies

In the absence of the physical understanding of the phenomenon, different empirical laws have been used as approximation for distribution of dark matter in galaxies and clusters of galaxies. We suggest a new profile which is not empirical in nature, but motivated with the physical idea that what we call dark matter is essentially the gravitational polarization of the quantum vacuum (containing virtual gravitational dipoles) by the immersed baryonic matter. It is very important to include this new profile in forthcoming studies of dark matter halos and to reveal how well it performs in comparison with empirical profiles. A good agreement of the profile with observational findings would be the first sign of unexpected gravitational properties of the quantum vacuum.     

Is dark matter an illusion created by the gravitational polarization of the quantum vacuum?

Assuming that a particle and its antiparticle have the gravitational charge of the opposite sign, the physical vacuum may be considered as a fluid of virtual gravitational dipoles. Following this hypothesis, we present the first indications that dark matter may not exist and that the phenomena for which it was invoked might be explained by the gravitational polarization of the quantum vacuum by the known baryonic matter.     

Dark matter as an effect of the quantum vacuum

The interaction between the quantum vacuum and a weak gravitational field is calculated for the vacuum fields of quantum electrodynamics. The result shows that the vacuum state is modified by the gravitational field, giving rise to a nonzero interaction energy. This suggests a model that fits in the main properties of the hypothetical dark matter in galactic haloes.     

The tightening of wide binaries in dSph galaxies through dynamical friction as a test of the dark matter hypothesis

We estimate the time-scales for orbital decay of wide binaries embedded within dark matter haloes, due to dynamical friction against the dark matter particles. We derive analytical scalings for this decay and calibrate and test them through the extensive use of N -body simulations, which accurately confirm the predicted temporal evolution. For density and velocity dispersion parameters as inferred for the dark matter haloes of local dSph galaxies, we show that the decay time-scales become shorter than the ages of the dSph stellar populations for binary stars composed of  1 M_⊙  stars, for initial separations larger than 0.1 pc. Such wide binaries are conspicuous and have been well measured in the solar neighbourhood. The prediction of the dark matter hypothesis is that they should now be absent from stellar populations embedded within low velocity dispersion, high-density dark mater haloes, as currently inferred for the local dSph galaxies, having since evolved into tighter binaries. Relevant empirical determinations of this will become technically feasible in the near future, and could provide evidence to discriminate between dark matter particle haloes or modified gravitational theories, to account for the high dispersion velocities measured for stars in local dSph galaxies.     

Nature and distribution of dark matter: 1. Dwarf spheroidals and milky way

We argue that observations on Milky Way and dwarf spheroidals imply existence of individual haloes around dwarf spheroidals. If neutrinos (or any other ‘hot’ particle) provide the dark matter then we show that: (i) Embedding of visible matter inside large (∼ few Mpc) dark matter islands is observationally untenable. (ii) Dwarf spheroidals possess dark matter haloes of about 10 kpc radius around them, and have an (M/L) ratio of about 10⁴. (iii) The haloes of spiral galaxies (e.g. Milky Way) extend to about 100 kpc in radius. If ‘cold’ dark matter makes up the haloes, then no significant constraints are obtained. We discuss briefly the effect of these constraints on larger scales.     

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.     

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 .     

On the vacuum fluctuations, Pioneer Anomaly and Modified Newtonian Dynamics

We argue that the so-called “Pioneer Anomaly” is related to the quantum vacuum fluctuations. Our approach is based on the hypothesis of the gravitational repulsion between matter and antimatter, what allows considering, the virtual particle–antiparticle pairs in the physical vacuum, as gravitational dipoles. Our simplified calculations indicate that the anomalous deceleration of the Pioneer spacecrafts could be a consequence of the vacuum polarization in the gravitational field of the Sun. At the large distances, the vacuum polarization by baryonic matter could mimic dark matter what opens possibility that dark matter do not exist, as advocated by the Modified Newtonian Dynamics (MOND).     

The effects of photoionization on galaxy formation – I. Model and results at z=0

We develop a coupled model for the evolution of the global properties of the intergalactic medium (IGM) and the formation of galaxies, in the presence of a photoionizing background due to stars and quasars. We use this model to predict the thermodynamic history of the IGM when photoionized by galaxies forming in a cold dark matter (CDM) universe. The evolution of the galaxies is calculated using a semi-analytical model, including a detailed treatment of the effects of tidal stripping and dynamical friction on satellite galaxies orbiting inside larger dark matter haloes. We include in the model the negative feedback on galaxy formation from the photoionizing background. Photoionization inhibits galaxy formation in low-mass dark matter haloes in two ways: (i) heating of the IGM and inhibition of the collapse of gas into dark haloes by the IGM pressure, and (ii) reduction in the rate of radiative cooling of gas within haloes. The result of our method is a self-consistent model of galaxy formation and the IGM. The IGM is reheated twice (during reionization of H  i and He  ii ), and we find that the star formation rate per unit volume is slightly suppressed after each episode of reheating. We find that galaxies brighter than L _★ are mostly unaffected by reionization, while the abundance of faint galaxies is significantly reduced, leading to present-day galaxy luminosity functions with shallow faint-end slopes, in good agreement with recent observational data. Reionization also affects other properties of these faint galaxies, in a readily understandable way.     

Completely dark galaxies: their existence, properties and strategies for finding them

There are a number of theoretical and observational hints that large numbers of low-mass galaxies composed entirely of dark matter exist in the field. The theoretical considerations follow from the prediction of cold dark matter theory that there exist many low-mass galaxies for every massive one. The observational considerations follow from the observed paucity of these low-mass galaxies in the field but not in dense clusters of galaxies; this suggests that the lack of small galaxies in the field is due to the inhibition of star formation in the galaxies as opposed to the fact that their small dark matter haloes do not exist. In this work we outline the likely properties of low-mass dark galaxies, and describe observational strategies for finding them, and where in the sky to search. The results are presented as a function of the global properties of dark matter, in particular the presence or absence of a substantial baryonic dark matter component. If the dark matter is purely cold and has a Navarro, Frenk & White density profile, directly detecting dark galaxies will only be feasible with present technology if the galaxy has a maximum velocity dispersion in excess of 70 km s⁻¹, in which case the dark galaxies could strongly lens background objects. This is much higher than the maximum velocity dispersions in most dwarf galaxies. If the dark matter in galaxy haloes has a baryonic component close to the cosmic ratio, the possibility of directly detecting dark galaxies is much more realistic; the optimal method of detection will depend on the nature of the dark matter. A number of more indirect methods are also discussed.     

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.     

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.     

Properties of dark matter haloes

An overview is presented of the main properties of dark matter haloes, as we know them from observations, essentially from rotation curves around spiral and dwarf galaxies. Detailed rotation curves are now known for more than a thousand galaxies, revealing that they are not so flat in the outer parts, but rising for late-types, and falling for early-types. A well-established result now is that most bright galaxies are not dominated by dark matter inside their optical disks. Only for dwarfs and LSB (Low Surface Brightness galaxies) dark matter plays a dominant role in the visible regions. The 3D-shape of haloes are investigated through several methods that will be discussed: polar rings, flaring of HI planes, X-ray isophotes. It is not yet possible with rotation curves to know how far haloes extend, but tentatives have been made. It will be shown that the dark matter appears to be coupled to the gas in spirals and dwarfs, suggesting that dark baryons could play a major role in rotation curves. Theories proposing to replace the non-baryonic dark matter by a different dynamical or gravity law, such as MOND, have to take into account the dark baryons, especially since their spatial distribution is likely to be quite different from the visible matter.     

The orientation of galaxy dark matter haloes around cosmic voids

Using the Millennium N -body Simulation we explore how the shape and angular momentum of galaxy dark matter haloes surrounding the largest cosmological voids are oriented. We find that the major and intermediate axes of the haloes tend to lie parallel to the surface of the voids, whereas the minor axis points preferentially in the radial direction. We have quantified the strength of these alignments at different radial distances from the void centres. The effect of these orientations is still detected at distances as large as 2.2 R _void from the void centre. Taking a subsample of haloes expected to contain disc-dominated galaxies at their centres we detect, at the 99.9 per cent confidence level, a signal that the angular momentum of those haloes tends to lie parallel to the surface of the voids. Contrary to the alignments of the inertia axes, this signal is only detected in shells at the void surface  (1 < R < 1.07  R _void)  and disappears at larger distances. This signal, together with the similar alignment observed using real spiral galaxies, strongly supports the prediction of the Tidal Torque theory that both dark matter haloes and baryonic matter have acquired, conjointly, their angular momentum before the moment of turnaround.     

Strong-lensing optical depths in a ΛCDM universe – II. The influence of the stellar mass in galaxies

We investigate how strong gravitational lensing in the concordance ΛCDM cosmology is affected by the stellar mass in galaxies. We extend our previous studies, based on ray tracing through the Millennium Simulation, by including the stellar components predicted by galaxy formation models. We find that the inclusion of these components greatly enhances the probability for strong lensing compared to a 'dark matter only' universe. The identification of the 'lenses' associated with strong-lensing events reveals that the stellar mass of galaxies (i) significantly enhances the strong-lensing cross-sections of group and cluster haloes and (ii) gives rise to strong lensing in smaller haloes, which would not produce noticeable effects in the absence of the stars. Even if we consider only image splittings ≳10 arcsec, the luminous matter can enhance the strong-lensing optical depths by up to a factor of 2.     

The sizes of minivoids in the local Universe: an argument in favour of a warm dark matter model?

Using high-resolution simulations within the cold dark matter (CDM) and warm dark matter (WDM) models, we study the evolution of small-scale structure in the local volume, a sphere of 8-Mpc radius around the Local Group. We compare the observed spectrum of minivoids in the local volume with the spectrum of minivoids determined from the simulations. We show that the ΛWDM model can easily explain both the observed spectrum of minivoids and the presence of low-mass galaxies observed in the local volume, provided that all haloes with circular velocities greater than 20 km s⁻¹ host galaxies. On the contrary, within the ΛCDM model the distribution of the simulated minivoids reflects the observed one if haloes with maximal circular velocities larger than  35 km s⁻¹  host galaxies. This assumption is in contradiction with observations of galaxies with circular velocities as low as 20 km s⁻¹ in our local Universe. A potential problem of the ΛWDM model could be the late formation of the haloes in which the gas can be efficiently photoevaporated. Thus, star formation is suppressed and low-mass haloes might not host any galaxy at all.     

The two-point correlation of galaxy groups: probing the clustering of dark matter haloes

We analyse the two-point correlation function (2PCF) of galaxy groups identified from the 2-degree Field Galaxy Redshift Survey with the halo-based group finder recently developed by Yang et al. With this group catalogue we are able to estimate the 2PCFs for systems ranging from isolated galaxies to rich clusters of galaxies. The real-space correlation length obtained for these systems ranges from ∼4 to ∼15  h ⁻¹ Mpc, respectively. The observed correlation amplitude (and the corresponding bias factor) as a function of group abundance is well reproduced by associating galaxy groups with dark matter haloes in the standard Λ-cold dark matter model. Redshift distortions are clearly detected in the redshift-space correlation function, the degree of which is consistent with the assumption of gravitational clustering and halo bias in the cosmic density field. In agreement with previous studies we find a strong increase of the correlation length with the mean intergroup separation. Although well-determined observationally, we show that current theoretical predictions are not yet accurate enough to allow for stringent constraints on cosmological parameters. Finally, we use our results to explore the power-law nature of the 2PCF of galaxies. We split the 2PCF into one- and two-group terms, equivalent to the one- and two-halo terms in halo occupation models, and show that the power-law form of the 2PCF is broken, when only including galaxies in the more massive systems.     

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.     

Survival of substructure within dark matter haloes

Using high-resolution cosmological N -body simulations, we investigate the survival of dark matter satellites falling into larger haloes. Satellites preserve their identity for some time after merging. We compute their loss of mass, energy and angular momentum as they are dissolved by dynamical friction, tidal forces and collisions with other satellites. We also analyse the evolution of their internal structure. Satellites with less than a few per cent of the mass of the main halo may survive for several billion years, whereas larger satellites rapidly sink into the centre of the main halo potential well and lose their identity. Penetrating encounters between satellites are frequent and may lead to significant mass loss and disruption. Only a minor fraction of cluster mass (10–15 per cent on average) is bound to substructure at most redshifts of interest. We discuss the application of these results to the survival and extent of dark matter haloes associated with galaxies in clusters, and to their interactions. We find that a minor fraction of galaxy-size dark matter haloes are disrupted by redshift z  = 0. The fraction of satellites undergoing close encounters is similar to the observed fraction of interacting or merging galaxies in clusters at moderate redshift.     

Simulating subhaloes at high redshift: merger rates, counts and types

Galaxies are believed to be in one-to-one correspondence with simulated dark matter subhaloes. We use high-resolution N -body simulations of cosmological volumes to calculate the statistical properties of subhalo (galaxy) major mergers at high redshift ( z = 0.6–5). We measure the evolution of the galaxy merger rate, finding that it is much shallower than the merger rate of dark matter host haloes at   z > 2.5  , but roughly parallels that of haloes at   z < 1.6  . We also track the detailed merger histories of individual galaxies and measure the likelihood of multiple mergers per halo or subhalo. We examine satellite merger statistics in detail: 15–35 per cent of all recently merged galaxies are satellites, and satellites are twice as likely as centrals to have had a recent major merger. Finally, we show how the differing evolution of the merger rates of haloes and galaxies leads to the evolution of the average satellite occupation per halo, noting that for a fixed halo mass, the satellite halo occupation peaks at   z ∼ 2.5  .