Dark Matter and Cosmic Web Story

by Einasto, Jaan

The strong lensing effect is observed in rich clusters, and allows us to determine the distribution of the gravitating mass in clusters. Massive galaxies can distort images of distant single objects, such as quasars: as a result we observe multiple images of the same quasar. The masses of clusters of galaxies determined using this method confirm the results obtained by the virial theorem and the X-ray data.

  Weak lensing allows us to determine the distribution of dark matter in clusters as well as in superclusters.

  A fraction of the invisible baryonic matter can lie in small compact objects — brown dwarf stars or Jupiter-like objects. To find the fraction of these objects in the cosmic balance of matter, special studies have been initiated, based on the microlensing effect. Microlensing effects were used to find Massive Compact Halo Objects (MACHOs). MACHOs are small objects such as planets, dead stars (white dwarfs) or brown dwarfs, which emit so little radiation that they are invisible most of the time. A MACHO may be detected when it passes in front of a star and the MACHO’s gravity bends the light, causing the star to appear brighter. Several groups have used this method to search for baryonic dark matter. The total mass of these objects forms only a small fraction of the mass of stellar populations observed in galaxies. In other words, MACHOs do not solve the dark matter problem in galaxies.

  4.3 Dark matter in galaxies

  4.3.1 The density distribution of dark matter

  Flat rotation curves of galaxies suggest that the radial density distribution in galaxies, including stellar populations, interstellar gas and dark matter, is approximately isothermal: p(r) ~ r−2. As dark matter is the dominating population, its density profile should also be close to an isothermal sphere. Thus in our models of galaxies we approximated the dark matter population density with a truncated isothermal profile to avoid infinite total mass and infinite density at the center.

  In the early 1990’s, the results of high-resolution numerical N-body simulations of dark matter halos based on the collisionless CDM model became available. The simulations did not show the core-like smooth behaviour in the inner halos, but were better described by a power-law density distribution, the so-called cusp. Navarro et al. (1997) investigated systematically simulated DM halos for many different sets of cosmological parameters. They found that the whole mass density distribution could be well described by an “universal density profile”. This profile, known as the “NFW profile”, cannot be applied to the very centre of the halo, since in this case the density would be infinite. Near the centre of the halo the density rises sharply, forming a “cusp”.

  Bullock et al. (2001) analysed the evolution of profiles of dark halos. They defined the halo concentration parameter cvir ≡ Rvir/rs, where Rvir is the virial radius of the halo, and rs is the halo inner radius, where the logarithmic slope of the density profile is −2. The virial radius of the halo of mass Mvir is defined as the radius within which the mean density is ∆vir times the mean density. The range of the last quantity is from 178 to 337. The authors fit halo profiles with the NFW profile, and find that the median concentration parameter depends on the redshift: cvir ∝ (1+z)−1, i.e. with decreasing redshift the concentration parameter increases. Further the authors find that subhalos and halos in dense environments tend to be more concentrated than isolated halos, and that low-mass halos have a larger concentration parameter.

  Navarro et al. (2004) proposed another model that fits the density profiles of halos in ΛCDM simulations even better than the NFW model. It was realized by Merritt et al. (2006) that the model advocated by Navarro et al. (2004) had previously been introduced by Einasto (1965, 1968c, 1969a).

  The paper by Einasto (1965) was not available in the SAO/NASA Astrophysics Data System (ADS), thus initially this model was often referenced as the Einasto profile without any citation. To help the astronomical community read the original paper we scanned it, and made great efforts to clean the scan — the original was rather unsharp and gray. Now it is available in ADS and has collected 115 citations as of the middle of March 2013. For comparison, the Navarro et al. (1997) paper has over 4000 citations now!!!

  Recent studies have shown that the Einasto profile represents the spatial density profiles of dark matter halos rather well (Merritt et al., 2005, 2006; Graham et al., 2006; Ludlow et al., 2010). Ludlow et al. (2011) used Millennium-II simulations as part of the Virgo Consortium of high resolution N-body simulations to investigate the density and pseudo-phase-space density profiles of CDM halos. The Millennium-II simulations is a 1010-particle cosmological simulation of the evolution of dark matter in a 100 h−1 Mpc box. The run adopted a standard ΛCDM cosmogony with the same parameters as the Millennium simulation presented by Springel et al. (2005). The authors find that the pseudo-phase-space density profiles are best reproduced by the Einasto profile. The origin of this behaviour is unclear, but its similarity for all halos may reflect a fundamental structural property of DM halos.

  A high-resolution 21-cm observation survey of 34 nearby galaxies by Chemin et al. (2011) shows that this profile represents very accurately the density profiles of visible populations. These observations were carried out using The HI Nearby Galaxy Survey (THINGS), see de Blok et al. (2008); de Blok (2010); Oh et al. (2008,2011); Trachternach et al. (2008) and Walter et al. (2008) for details. Retana- Montenegro et al. (2012) and Salvador-Solé et al. (2012) investigated properties of the Einasto family of density profiles.

  In our models of galaxies we have always used the profile (3.1) to represent the density of visible galactic populations. Recent studies demonstrate that the dark matter has a density distribution, which is very similar to the distribution of stars in galaxies.

  4.3.2 Distribution of luminous and dark matter in galaxies

  In the last twenty years the study of the distribution of luminous and dark matter has made great progress. Here I shall describe only the most important results of these studies.

  The basic problem in the comparative study of the distribution of luminous and dark matter is the decomposition of the total matter distribution into the luminous and dark populations. This problem has been adressed by many authors using various methods. One of the key issues is the amount of dark matter in dwarf galaxies. This problem has been studied, among others, by John Kormendy. He writes in a review paper (Kormendy & Freeman, 2004) that probably these dwarf galaxies formed in an early period of galaxy formation: their central densities 0 ∼ (1 + zcoll)3, where zcoll is the collapse redshift. The smallest dwarfs formed at least ∆zcoll ≃ 7 earlier than the biggest spiral galaxies. The high DM densities of dSphs implies that they are real galaxies formed from primeval density fluctuations. Their central densities are about 100 times larger than DM central densities of giant galaxies. The paucity of stars in these galaxies can probably be explained by supernova winds which blew out most of the remaining gas. High M/L ≈ 100 ratios of dSph galaxies were confirmed by velocity dispersion measurements of stars. Kormendy & Freeman (2004) found a number of scaling laws between the central density and other quantities (velocity dispersion, absolute magnitude, core radius).

  Humphrey et al. (2006); Humphrey & Buote (2010) used Chandra X-ray observatory data to investigate the mass profiles of samples of galaxies, groups and clusters, spanning about 2 orders of magnitude in virial mass. They find that the total as well as DM mass density distributions can be well represented by a NFW/Einasto profile. This coincidence is remarkable, since the fraction of baryonic matter in the total mass distribution in clusters varies with radius considerably. This “galaxy–halo conspiracy” is similar to that which establishes flat rotation curves in galaxies — the “bulge–halo conspiracy”. These coincidences suggest the presence of some sort of interaction between the dominating stellar population (bulge) and the dark matter halo, both on galactic and cluster scales. We note that an analogous relation exists between the mass of the central black hole and the velocity dispersion of the bulge of elliptical galaxies, see Kormendy & Bender (2011); Kormendy et al. (2011) for a recent analysis of t
his problem.

  The “core–cusp problem” has been the subject of many recent studies, based both on observational data as well as on results of very high-resolution numerical simulations. To find the DM-halo density profile de Blok (2010) used a collection of HI rotation curves of dwarf galaxies, which are dominated by dark matter. To get a better resolution near the centre Hα long-slit rotation curves were analysed. These rotation curves indicate the presence of constant-density or mildly cuspy dark matter cores.

  Wolf et al. (2010) investigated the mass distribution for dispersion-supported (elliptical) galaxies. For many local spheroidal galaxies redshifts of a large number of individual stars have been determined. This allows one to use conventional Jeans equations to derive the masses of these galaxies. Luminosities are also known, which allows one to find M/L ratios for a wide range of galaxies of different magnitude. The authors derive the dynamical I-band half-light mass-to-luminosity ratio versus the half-light mass in mass interval 104 (globular clusters) to 1015 (giant elliptical galaxies) Solar masses. Globular clusters are located far from the general trend — evidently they do not contain dark matter. For dark matter dominated systems the M/L ratio has a minimum of about 3 for galaxies of half-light mass 1010 Solar masses, for the faintest dwarf and most massive giant galaxies the ratio increases up to a value of about 1000.

  Dhar & Williams (2011) analysed the density distribution of a large sample of high-resolution images of elliptical galaxies in the Virgo cluster, using the Hubble Space Telescope and ground-based data which span 106 in surface brightness and up to 105 in radius down to the resolution limit of the HST. The authors used 2D projections of the spatial (3D) Einasto density profile. All observed galaxies can be fit with 2 or 3 populations with different values of the normalizing and shape parameters of the Einasto model.

  In the framework of the Phoenix Project Gao et al. (2012) performed detailed numerical simulations of rich clusters of galaxies. The Phoenix Project follows the design of the Aquarius Project and consists of zoomed-in resimulations of individual galaxy clusters drawn from a cosmologically representative volume. Each cluster is simulated with at least two different numerical resolutions. The highest resolution corresponds to over one billion particles within the cluster virial radius. TheAquarius and Phoenix halos differ by roughly three orders of magnitude in virial mass. The most notable difference is that cluster halos have been assembled more recently and are thus significantly less relaxed than galaxy halos, which leads to decreased regularity. The multimodality of rich clusters of galaxies is well known observationally, see a recent study by Einasto et al. (2012). The density profile of rich clusters is best reproduced by the Einasto profile of various values of the shape parameter (Einasto index).

  4.3.3 Universal rotation curve of galaxies

  Rubin et al. (1985) compared rotation velocities of spiral galaxies of various morphological type and luminosity and found that the shape of the rotation curve depends strongly on the luminosity of the galaxy and the bulge-to-disk ratio. Galaxies of high luminosity have high rotational velocity and high central gradient of the velocity, low-luminosity galaxies have low rotational velocity and low central gradient of velocity. This correlation is almost independent of the morphological type of the galaxy. The infrared absolute magnitude of galaxies, MH, is strongly correlated with the mass within the isophotal radius, R25, deduced from the 25 mag arcsec−2 contour. The infrared mass-to-luminosity ratio, (R25)/LH = 2.1, is independent of the morphology of galaxies.

  Persic & Salucci (1991); Persic et al. (1996) extended the Rubin et al. (1985) study to find the correlation between the shape of rotation curves and luminosities of galaxies. Using a homogeneous sample of about 1100 optical and radio rotation curves and relative surface photometry Persic et al. (1996) investigated the distribution of mass in spiral galaxies over a range of 6 mag out to 1.5–2 optical radii. The authors find that there exists a Universal Rotation Curve (URC) of spiral galaxies. This curve implies a number of scaling properties between the dark (DM) and the luminous (LM) galactic structure parameters: the DM/LM mass ratio scales inversely with the luminosity; the halo core radius is comparable to the galaxy optical radius, but shrinks for low luminosities; the total halo mass scales as L0.5. Salucci et al. (2007) continued the URC of spiral galaxies and the corresponding mass distribution out to their virial radius. In low-luminosity galaxies the dark matter dominates at all distances from the galactic center; in high-luminosity galaxies dark matter domination begins in outer regions of galaxies.

  Donato et al. (2009) continued the study of the distribution of mass in spiral galaxies. The authors coadded rotation curves of ∼1000 spiral galaxies, and performed mass models of individual dwarf irregular and spiral galaxies of late and early types. Their basic finding is that the central projected mass density is constant over a wide range of galaxy masses. They find log 0r0 = 2.15 ± 0.2, where 0 is the central density, and r0 is the core radius of the adopted pseudo-isothermal cored dark matter density profile. The projected mass density is given in units of Solar masses per square parsec. Star clusters of the same luminosity as dwarf galaxies lie far from this relationship, showing a different mechanism of origin, as shown by Gilmore et al. (2007).

  Salucci et al. (2012) continued the study of this phenomenon. Observational velocity dispersion profiles are now available for eight Milky Way dwarf spheroidal satellites, mean velocity dispersions range from 5 to 10 km/s. This allows one to calculate mass distribution models. The authors demonstrated that the relationship between the central density and core radius, found by Donato et al. (2009), is valid for galaxies of absolute B magnitude interval from –7 to –22.5, for galaxies of various morphological type from dwarf irregulars and spirals to ellipticals. The authors conclude that “This result is intriguing, and could point to a common physical process responsible for the formation of cores in galactic halos of all sizes, or to a strong coupling between the DM and luminous matter.”

  4.3.4 The formation of galaxies

  The galactic models discussed so far are static, i.e. the aim of the modelling was to describe the present structure of galaxies. Early studies of the evolution of galaxies considered only the role of gravity in the evolution. Using this approach Eggen et al. (1962) showed that our Galaxy was contracting in its early stage of evolution. Toomre & Toomre (1972) discussed the role of merging in the evolution of galaxies, and suggested that elliptical galaxies are probably remnants of merged spiral galaxies.

  Models by Tinsley (1968); Tinsley & Spinrad (1971) considered the physical evolution of galaxies — the change with time of their luminosity, colour, and mass-to-luminosity ratio. My model of the evolution of galaxies (Einasto, 1972b) had a similar aim. In these models the formation and evolution of stars was taken into account to find the evolution of stellar populations.

  But none of the earlier models analysed the problem of how galaxies were formed. The problem of the formation of galaxies was considered as a part of the more general theory of structure formation. Peebles (1971a) scenario of hierarchical clustering considers the formation of galaxies as part of the clustering process starting from globular-cluster sized objects. Zeldovich (1970) discussed the evolution of density perturbations assuming an adiabatic nature of the process; galaxy formation was not discussed specifically. In both cases only the role of gravity was taken into account.

  Numerical simulations performed in the mid 1970’s using the Zeldovich (1970) idea of pancaking showed the formation of a cellular network of high-density regions (Shandarin 1975, private communication). A similar picture was found in the distribution of galaxies (Jõeveer et al., 1977; Jõeveer & Einasto, 1978; Jõeveer et al., 1978). In other words — the pancaking scenario is actually a scenario of the formation of the structure of the Universe, not of the formation of galaxies.

  Galaxy formation in the framework of the pancake scenario was analysed by Doroshkevich et al. (1978). The authors calculated the temperature, pressure and density in a ‘pancake’, taking
into account also radiative cooling of the gas. Inside the ‘pancake’ shock fronts and cooling fronts form. The main feature of the formation of galaxies according to this scenario is the presence of three different processes inside the ‘pancake’. The essential process is the cooling and fragmentation due to gravitational and thermal instabilities of the thin layer of cooling gas, which leads to the formation of primeval gas clouds. Other processes are the clustering of these primeval clouds to form presently observed galaxies, and the clustering of galaxies to form clusters of galaxies. The main conclusion of the paper is that a protogalaxy has never been an integral gaseous cloud; the initial state of a galaxy was a complex of gas clouds formed within a ‘pancake’. The role of dark matter was not studied.

  When I understood that dark matter surrounding galaxies is a new population with properties very different from that of all known stellar populations, I tried to clarify its possible role in galaxy formation (Einasto, 1972a, 1974a). But at this time I did not realise that one of the main properties of the dark population, its spatial segregation from known stellar populations, has a deep physical meaning — it must be a non-dissipative population.

  The dissipationless character of dark matter was first clearly stated by White & Rees (1978). They investigated the role of dark matter in galaxy formation. The presence of dark matter hints that galaxy formation must be a two-stage process, where galaxies form inside dark matter halos by cooling and fragmentation of gas. Dark matter forms halos of radius and mass about ten times larger than galaxies, thus it must be collisionless, whatever its nature is. The authors suggest that the segregation of luminous and non-luminous material is incompatible with any theory which tries to build up galaxies and clusters from smaller units in an entirely dissipationless way, since one expects efficient mixing to occur during this process.The authors write that dark matter could be low-mass stars, remnants of high-mass stars, neutrinos, or black holes which formed before recombination.