Dark energy in the two-body problem: The local group of galaxies

The two-body problem of classical mechanics can be extended in a natural way by introducing a universal dark-energy background, which acts as a third dynamical factor. For real systems of galaxies, the corresponding additional acceleration is described by general relativity in the Newtonian limit, in which deviations from the Minkowski metric are very small. It is shown that this acceleration has the same form in different inertial and non-inertial reference frames. The invariance of the acceleration produced by dark energy reflects the fact that, according to its mechanical properties, dark energy is a vacuum that is comoving with any motion. In this generalized formulation, as in the classical case, the two-body problem with a dark-energy background reduces to the motion of a single body in a central field. Two problems of this kind are considered for the Local Group of galaxies. The first, “internal,” problem concerns the binary system formed by the main bodies of the Local Group: our galaxy and M31. The subject of the second, “external,” problem is the binary system formed by the Local Group as a whole and its closest neighbor, the Virgo Cluster. In the internal problem, the effect of the dark energy is that the binary system is not bound if its mass does not exceed 3 × 10¹² M_⊙, which is allowed by the observational data. The external problem demonstrates the possibility of an evolutionary scenario in which a group could initially be located in the volume of a cluster, but then leave it and, moving away with an acceleration created by dark energy, arrive at the observed distance from the cluster.     

The NGC 1023 galaxy group: An anti-hubble flow?

We discuss recently published data indicating that the nearby galaxy group NGC 1023 includes an inner, virialized, quasi-stationary component together with an outer component comprising a flow of dwarf galaxies falling toward the center of the system. The inner component is similar to the Local Group of galaxies, but the Local Group is surrounded by a receding set of dwarf galaxies forming the local Hubble flow, rather than a system of approaching dwarfs. This clear difference in the structures of these two systems, which are very similar in other respects, may be associated with the dark energy in which they are immersed. Self-gravity dominates in the inner component of the Local Group, while the anti-gravity created by the cosmic dark-energy background dominates in the surrounding Hubble flow. In contrast, self-gravity likewise dominates throughout the NGC 1023 Group, both in its central component and in the surrounding “anti-Hubble” flow. NGC 1023 as a whole is apparently in an ongoing state of formation and virialization. We expect that there exists a receding flow similar to the local Hubble flow at distances of 1.4–3 Mpc from the center of the group, where anti-gravity should become stronger than the gravity of the system.     

Dark matter and dark energy in dwarf galaxy systems

Quantitative estimates of themaximumallowed totalmasses and sizes of the dark-matter halos in groups and associations of dwarf galaxies—special types of metagalactic populations identified in recent astronomical observations with the Hubble Space Telescope—are presented. Dwarf-galaxy systems are formed of isolated dark-matter halos with a small number of dark galaxies embedded in them. Data on the sizes of these systems and the velocity dispersions of the embedded galaxies can be used to determine lower limits on the total dark-halo masses using the virial theorem. Upper limits follow from the conditions that the systems immersed in the cosmic dark-energy background be gravitationally bound. The median maximum masses are close to 10¹² M _⊙ for both groups and associations of dwarf galaxies, although the median virial masses for these two types of systems differ by approximately a factor of ten.     

The bulk motion of FGC galaxies on scales of 100 Mpc

Large-scale streaming is analyzed using a sample of 983 thin, edge-on galaxies from the FGC catalog with radial velocities cz<18000 km s^?1. The catalog covers the entire sky and contains galaxies with apparent axial ratios a/b>7 and angular diameters a>0.6 arcmin. The distances to the galaxies were determined using a multi-parameter “rotation amplitude-linear diameter” relation, which is similar to the Tully-Fisher relation and takes into account surface brightness, morphological type, and other global parameters. The bulk motion of the galaxy sample with respect to the frame of the microwave background radiation can be described by a dipole solution with amplitude V ^B =300±75 km s^?1 in the direction (l=328°, b=+7°)±15°. The apex parameters for the FGC galaxies agree well with the amplitude and direction of the bulk motion for the Mark III compiled catalog, although the two samples have no objects in common. The dipole solution provides only a rough approximation to the smoothed peculiar-velocity field of the FGC galaxies. Areas of maxima and minima on the V _pec map are not correlated with the locations of known nearby clusters and voids. A comparison of nearby and distant subsamples shows that the amplitude of the bulk motion with respect to the 3K reference frame does not decrease with distance. The observed large-scale galaxy streaming could be due to the Shapley concentration of rich clusters (311°, +30°), which is located within 2σ of the apex.     

The random-motion theorem in a local cosmology with dark energy

It is shown that the random-motion theorem in cosmology proven in the early 1960s can be generalized to take into account the presence of a uniform dark-energy background. The role of the dark energy is substantial: its repulsive force exceeds the gravitational force due to darkmatter and baryons, both on the scale of the Universe as a whole and on local scales of about 1 Mpc. The generalized random-motion theorem has the form of a differential equation relating the kinetic energy of the random motion and the potential energy of the particles due to their own gravitational field and the repulsive dark-energy field. One consequence of the generalized theorem is a virial relation containing the potential energy in the repulsive field.     

The cosmic vacuum and the rotation of galaxies

The rotational effect of the cosmic vacuum is investigated. The induced rotation of elliptical galaxies due to the anti-gravity of the vacuum is found to be 10⁻²¹ s⁻¹ for real elliptical galaxies. The effect of the vacuum rotation of the entire Universe is discussed, and can be described by the invariant ω _ν = ω ₀ ∼ $ \sqrt {G\rho v} $ \sqrt {G\rho v} . The corresponding numerical angular velocity of the Universe is 10⁻¹⁹ s⁻¹, in good agreement with modern data on the temperature fluctuations of the cosmic background radiation.     

Supermassive black holes and central star clusters: Connection with the host galaxy kinematics and color

The relationship between the masses of the central, supermassive black holes (M _bh) and of the nuclear star clusters (M _nc) of disk galaxies with various parameters galaxies are considered: the rotational velocity at R = 2 kpc V ₍₂₎, the maximum rotational velocity V _max, the indicative dynamical mass M ₂₅, the integrated mass of the stellar populationM _*, and the integrated color index B-V. The rotational velocities andmasses of the central objects were taken from the literature. ThemassM _nc correlatesmore closely with the kinematic parameters and the disk mass than M _bh, including with the velocity V _max, which is closely related to the virial mass of the dark halo. On average, lenticular galaxies are characterized by higher massesM _bh compared to other types of galaxies with similar characteristics. The dependence of the blackhole mass on the color index is bimodal: galaxies of the red group (red-sequence) with B-V >0.6–0.7 which are mostly early-type galaxies with weak star formation, differ appreciably from blue galaxies, which have higher values of M _nc and M _bh. At the dependences we consider between the masses of the central objects and the parameters of the host galaxies (except for the dependence of M _bh on the central velocity dispersion), the red-group galaxies have systematically higher M _bh values, even when the host-galaxy parameters are similar. In contrast, in the case of nuclear star clusters, the blue and red galaxies form unified sequences. The results agree with scenarios in which most red-group galaxies form as a result of the partial or complete loss of interstellar gas in a stage of high nuclear activity in galaxies whose central black-hole masses exceed 10⁶?10⁷ M _⊙ (depending on the mass of the galaxy itself). The bulk of disk galaxies with M _bh > 10⁷ M _⊙ are lenticular galaxies (types S0, E/S0) whose disks are practically devoid of gas.     

Evolution of galaxies and the Tully-Fisher relation

We study the evolution of the [O/Fe]-[Fe/H] relation and the dependence of the iron abundance on distance from the galactic plane z in a one-zone model for a disk galaxy, starting from the beginning of star formation. We obtain good agreement with the observational data, including, for the first time, agreement for the [Fe/H]-z relation out to heights of 16 kpc. We also study the influence of the presence of dark matter in the galaxies on the star-formation rate. Comparison of the observed luminosity of the Galaxy with the model prediction places constraints on the fractional mass of dark matter, which cannot be much larger than the fractional mass of visible matter, at least within the assumed radius of the Galaxy, ～20 kpc. We studied the evolution of disk galaxies with various masses, which should obey the Tully-Fisher relation, M ? R². The Tully-Fisher relation can be explained as a combination of a selection effect related to the observed surface brightnesses of galaxies with large radii and the conditions for the formation for elliptical galaxies.     

Supermassive black holes and galaxy kinematics

The statistical relation between the masses of supermassive black holes (SMBHs) in disk galaxies and the kinematic properties of their host galaxies is analyzed. Velocity estimates for several galaxies obtained earlier at the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences and the data for other galaxies taken from the literature are used. The SMBH masses correlate well with the rotational velocities at a distance of R ≈ 1 kpc, V ₁, which characterize the mean density of the central region of the galaxy. The SMBH masses correlate appreciably weaker with the asymptotic velocity at large distances from the center and the angular velocity at the optical radius R ₂₅. We have found for the first time a correlation between the SMBH mass and the total mass of the galaxy within the optical radius R ₂₅, M ₂₅, which includes both baryonic and “dark” mass. The masses of the nuclear star clusters in disk galaxies (based on the catalog of Seth et al.) are also related to the dynamical mass M ₂₅; the correlations with the luminosity and rotational velocity of the disk are appreciably weaker. For a given value of M ₂₅, the masses of the central cluster are, on average, an order of magnitude higher in S0-Sbc galaxies than in late-type galaxies, or than the SMBH masses. We suggest that the growth of the SMBH occurs in the forming “classical” bulge of the galaxy over a time < 10⁹ yr, during a monolithic collapse of gas in the central region of the protogalaxy. The central star clusters form on a different time scale, and their stellar masses continue to grow for a long time after the growth of the central black hole has ceased, if this process is not hindered by activity of the nucleus.     

Dynamical evolution of galaxy clusters in the framework of the <Emphasis Type="Italic">N</Emphasis>-body problem. The formation of supermassive cD galaxies

We have carried out numerical simulations of the dynamical evolution of galaxy clusters taking into account merging when the relative velocities of the colliding galaxies are low. In particular, we study the evolution of the structure, mass spectrum, and velocity spectrum of a cluster of a thousand galaxies, as well as the growth of the central supermassive cD galaxy. The initial velocity dispersion of the galaxies and the rotation of the cluster were taken into account. The observed logarithmic spectrum dN ～ \(\tfrac{{dM}}{M}\) was adopted as the initial mass spectrum. The dynamical evolution of galaxy clusters, allowing for the possible merging of colliding galaxies, results in the emergence of a central supermassive galaxy, whose mass continuously increases due to mergers. This occurs only if the mass of the central galaxy becomes greater than ～0.1 of the total mass of the cluster. The observation of cD galaxies with relative masses of ～0.01 suggests that they initially formed in the cluster core, merged with nearby galaxies, and accreted intergalactic gas. The model indicates that a logarithmic galaxy mass spectrum is preserved during the cluster evolution, despite the substantial decrease in the number of galaxies in the cluster with time. The model can also reproduce the observed mass distribution with distance from the cluster center, M _r ～ r ^1.7.     

A correlation between dark matter and neutral hydrogen in spiral galaxies

We test the hypothesis put forward by Bosma (1981) that the surface density of dark matter is proportional to the surface density of HI, using decompositions of the rotation curves of a number of galaxies according to the THINGS, along with data for the galaxy NGC 6822. The rotation curves of these galaxies can be explained by assuming the existence of a massive gaseous disk in the absence of a dark halo, although the proportionality factor ??_dark/??_HI between the surface densities of dark matter and HI is different for different galaxies. However, there emerges the problem of the gravitational stability of galaxies whose stellar-velocity dispersions have been estimated, if the thickness of the dark-matter disk is similar to or less than the thickness of the stellar disk. The proportionality between ?? _dark and ??_HI is probably due to the fact that the radial profiles of ??_HI for galaxies with flat rotational curves are close to the critical density of a gravitationally stable gaseous layer (??_HI ?? R ^?1), and ??_dark(R) for a pseudo-isothermal halo obeys the same law.     

Southern isolated galaxy triplets

Seventy-six isolated triple systems of galaxies with declinatiosn δ?3°.     

Characteristics of motions in the 2D isosceles three-body problem with unequal masses

We analyze the general 2D isosceles three-body problem for various ratios ? of the mass of the central body to the mass of each of the other two bodies. We set the initial conditions using two parameters: the virial coefficient k and the parameter \(\mu = \dot r/\sqrt {\dot r^2 + \dot R^2 }\), where \(\dot r\) is the relative velocity of the two outer bodies and \(\dot R\) is the velocity of the central body relative to the center of mass of the outer bodies. We compare statistical dependences between evolutionary parameters of triple systems with various values of ?, and analyze the k and μ dependences of the number of crossings of the center of mass of the triple system by the central body and the lifetime of the system. We construct the functions R_max(r_max), where r_max and R_max are the maximum achievable distances between the outer bodies, and between the central body and the center of mass of the outer bodies in the triple system. The parameter ? proves to be the most important parameter of the problem, and determines the relationship between the measures of the regular and stochastic trajectories. However, there exist “seeds” of stochasticity, even at small ?～10^?2. The measure of the stochastic orbits increases with ?; when ?≥10, virtually the entire region of the initial conditions corresponds to stochastic trajectories.     

New dwarf galaxy candidates in the Leo-I Group

We have carried out a search for low-surface-brightness dwarf galaxies in the region of the Leo-I Group (M96) in images of the second Palomar Sky Survey. We found a total of 36 likely dwarf members of the group with typical magnitudes B _t ～18^m–19^m in an area of sky covering 120 square degrees. Half of these galaxies are absent from known catalogs and lists of galaxies. The radial-velocity dispersion calculated for 19 galaxies is 130 km/s. The Leo-I Group has a mean distance from the Sun of 10.4 Mpc, a mean projected radius of 352 kpc, an integrated luminosity of 6.7 × 10¹⁰L_⊙, a virial mass-to-luminosity ratio of 107 M_⊙/L_⊙, and a mean crossing time of 2.7 Gyr. The group shows evidence for a radial segregation of the galaxies according to morphological type and luminosity, suggesting that the group is in a state of dynamical relaxation. The subsystem of bright galaxies in the Leo-I Group is smaller in size (250 kpc) and has a lower velocity dispersion (92 km/s), resulting in a lower virial mass-to-luminosity ratio (34 M_⊙/L_⊙), as is typical of the Local Group and other nearby groups of galaxies.     

Formation of supermassive black holes due to the tidal deceleration of stellar black holes, globular clusters, and galaxies

The formation and evolution of supermassive (10²?10¹⁰ M _⊙) black holes (SMBHs) in the dense cores of globular clusters and galaxies is investigated. The raw material for the construction of the SMBHs is stellar black holes produced during the evolution of massive (25?150M _⊙) stars. The first SMBHs, with masses of ～1000M _⊙, arise in the centers of the densest and most massive globular clusters. Current scenarios for the formation of SMBHs in the cores of globular clusters are analyzed. The dynamical deceleration of the most massive and slowly moving stellar-mass (< 100M _⊙) black holes, accompanied by the radiation of gravitational waves in late stages, is a probable scenario for the formation of SMBHs in the most massive and densest globular clusters. The dynamical friction of the most massive globular clusters close to the dense cores of their galaxies, with the formation of close binary black holes due to the radiation of gravitational waves, leads to the formation of SMBHs with masses ? 10³ M _⊙ in these regions. The stars of these galaxies form galactic bulges, providing a possible explanation for the correlation between the masses of the bulge and of the central SMBHs. The deceleration of the most massive galaxies in the central regions of the most massive and dense clusters of galaxies could lead to the appearance of the most massive (to 10¹⁰ M _⊙) SMBHs in the cores of cD galaxies. A side product of this cascade scenario for the formation of massive galaxies with SMBHs in their cores is the appearance of stars with high spatial velocities (> 300 km/s). The velocities of neutron stars and stellar-mass black holes can reach ～10⁵ km/s.     

Early formation of galaxies induced by clusters of black holes

A model for the formation of supermassive black holes at the center of a cluster of primordial black holes is developed. It is assumed that ～10^?3 of the mass of the Universe consists of compact clusters of primordial black holes that arose as a result of phase transitions in the early Universe. These clusters also serve as centers for the condensation of dark matter. The formation of protogalaxies with masses of the order of 2 × 10⁸ M _⊙ at redshift z = 15 containing clusters of black holes is investigated. The nuclei of these protogalaxies contain central black holes with masses ～10⁵ M _⊙, and the protogalaxies themselves resemble dwarf spherical galaxies with their maximum density at their centers. Subsequent merging of these induced protogalaxies with ordinary halos of dark matter leads to the standard picture for the formation of the large-scale structure of the Universe. The merging of the primordial black holes leads to the formation of supermassive black holes in galactic nuclei and produces the observed correlation between the mass of the central black hole and the bulge velocity dispersion.     

Spiral galaxies with non-typical mass-to-light ratios

Total mass-to-light ratio M/L _B for S0 — Irr galaxies, whereM is the dynamical mass within the optical radius R ₂₅ (corresponding to 25 ^m /sq. arcsec in the B band), increases systematically with (B-V)₀ color, but slower than that is predicted by stellar population evolution models without dark halo. It shows that the mean ratio between dark halo and stellar masses is higher for more “blue“ galaxies. However some galaxies don’t follow this general trend. The properties of galaxies with extremely high and extremely low values of M/L _B ratios are compared, and different factors, accounting for the extremes, are analyzed. The conclusion is that in some cases too high or too low M/L _B ratios are associated with observational errors, in other cases—with non-typical dark halo mass fraction, and in some cases — with peculiarities of disc stellar population. Particularly, discs of some galaxies with low M/L _B ratios turn out to be unusually “light” for their luminosity and colors, which indicates a substantial deficit of low mass stars as the most probable cause of low M/L _B .     

The role of dark matter in the dynamical evolution of galaxy clusters in the framework of the <Emphasis Type="Italic">N</Emphasis>-body problem

NumericalN-body studies of the dynamical evolution of a cluster of 1000 galaxies were carried out in order to investigate the role of dark matter in the formation of cD galaxies. Two models explicitly describing the darkmatter as a full-fledged component of the cluster having its own physical characteristics are constructed. These treat the dark matter as a continuous underlying substrate and as “grainy” matter. The ratio of the masses of the dark and luminous matter of the cluster is varied in the range 3–100. The observed logarithmic spectrum dN ∼ dM / M is used as an initial mass spectrum for the galaxies. A comparative numerical analysis of the evolution of the mass spectrum, the dynamics of mergers of the cluster galaxies, and the evolution of the growth of the central, supermassive cD galaxy suggests that dynamical friction associated with dark matter accelerates the formation of the cD galaxy via the absorption of galaxies colliding with it. Taking into account a dark-matter “substrate” removes the formation of multiple mass-accumulation centers, and makes it easier to form a cD galaxy that accumulates 1–2% of the cluster mass within the Hubble time scale (3–8 billion years), consistent with observations.     

The role of external factors in the evolution of galaxies

We consider the evolution of galaxies in dense galactic clusters. Observations and theoretical estimates indicate that this evolution may be specified to a large extent by collisions between galaxies, as well as interactions between the gaseous components of disk galaxies and intergalactic gas. We analyze collisions between disk galaxies with gaseous components using a simple model based on a comparison of the duration of a collision and the characteristic cooling time for the gas heated by the collision, and also of the relative masses of stars and gas in the colliding disk galaxies. This model is used to analyze scenarios for collisions between disk galaxies with various masses as a function of their relative velocities. Our analysis indicates that galaxies can merge, lose one or both of their gaseous components, or totally disintegrate as a result of a collision; ultimately, a new galaxy may form from the gas lost by the colliding galaxies. Disk galaxies with mass M _G and velocities exceeding ～300 (M _G/10¹⁰ M _⊙)^1/2 km/s in intergalactic gas in clusters with densities ～10^?27 g/cm³ can lose their gas due to the pressure of inflowing intergalactic gas, thereby developing into E(SO) galaxies.     

Supermassive black holes in interacting galaxies

The possible influence of galactic interaction on the formation and growth of supermassive black holes in their nuclei and the dynamics of their circumnuclear regions are considered, based on new data from the updated Vorontsov-Velyaminov catalog of interacting galaxies and modern estimates of the masses of supermassive black holes. A sample of interacting galaxies with known black-hole masses is created, and the dependence of the masses of the central black holes on the absolute B magnitudes and central stellar velocity dispersions in the host galaxy derived for this sample. A statistical analysis of the sample shows that the black-hole masses in interacting galaxies satisfy the same mass-velocity dispersion relation as non-interacting galaxies. A higher mass dispersion is characteristic of merging pairs than for galaxies that interact in other ways. The maximum masses of the central black holes are observed in radio galaxies.