Minimum velocity dispersion in stable stellar disks. Numerical simulations

N-body dynamical simulations are used to analyze the conditions for the gravitational stability of a three-dimensional stellar disk in the gravitational field of two rigid spherical components—a bulge and halo whose central concentrations and relative masses vary over wide ranges. The number of point masses N in the simulations varies from 40 to 500 000 and the evolution of the simulated systems is followed over 10–20 rotation periods of the outer edge of the disk. The initially unstable disks are heated and, as a rule, reach a quasi-stationary equilibrium with a steady-state radial-velocity dispersion c_r over five to eight turns. The radial behavior of the Toomre stability parameter Q_T(r) for the final state of the disk is estimated. Simple models are used to analyze the dependence of the gravitational stability of the disk on the relative masses of the spherical components, disk thickness, degree of differential rotation, and initial state of the disk. Formal application of existing, analytical, local criteria for marginal stability of the disk can lead to errors in c_r of more than a factor of 1.5. It is suggested that the approximate constancy of Q_T?1.2–1.5 for r?(1–2)×L (where L is the radial scale of disk surface density), valid for a wide range of models, can be used to estimate upper limits for the mass and density of a disk based on the observed distributions of the rotational velocity of the gaseous component and of the stellar velocity dispersion.     

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: Relation to dark halos

Estimates of the masses of supermassive black holes (M _bh ) in the nuclei of disk galaxies with known rotation curves are compared with estimates of the rotational velocities V _m and the “indicative” masses of the galaxies M _i . Although there is a correlation between M _bh and V _m or M _i , it is appreciably weaker than the correlation with the central velocity dispersion. The values of M _bh for early-type galaxies (S0-Sab), which have more massive bulges, are, on average, higher than the values for late-type galaxies with the same rotational velocities. We conclude that the black-hole masses are determined primarily by the properties of the bulge and not the rotational velocity or the mass of the galaxy.     

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.     

The galactic constants and rotation curve from molecular-gas observations

We obtained the photometric distances and radial velocities for the molecular gas for 270 star-forming regions and estimated the distance to the Galactic center from ten tangent points to be R₀ = 8.01 ± 0.44 kpc. Estimates of R₀ derived over the last decade are summarized and discussed; the average value is R₀ = 7.80 ± 0.33 kpc. We analyze deviations from axial symmetry of the gas motion around the Galactic center in the solar neighborhood. Assuming a flat rotation curve, we obtain Θ₀ ～ 200 km/s for the circular velocity of the Sun from regions beyond the Perseus arm. We used these Galactic constants to construct the Galactic rotation curve. This rotation curve is flat along virtually its total extent from the central bar to the periphery. The velocity jump in the corotation region of the central bar in the first quadrant is 20 km/s. We present analytical formulas for the rotation curves of the Northern and Southern hemispheres of the Galaxy for R₀ = 8.0 kpc and Θ₀ = 200 km/s.     

Properties of galactic disks at optical and near-IR wavelengths

We have analyzed the radial scales, central surface brightnesses, and colors of 400 disks of various types of galaxies. For nine galaxies, the brightness decrease and the central disk brightness were obtained via a two-dimensional decomposition of the U BV RI J H K photometric images into bulge and disk components. We used published disk parameters for 392 of the galaxies. The central surface brightness μ _0,i ⁰ and linear (disk) scale length h vary smoothly along the Hubble sequence of galaxies within a rather narrow interval. The disks of relatively early-type galaxies display higher central K surface brightnesses, higher central surface densities, higher central mass-to-luminosity ratios M/L(B), smaller sizes (relative to the diameter of the galaxy D ₂₅), redder integrated colors, and redder central colors. The color gradient normalized to the radius of the galaxy and the “blue” central surface brightness of the disk, μ _0,i/0(B), are both independent of the galaxy type. The radial disk scales in different photometric bands differ less in early-type than in late-type galaxies. A correlation between the central disk surface brightness and the total luminosity of the galaxy is observed. We also consider the influence of dust on the photometric parameters of the disks.     

Timescales for mechanisms for the dynamical evolution of open star clusters

We have obtained the stellar velocity dispersion in three mutually perpendicular directions in the halos and cores of clusters as a function of time for several non-stationary open-cluster models. During the dynamical evolution of the open-cluster models, the velocity dispersions undergo oscillations that do not decay during 5–10 violent-relaxation timescales, τ _vr . We estimated the time for synchronization of the rotation of the open-cluster models and their motion around the center of the Galaxy, t _s , which, depending on the model parameters, is t _s ? (5–27)τ _vr . Synchronization mechanisms for the models are discussed. The disruption of the systems in the force field of the Galaxy is strongly affected by tidal friction. We have also estimated the time for the formation of a spherical stellar-velocity distribution in the cluster models, t _σ ? (6 ? 25)τ _vr . The impact of instability in the stellar motions in a cluster on the formation of a spherical velocity distribution in the open-cluster models is discussed. We have noted a tendency for a weakening of the dependence of the coarse phase density of the cluster on small initial perturbations of the stellar phase coordinates in the model cluster cores for times about five times longer than the violent-relaxation time.     

Is NGC 7006 a globular cluster with a primarily red horizontal branch?

A CCD BV R photometric study of the central region (15″ ≤ r ≤ 100″) of the globular cluster NGC 7006 based on color-magnitude diagrams is presented. We find for the main parameters of the cluster [Fe/H] = ?1.62, Y = 0.21, E _B?V = 0.15 ^m , V _HB = 18.84 ^m , M _V ^HB =+0.56 ^m , R _⊙ = 37.1 kpc). Two previously unknown RR Lyr variables were discovered in the central region of the cluster. The morphological index of the horizontal branch for the entire region studied indicates that the red stellar population dominates, consistent with previous studies: HB _mi = ?0.13. Such anomalously negative morphological indices are possessed by a whole group of Ool clusters with intermediate metallicities, which also display a characteristic distribution of stars along the horizontal branch. There is a radial dependence for the horizontal-branch morphology, with the color becoming primarily blue with approach toward the cluster center. One possible origin for this behavior could be the effect of inner dynamical processes on the spatial distribution of hot stars.     

Non-stationary wind in the system of the infrared source RAFGL 5081

Based on long-term spectral monitoring with high spectral resolution, the optical spectrum of the weak central star of the IR source RAFGL 5081 has been studied for the first time. The spectral type of the star is close to G5–8 II, and its effective temperature is T_eff ≈ 5400 K. An unusual spectral phenomenon was discovered: splitting of the profiles of broad, stationary absorption lines of medium and low intensity. The heliocentric radial velocities V _r of all components of metal absorption lines, the Na I D lines, and the Hα line were measured for all the observation epochs. The constancy of the absorption lines rules out the possibility that the line splitting is due to binarity. The radial velocities of the wind components in the profiles of the Na I D and Hα lines reach ?250 and ?600 km/s, respectively. These profiles have narrow components, whose number, depth, and position vary with time. The time variability and multicomponent structure of the profiles of the Na I D and Hα lines indicates inhomogeneity and instability of the circumstellar envelope of RAFGL 5081. The presence of components with velocity V _r (IS) = ?65 km/s in the Na I (1) lines provides evidence that RAFGL 5081 is located behind the Perseus arm, i.e, no closer than 2 kpc. It is noted that RAFGL 5081 is associated with the reflection nebula GN 02.44.7.     

Early-type disk galaxies: Structure and kinematics

Spectroscopic observations of three lenticular (S0) galaxies (NGC 1167, NGC 4150, and NGC 6340) and one SBa galaxy (NGC 2273) have been taken with the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences aimed to study the structure and kinematic properties of early-type disk galaxies. The radial profiles of the stellar radial velocities and the velocity dispersion are measured. N-body simulations are used to construct dynamical models of galaxies containing a stellar disk, bulge, and halo. The masses of individual components are estimated formaximum-mass disk models. A comparison of models with estimated rotational velocities and the stellar velocity dispersion suggests that the stellar disks in lenticular galaxies are “overheated”; i.e., there is a significant excess velocity dispersion over the minimum level required to maintain the stability of the disk. This supports the hypothesis that the stellar disks of S0 galaxies were subject to strong gravitational perturbations. The relative thickness of the stellar disks in the S0 galaxies considered substantially exceed the typical disk thickness of spiral galaxies.     

Galactic orbits of globular clusters in the region of the Galactic bulge

Galactic orbits have been constructed over long time intervals for ten globular clusters located near the Galactic center. A model with an axially symmetric gravitational potential for the Galaxy was initially applied, after which a non-axially symmetric potential corresponding to the central bar was added. Variations in the trajectories of all these globular clusters in the XY plane due to the influence of the bar were detected. These were greatest for the cluster Terzan 4 in the meridional (RZ) plane. The globular clusters Terzan 1, Terzan 2, Terzan 4, Terzan 9, NGC 6522, and NGC 6558 always remained within the Galactic bulge, no farther than 4 kpc from the Galactic center.     

High-velocity stars as a result of encounters between stars and massive binary black holes in galactic nuclei

Numerical simulations of the motions of stars in the gravitational fields of binary black holes with various component mass ratios have been carried out. Two models are considered: (1) the two-body problem with two fixed centers; (2) the general three-body problem. The first model is applicable only over short times Δt ? T, where T is the period of the binary system. The second model is applicable at all times except for during close encounters of stars with one of the binary components, r ≤ 0.00002 pc, where r is the distance from the star to the nearer black hole. In very close passages, relativistic corrections must be taken into account. Estimates of the probability of formation of high-velocity stars as a result of such interactions are obtained. It is shown that this mechanism is not suitable for the nucleus of our Galaxy due to the probable absence of a second massive black hole in the central region of the Galaxy.     

Physical and dynamical parameters of the multiple system HD 222326

We present the results of our study of the physical and dynamical parameters of the multiple system HD 222326. A new method for determining the individual radial velocities of components in wide binary and multiple systems in the case of small radial-velocity differences (δV _r ≤ the FWHMfor the line profiles) is suggested and tested for both model systems and the binary HD 10009. This testing yielded the component radial velocities V _{r 1,2} for HD 10009, enabling us to derive the center-of mass velocity, V _γ, for the first time. We determined the radial velocities of the components of HD 222326 from high-resolution spectra, and refined the orbital parameters of the subsystems using speckle-interferometric observations. A combined spectroscopic and speckle interferometric analysis enabled us to find the positions of the components in the spectral type—luminosity diagram and to estimate their masses. It is likely that the components are all in various evolutionary stages after leaving the main sequence. We analyzed the dynamical evolution of the system using numerical modeling in the gravitational three-body problem and the known stability criteria for triple systems. The system is probably stable on time scales of at least 10⁶ years. The presence of a fourth component in the system is also suggested.     

Evolutionary status of the spectral variable BD + 48°1220 = IRAS 05040+4820

Based on high-resolution observations (R = 60 000 and 75 000), we have studied the optical spectral variability of the star BD + 48°1220, identified with the IR source IRAS 05040+4820. We have measured the equivalent widths of numerous absorption lines of neutral atoms and ions at wavelengths from 4500 Å to 6760 Å, as well as the corresponding radial velocities. We use model atmospheres to determine the effective temperature T _eff = 7900 K, surface gravity log g = 0.0, microturbulence velocity ξ _t = 6.0, and the abundances for 16 elements. The star’s metallicity differs little from the solar value: [Fe/H] = ?0.10 dex. The main peculiarity of the chemical composition of the star is a large helium excess, derived from the Hel λ 5876 Å absorption, [He/H] = +1.04, and the equally large oxygen excess, [O/Fe] = +0.72 dex. The carbon excess is small, [C/Fe] = +0.09 dex, and the ratio [C/O] < 1. We obtained an altered relation for the light-metal abundances: [Na/Fe] = +0.87 dex with [Mg/Fe] = ?0.31 dex. The barium abundance is low, [Ba/Fe] = ?0.84 dex. It is concluded that the selective separation of elements onto dust grains of the envelope is probably efficient. The radial velocity of the star measured from photospheric absorption lines over three years of observations varies in the interval V _⊙ = ?(7–15) km/s. Time-variable differential line shifts have been revealed. The entire set of available data (the luminosity M _v ≈ ?5 ^m , velocity V _lsr ≈ ?20 km/s, metallicity [Fe/H] = ?0.10, and peculiarities of the optical spectrum and chemical composition) confirms the status of BD + 48°1220 as a post-AGB star with He and O excesses belonging to the Galactic disk.     

Galactic parameters derived from open-cluster data

The components U₀ and V₀ of the solar motion and the Oort constant A₀ are determined using the data of a homogeneous open-cluster catalog with corrected distance moduli. The results are based on a sample of 146 open clusters with known radial velocities located in the Galactic plane (b<7°) within 4 kpc of the Sun. The solar Galactocentric distance R₀ is determined using two kinematic methods. The following results are obtained: A₀=17.0±0.9 km/s kpc, U₀=10.5±1.0 km/s, V₀=11.5±1.1 km/s, R₀=8.3±0.3 pc.     

The magnetic-field structure in a stationary accretion disk

The magnetic-field structure in regions of stationary, planar accretion disks around active galactic nuclei where general-relativistic effects can be neglected (from 10 to 200 gravitational radii) is considered. It is assumed that the magnetic field in the outer edges of the disk, which forms in the magnetosphere of the central black hole during the creation of the relativisitic jets, corresponds to the field of a magnetic dipole perpendicular to the plane of the disk. In this case, the azimuthal field component B_φ in the disk arises due to the presence of the radial field B_ρ and the azimuthal velocity component U_φ. The value of the magnetic field at the inner radius of the disk is taken to correspond to the solution of the induction equation in a diffusion approximation. Numerical solutions of the induction equation are given for a number of cases.     

Mixing of metals during stripping of galactic gaseous halos

The mixing of metals in the intergalactic gas when a galaxy with a metal-rich envelope moves through the intergalactic medium is analyzed. Two simple models for the initial distribution of metals are considered. In the first case, the metals are concentrated in a fairly thin envelope with thickness ΔR _s =1 kpc, outer radius R _s =31 kpc, and metallicity Z=10^?3. In the second case, material with the same metallicity uniformly fills an entire spherical region of radius R _s . After 2.85 Gyr, the metals are distributed over a fairly extended volume with a typical size of ?200 kpc in the direction of the motion of the intergalactic gas, with a mean metallicity of ?4.6×10^?4 in metal-enriched regions. However, the distribution of metals remains extremely nonuniform, so that the main contribution to the overall metallicity is provided by metal-rich islands Z?6×10^?4 that occupy only ～10% of the total mixing volume. Moreover, metal-free regions remain in this volume.     

Analysis of Methods for Computing the Trajectories of Dust Particles in a Gas–Dust Circumstellar Disk

A systematic analysis ofmethods for computing the trajectories of solid-phase particles applied in modern astrophysics codes designed for modeling gas–dust circumstellar disks has been carried out for the first time. Themotion of grains whose velocities are determinedmainly by the gas drag, that is, for which the stopping time or relaxation time for the velocity of the dust to the velocity of the gas t_stop is less than or comparable to the rotation period, are considered. The methods are analyzed from the point of view of their suitability for computing the motions of small bodies, including dust grains less than 1 μm in size, which are strongly coupled to the gas. Two test problems are with analytical solutions. Fast first order accurate methods that make it possible to avoid additional restrictions on the time step size τ due to gas drag in computations of the motion of grains of any size are presented. For the conditions of a circumstellar disk, the error in the velocity computations obtained when using some stable methods becomes unacceptably large when the time step size is τ > t_stop. For the radial migration of bodies that exhibit drifts along nearly Keplerian orbits, an asymptotic approximation, sometimes called the short friction time approximation or drift flux model, gives a relative error for the radial-velocity computations equals to St², where St is the Stokes number, the ratio of the stopping time of the body to some fraction of the rotation period (dynamical time scale) in the disk.     

Distribution of interstellar plasma in the direction of PSR B0525+21 from data obtained on a ground–space interferometer

Observations on the RadioAstron ground–space interferometer with the participation of the Green Bank and Arecibo ground telescopes at 1668 MHz have enabled studies of the characteristics of the interstellar plasma in the direction of the pulsar PSR B0525+21. The maximum projected baseline for the ground–space interferometer was 233 600 km. The scintillations in these observations were strong, and the spectrum of inhomogeneties in the interstellar plasma was a power law with index n = 3.74, corresponding to a Kolmogorov spectrum. A new method for estimating the size of the scattering disk was applied to estimate the scattering angle (scattering disk radius) in the direction toward PSR B0525+21, θ _scat = 0.028 ± 0.002 milliarcsecond. The scattering in this direction occurs in a plasma layer located at a distance of 0.1Z from the pulsar, where Z is the distance from the pulsar to the observer. For the adopted distance Z = 1.6 kpc, the screen is located at a distance of 1.44 kpc from the observer.     

Masses of the visual components and black holes in X-ray novae: Effects of proximity of the components

It is shown that the approximation of the complex, tidally distorted shape of a star as a circular disc with local line profiles and a linear limb-darkening law, which is usually applied when deriving equatorial stellar rotation velocities from line profiles, leads to overestimation of the equatorial velocity V _rot sin i and underestimation of the component mass ratio q = M _x /M _v . A formula enabling correction of the effect of these simplifying assumptions on the shape of a star is used to re-determine the mass ratios q and the masses of the black holes M _x and visual components M _v in low-mass X-ray binary systems containing black holes. Taking into account the tidal–rotational distortion of the stellar shape can significantly increase the mass ratios q = M _x /M _v , reducing M _v , while M _x changes only slightly. The resulting distribution of M _v attains its maximum near M _v ? 0.35M _⊙, in disagreement with the results of population synthesis computations realizing standard models for Galactic X-ray novae with black holes. Possible ways to overcome this inconsistency are discussed. The derived distribution of M _x also differs strongly from the mass distribution for massive stars in the Galaxy.