Refinement of the parameters of three selected model Galactic potentials based on the velocities of objects at distances up to 200 kpc

This paper is a continuation of our recent paper devoted to refining the parameters of threecomponent (bulge, disk, halo) axisymmetric model Galactic gravitational potentials differing by the expression for the dark matter halo using the velocities of distant objects. In all models the bulge and disk potentials are described by the Miyamoto–Nagai expressions. In our previous paper we used the Allen–Santillán (I), Wilkinson–Evans (II), and Navarro–Frenk–White (III) models to describe the halo. In this paper we use a spherical logarithmic Binney potential (model IV), a Plummer sphere (model V), and a Hernquist potential (model VI) to describe the halo. A set of present-day observational data in the range of Galactocentric distances R from 0 to 200 kpc is used to refine the parameters of the listed models, which are employed most commonly at present. The model rotation curves are fitted to the observed velocities by taking into account the constraints on the local matter density ρ_⊙= 0.1 M _⊙pc^?3 and the force K _z=1.1/2πG = 77M _⊙pc^?2 acting perpendicularly to the Galactic plane. The Galactic mass within spheres of radius 50 and 200 kpc are shown to be, respectively, M ₅₀ = (0.409 ± 0.020) × 10¹² M _⊙ and M ₂₀₀ = (1.395 ± 0.082) × 10¹² M _⊙ in model IV, M ₅₀ = (0.417 ± 0.034) × 10¹² M _⊙ and M ₂₀₀ = (0.469 ± 0.038) × 10¹² M _⊙in model V, and M ₅₀ = (0.417 ± 0.032) × 10¹² M _⊙ and M ₂₀₀ = (0.641 ± 0.049)× 10¹² M _⊙ in model VI. Model VI looks best among the three models considered here from the viewpoint of the achieved accuracy of fitting the model rotation curves to the measurements. This model is close to the Navarro–Frenk–White model III refined and considered best in our previous paper, which is shown using the integration of the orbits of two globular clusters, Lynga 7 and NGC 5053, as an example.     

The galactic surface density derived from K giants

We compare theW velocity dispersions of Brosche, Schwan & Schwarz (2001) with more recent results. The increase with the distance |z | from the galactic plane is confirmed, although perhaps with reduced amplitude. This could be interpreted either as one homogenous population or as a superposition of (at least) two populations with two constant dispersions and two scale heights. For each of the possibilities we propose a simple model. Combined with two observational variants for the velocity variation, we obtain surface densities up to |z | = 250 pc ranging from 5 to 44 M_⊙ pc^–2. Thus the case for considerable dark matter in the neighbourhood of the galactic plane is not supported     

Rotation curve and mass distribution in the Galaxy from the velocities of objects at distances up to 200 kpc

Three three-component (bulge, disk, halo) model Galactic gravitational potentials differing by the expression for the dark matter halo are considered. The central (bulge) and disk components are described by the Miyamoto–Nagai expressions. The Allen–Santillán (I), Wilkinson–Evans (II), and Navarro–Frenk–White (III) models are used to describe the halo. A set of present-day observational data in the range of Galactocentric distances R from 0 to 200 kpc is used to refine the parameters of thesemodels. For the Allen–Santillán model, a dimensionless coefficient γ has been included as a sought-for parameter for the first time. In the traditional and modified versions, γ = 2.0 and 6.3, respectively. Both versions are considered in this paper. The model rotation curves have been fitted to the observed velocities by taking into account the constraints on the local matter density ρ _⊙ = 0.1 M _⊙ pc^?3 and the force K _z =1.1/2πG = 77 M _⊙ pc^?2 acting perpendicularly to the Galactic plane. The Galactic mass within a sphere of radius 50 kpc, M _G (R ≤ 50 kpc) ≈ (0.41 ± 0.12) × 10¹² M _⊙, is shown to satisfy all three models. The differences between the models become increasingly significant with increasing radius R. In model I, the Galactic mass within a sphere of radius 200 kpc at γ = 2.0 turns out to be greatest among the models considered, M _G (R ≤ 200 kpc) = (1.45 ±0.30)× 10¹² M _⊙, M _G (R ≤ 200 kpc) = (1.29± 0.14)× 10¹² M _⊙ at γ = 6.3, and the smallest value has been found in model II, M _G (R ≤ 200 kpc) = (0.61 ± 0.12) × 10¹² M _⊙. In our view, model III is the best one among those considered, because it ensures the smallest residual between the data and the constructed model rotation curve provided that the constraints on the local parameters hold with a high accuracy. Here, the Galactic mass is M _G (R ≤ 200 kpc) = (0.75 ± 0.19) × 10¹² M _⊙. A comparative analysis with the models by Irrgang et al. (2013), including those using the integration of orbits for the two globular clusters NGC 104 and NGC 1851 as an example, has been performed. The third model is shown to have subjected to a significant improvement.     

The virial mass of the nucleus of M32

By means of the virial theorem we derive the dependence of the mass of an oblate spheroid in solid body rotation from the velocity dispersion and the space light density. The latter is obtained from a calibrated and seeing deconvolved brightness profile as numerical and stable solution of the Abel integral equation. The application of the nucleus of M32 gives a central density of 2.1×10^?5 M _⊙ pc^?3, a nuclear mass of 4.3×10^?7 M _⊙ and a mass-to-light ratio of 4.6 inV-band.     

A stochastic model for correlations between central black hole masses and galactic bulge velocity dispersions

We consider a cosmological model in which part of the Universe, Ω_h～10^?5, is in the form of primordial black holes with masses of ～ 10⁵ M _⊙. These primordial black holes were the centers for growing protogalaxies, which experienced multiple mergers with ordinary galaxies and with each other. The galaxy formation is accompanied by the merging and growth of central black holes in the galactic nuclei. We show that the recently discovered correlations between central black hole masses and galactic bulge parameters naturally arise in this scenario.     

He-rich white dwarfs: Birth-rate and kinematics of different groups of white dwarfs

The temperatures, radii, and masses of 81 He-rich white dwarfs are calculated from photometric data. It is shown that, on the average, they are less massive than DA white dwarfs: 70% of He-rich white dwarfs have masses<0.55M _⊙. Space density and birth-rate for different mass groups of H-rich and He-rich white dwarfs are obtained. Birth-rate is 1×10^?12 pc^?3 yr^?1 and 1.5×10^?12pc^?3yr^?1 for He-rich and H-rich white dwarfs, respectively. The mean mass of nascent white dwarfs is about 0.55M _⊙. It is shown thatV _Tand its dispersion σ are correlated with the mass of white dwars, and from this progenitors' masses — of different mass groups of white dwarfs are estimated.     

Local galactic field of forces and the interstellar matter

The density distributions of the two main components in interstellar hydrogen are calculated using 21 cm line data from the Berkeley Survey and the Pulkovo Survey. The narrow, dense component (state I of neutral hydrogen) has a Gaussianz-distribution with a scale-height of 50 pc in the local zones (the galactic disk). For the wide, tenuous component (hydrogen in state II) we postulate a distribution valid in the zones where such a material predominates (70 pc?z? 350 pc the galactic stratum) i.e., $$n_H \left( z \right) = n_H \left( 0 \right)exp \left( { - \left( {z/300{\text{ }}pc} \right)^{3/2} } \right).$$ Similar components are found in the dust distribution and in the available stellar data reaching sufficiently highz-altitudes. The scale-heights depend on the stellar type: the stratum in M III stars is considerably wider than in A stars (500–700 pc against 300 pc). The gas to dust ratio is approximately the same in both components: 0.66 atom cm^?3 mag^?1 kpc in the galactic plane. A third state of the gas is postulated associating it the observed free electron stratum at a scale-height of 660 pc (hydrogen fully ionized at high temperatures). The ratio between the observed dispersions in neutral hydrogen (thermal width plus turbulence) and the total dispersions corresponding to the real inner energies in the medium is obtained by a comparison with the dispersion distribution σ(z) of the different stellar types associated with the disk and the stratum $$\sigma ^2 \left( {total} \right) = \sigma ^2 \left( {21{\text{ cm line}}} \right) \cdot {\text{ }}Q^2 ,$$ from which we graphically obtainedQ ²=2.9 ± 0.3, although that number could be lower in the densest parts of the spiral arms. Its dependence on magnetic field and cosmic rays is analysed, indicating equipartition of the different energy components in the interstellar medium and consistency with the observed values of the magnetic field: i.e., fluctuations with an average of ～ 3 μG (associated with the disk) in a homogeneous background of ～ 1 μG (associated with the stratum). A minimum and maximumK _z-force are obtained assuming extreme conditions for the total density distribution (gas plus stars). TheK _z-force obtained from the interstellar gas in its different states using approximations of the Boltzmann equation is a reasonable intermediate case between maximum and minimumK _z. The mass density obtained in the galactic plane is 0.20±0.05M _⊙ pc^?3, and the results indicate that the galactic disk is somewhat narrower and denser than has usually been believed. The effects of wave-like distributions of matter in thez-coordinate are analysed in relation with theK _z-force, and comparisons with theoretical results are performed. A qualitative model for the galactic field of force is postulated together with a classification of the different zones of the Galaxy according to their observed ranges in velocity dispersions and the behaviour of the potential well at differentz-altitudes. The disk containing at least two-thirds of the total mass atz<100 pc, the stratum containing one-third or less of the total mass atz≤600–800 pc, and the halo at higherz-altitudes with a small fraction of such a mass which is difficult to evaluate.     

Shaping the relation between the mass of supermassive black holes and the velocity dispersion of galactic bulges

I use the fact that the radiation emitted by the accretion disk of supermassive black hole can heat up the surrounding gas in the protogalaxy to achieve hydrostatic equilibrium during the galaxy formation. The correlation between the black hole mass M _BH and velocity dispersion σ thus naturally arises. The result generally agrees with empirical fittings from observational data, even with M _BH ≤10⁶ M _⊙. This model provides a clear picture on how the properties of the galactic supermassive black holes are connected with the kinetic properties of the galactic bulges.     

Graphite grain formation in the atmospheres of R coronae borealis stars

The results of calculations of graphite grain formation in the atmospheres of R CrB stars are given. The parameters for the models wereM=1M _⊙,M _bol=?6 mag. The effective temperature ranged from 5300K to 8300K. The chemical composition corresponded to the hydrogen-deficient carbon rich mixture:X=0,Y=0.9,Z _c=0.1. The results obtained show the existence of a critical mass loss rate which is ranged fromM _*≈10^?6 M _⊙yr^?1 forT _eff=5300 K toM _*≈10^?5 M _⊙ yr^?1 forT _eff=8300 K. As soon as the rate of mass loss exceedsM _* by 3–5 times the degree of condensation of carbon changes from 0 to 0.7. The finite radii of grains are about from 0.01 μm to 0.6 μm depending on the density near the condensation point, the velocity of matter outflow, and the stellar effective temperature. The duration of grain growth should amount to some dozens of days. It is supposed that the most probable explanation of dust-shell formation around R CrB stars is graphite condensation behind a shock wave arising from nonlinear stellar pulsation.     

Star formation efficiency in low-density regions in galactic disks

The radial dependences of the star formation efficiency??_SFE = ??_SFR/??_gas (per unit disk surface area) in normal surface brightness spiral galaxies and low surface brightness (LSB) galaxies are compared with the radial variations of the gas and stellar disk surface and volume densities. The volume density of the components in the disk midplane is found through a self-consistent solution of the disk equilibrium equations by taking into account the dark halo. The disk thickness variation with radius R is calculated within the model of a galaxy with a marginally stable disk by taking into account the increase of the stability parameter Q _T,c along the radius. We show that the star formation efficiency depends weakly (for LSB galaxies, does not depend at all) on the gas density but correlates well with the disk surface and volume density, with the normal and LSB galaxies forming a single sequence. The dependence vanishes only at extremely low disk densities (?? _disk ? (1?3) M _?? pc^?2, ?? _stars ?? (1?3) × 10^?24 g cm^?3), where star formation probably ceases to be related to disk properties. Estimations of the gas volume density allow us to check the expected form of the ??_SFR-?? _disk relationship that follows from the model by Ostriker et al., which relates the star formation rate to the pressure of the diffuse gas medium. For most of the galaxies considered, there is satisfactory agreement with the model, except for the densest (of the order of several hundred M _?? pc^?2) and least dense (several M?? pc^?2 or less) disk regions.     

Disk models for cataclysmic variables

This paper presents disk models for cataclysmic variables in which convection in the central layers has been included. The calculation of the vertical structure at different points is presented. The models have a central mass of 1M _⊙ and matter fluxes of 10^?9, 10^?8, and 10^?7 M _⊙ yr^?1. The corresponding luminosities are 1.86, 1.86×10 and 1.86×10² L _⊙.     

Preliminary results of the multisite time-series campaign on the sdB pulsator PG 1325+101

I present a model for the formation and evolution of a massive disk galaxy, within a growing dark halo whose mass evolves according to cosmological simulations of structure formation. The galactic evolution is simulated with a new 3D chemo-dynamical code, including dark matter, stars and a multi-phase ISM. We follow the evolution from redshift z = 4.85 until the present epoch. The energy release by massive stars and supernovae prevents a rapid collapse of the baryonic matter and delays the maximum star formation until redshift z ≈ 1. The galaxy forms radially from inside-out and vertically from top-to-bottom. The feedback of stars leads to turbulent motions and large-scale flows in the ISM. As one result the galactic disk is significantly enriched by chemical elements synthesized in bulge stars.     

Supersonic steady accretion of a rotating cold “Iron Gas” onto a neutron star after gravitational collapse

We analytically generalize the well-known solution of steady supersonic spherically symmetric gas accretion onto a star (Bondi 1952) for an iron atmosphere with completely degenerate electrons with an arbitrary degree of relativity. This solution is used for typical physical conditions in the vicinity of protoneutron stars produced by gravitational collapse with masses M ₀=(1.4?1.8)M _⊙ and over a wide range of nonzero “iron gas” densities at infinity, ρ_∞=(10⁴?5×10⁶)g cm^?3. Under these conditions, we determine all accretion parameters, including the accretion rate, whose value is ～(10?50)M _⊙s^?1 at M ₀=1.8M _⊙ (it is a factor of 1.7 lower for M ₀=1.4M _⊙, because the accretion rate is exactly ∝M ₀ ² ). We take into account the effect of accreting-gas rotation in a quasi-one-dimensional approximation, which has generally proved to be marginal with respect to the accretion rate.     

Very massive close binaries and the puzzling temporal evolution of 14N in the Solar Neighbourhood

Low metallicity very massive stars with an initial mass between 140M_⊙ and 260M_⊙ can be subdivided into two groups: those between 140M_⊙ and 200M_⊙ which produce a relatively small amount of Fe, and those with a mass between 200M_⊙ and 260M_⊙ where the Fe-yield ejected during the supernova explosion is enormous. We first demonstrate that the inclusion of the second group into a chemical evolutionary model for the Solar Neighbourhood predicts an early temporal evolution of Fe, which is at variance with observations whereas it cannot be excluded that the first group could have been present. We then show that a low metallicity binary with very massive components (with a mass corresponding to the first group) can be an efficient site of primary ¹⁴N production through the explosion of a binary component that has been polluted by the pair instability supernova ejecta of its companion. When we implement these massive binary ¹⁴N yields in a chemical evolution model, we conclude that very massive close binaries may be important sites of ¹⁴N enrichment during the early evolution of the Galaxy.     

Numerical experiments on the stability of preplanetary disks

Gravitational stability of gaseous protostellar disks is relevant to theories of planetary formation. Stable gas disks favor formation of planetesimals by the accumulation of solid material; unstable disks allow the possibility of direct condensation of gaseous protoplanets. We present the results of numerical experiments designed to test the stability of thin disks against large-scale, self-gravitational disruption. The disks are represented by a distribution of about 6 × 10⁴ point masses on a two-dimensional (r, φ) grid. The motions of the particles in the self-consistent gravity field are calculated, and the evolving density distributions are examined for instabilities. Two parameters that have major influences on stability are varied: the initial temperature of the disk (represented by an imposed velocity dispersion), and the mass of the protostar relative to that of the disk. It is found that a disk as massive as 1M_⊙, surrounding a 1M_⊙ protostar, can be stable against long-wavelength gravitational disruption if its temperature is about 300°K or greater. Stability of a cooler disk requires that it be less massive, but even at 100°K a stable disk can have an appreciable fraction ($\text{～}\text{1}\text{3}$) of a solar mass.     

Flat rotation curves and mass distribution for spiral galaxies with a disk model

A method to fit flat rotation curves is presented, wherein the galactic density for a disk model is expressed in terms of a Dirichlet polynomial. This procedure allows us to obtain the total galactic mass and to predict the circular velocity at large galactocentric distances.Application of the method to the Galaxy, M31 and four Sc galaxies shows that a significant galactic mass is located beyond the optical radius although it is considerably smaller than the integral mass values obtained from current models with a massive corona included. Observed rotation curves and convergent total mass are obtained, thus the total mass for the Milky Way Galaxy is 5.69×10¹¹ M .     

Pulsations of intermediate–mass stars on the asymptotic giant branch

Evolutionary tracks from the zero age main sequence to the asymptotic giant branch were computed for stars with initial masses 2 M _⊙ ≤ M _ZAMS ≤ 5 M _⊙ and metallicity Z = 0.02. Some models of evolutionary sequences were used as initial conditions for equations of radiation hydrodynamics and turbulent convection describing radial stellar pulsations. The early asymptotic giant branch stars are shown to pulsate in the fundamental mode with periods 30 day ? Π ? 400day. The rate of period change gradually increases as the star evolves but is too small to be detected (Π?/Π < 10^?5 yr^?1). Pulsation properties of thermally pulsing AGB stars are investigated on time intervals comprising 17 thermal pulses for evolutionary sequences with initial masses M _ZAMS = 2 M _⊙ and 3 M _⊙ and 6 thermal pulses for M _ZAMS = 4 M _⊙ and 5 M _⊙. Stars with initial masses M _ZAMS ≤ 3 M _⊙ pulsate either in the fundamental mode or in the first overtone, whereas more massive red giants (M _ZAMS ≥ 4 M _⊙) pulsate in the fundamental mode with periods Π ? 10³ day. Most rapid pulsation period change with rate ?0.02 yr^?1 ? Π?/Π ? ?0.01 yr^?1 occurs during decrease of the surface luminosity after the maximum of the luminosity in the helium shell source. The rate of subsequent increase of the period is Π?/Π ? 5 × 10^?3 yr^?1.     

Analysis of HST ultraviolet spectra for T Tauri stars: DR Tau

We analyze the spectra of DR Tau in the wavelength range 1200 to 3100 Å obtained with the GHRS and STIS spectrographs from the Hubble Space Telescope. The profiles for the C IV 1550 and He II 1640 emission lines and for the absorption features of some lines indicate that matter falls to the star at a velocity ～300 km s^?1. At the same time, absorption features were detected in the blue wings of the N I, Mg I, Fe II, Mg II, C II, and Si II lines, suggesting mass outflow at a velocity up to 400 km s^?1. The C II, Si II, and Al II intercombination lines exhibit symmetric profiles whose peaks have the same radial velocity as the star. This is also true for the emission features of the Fe II and H₂ lines. We believe that stellar activity is attributable to disk accretion of circumstellar matter, with matter reaching the star mainly through the disk and the boundary layer. At the time of observations, the accretion luminosity was L_ac ? 2L_⊙ at an accretion rate ?10^?7M_⊙ yr^?1. Concurrently, a small (<10%) fraction of matter falls to the star along magnetospheric magnetic field lines from a height ～R_*. Within a region of size ?3.5R_*, the disk atmosphere has a thickness ～0.1R_* and a temperature ?1.5 × 10⁴ K. We assume that disk rotation in this region significantly differs from Keplerian rotation. The molecular hydrogen lines are formed in the disk at a distance <1.4 AU from the star. Accretion is accompanied by mass outflow from the accretion-disk surface. In a region of size <10R_*, the wind gas has a temperature ～7000 K, but at the same time, almost all iron is singly ionized by H I L _α photons from inner disk regions. Where the warm-wind velocity reaches ?400 km s^?1, the gas moves at an angle of no less than 30° to the disk plane. We found no evidence of regions with a temperature above 10⁴ K in the wind and leave open the question of whether there is outflow in the H₂ line formation region. According to our estimate, the star has the following set of parameters: M_* ? 0.9M_⊙, R_* ? 1.8R_⊙, L_* ? 0.9L_⊙, and \(A_V \simeq 0\mathop .\limits^m 9\). The inclination i of the disk axis to the line of sight cannot be very small; however, i≤60°.     

A rare reflection effect eclipsing sdB+dM binary: 2M 1533+3759

In this paper, we report a rare reflection effect eclipsing sdB+dM binary, 2M?1533+3759. It is the seventh eclipsing sdB+dM binary that has been discovered to date. This system has an orbital period of 0.16177042 day and a velocity semi-amplitude of 71.1 km?s^?1. Using a grid of zero-metallicity NLTE model atmospheres, we derived T _eff=29250 K, log?g=5.58 and [He/H]=?2.37 from spectra taken near the reflection effection minimum. Lightcurve modeling resulted in a system mass ratio of 0.301 and an orbital inclination angle of 86.6°. The derived primary mass for 2M?1533+3759, 0.376±0.055 M _⊙, is significantly lower than the canonical mass (0.48 M _⊙) found for most previously investigated sdB stars. This implies an initial progenitor mass >1.8 M _⊙, at least a main sequence A star and perhaps even one massive enough to undergo non-degenerate helium ignition.