Similarity solution for unsteady accretion flow,II

Similarity solution for unsteady accretion flow is obtained. The density distribution of the initial state of the gas surrounding the star is given as ?₀ ∝r ^?ω. The flow patterns are compared with the results of the numerical computation by Zel'dovichet al. (1972), and it is shown that the similarity solution reproduces the results of the numerical computations well. An unsteady accretion model for the nova-like X-ray source is discussed briefly.     

The toroidal iron atmosphere of a protoneutron star: Numerical solution

A numerical method presented by Imshennik et al. (2002) is used to solve the two-dimensional axisymmetric hydrodynamic problem on the formation of a toroidal atmosphere during the collapse of an iron stellar core and outer stellar layers. An evolutionary model from Boyes et al. (1999) with a total mass of 25M_⊙ is used as the initial data for the distribution of thermodynamic quantities in the outer shells of a high-mass star. Our computational region includes the outer part of the iron core (without its central part with a mass of 1M_⊙ that forms the embryo of a protoneutron star at the preceding stage of the collapse) and the silicon and carbon-oxygen shells with a total mass of (1.8–2.5)M_⊙. We analyze in detail the results of three calculations in which the difference mesh and the location of the inner boundary of the computational region are varied. In the initial data, we roughly specify an angular velocity distribution that is actually justified by the final result—the formation of a hydrostatic equilibrium toroidal atmosphere with reasonable total mass, M^tot=(0.117–0.122)M_⊙, and total angular momentum, J^tot=(0.445–0.472)×10⁵⁰ erg s, for the two main calculations. We compare the numerical solution with our previous analytical solution in the form of toroidal atmospheres (Imshennik and Manukovskii 2000). This comparison indicates that they are identical if we take into account the more general and complex equation of state with a nonzero temperature and self-gravitation effects in the atmosphere. Our numerical calculations, first, prove the stability of toroidal atmospheres on characteristic hydrodynamic time scales and, second, show the possibility of sporadic fragmentation of these atmospheres even after a hydrodynamic equilibrium is established. The calculations were carried out under the assumption of equatorial symmetry of the problem and up to relatively long time scales (～10 s).     

The structure of dust tails of comets II. The tail and dust content of comet Arend-Roland

The modified distribution function of dust particles, f(γ), which can be determined from tail brightness profiles on the basis of mechanical theory, is discussed with special regard to its reliability and accuracy. Physical significance of f(γ) is also discussed in terms of dust model parameters, and it is shown that f(γ), if treated carefully, will serve as an effective tool in studying cometary dust. Four isophotes of Comet Arend-Roland, 1957 III, in the orange-red light (λλ 0.53–0.68 micron) obtained by Ceplecha (1958), are analysed by the numerical method described in Paper I (KIMURA and LIU 1975) with some improvements and higher approximations. The distribution f(γ) thus obtained shows a bimodal character with peaks at γ = 0.10 and 0.010 with a relative height ratio of 1 to 0.6. Dust emission rate, which is assumed to follow the inverse square law of heliocentric distance, is estimated to give P_dC_sca = (1.3±0.5) × 10⁹ cm²/sec, where P_d is the rate of particle emission at 1 a.u. and the C_sca is a mean effective cross section of particles for light scattering including the phase effect (the scattering angles of present interest range from about 80 to 100 degrees).     

Numerical simulation of the final stages of terrestrial planet formation

Three representative numerical simulations of the growth of the terrestrial planets by accretion of large protoplanets are presented. The mass and relative-velocity distributions of the bodies in these simulations are free to evolve simultaneously in response to close gravitational encounters and occasional collisions between bodies. The collisions between bodies, therefore, arise in a natural way and the assumption of expressions for the relative velocity distribution and the gravitational collision cross section is unnecessary. These simulations indicate that the growth of bodies with final masses approaching those of Venus and the Earth is possible, at least for the case of a two-dimensional system. Simulations assuming an initial uniform distribution of orbital eccentricities on the interval from 0 to e_max are found to produce final states containing too many bodies with masses which are too small when e_max < 0.10, while simulations with e_max > 0.20 result in too many catastrophic collisions between bodies thus preventing rapid accretion of planetary-size bodies. The e_max = 0.15 simulation ends with a state surprisingly similar to that of the present terrestrial planets and, therefore, provides a rough estimate of the range of radial sampling to be expected for the terrestrial planets.     

A parametric study of stability and resonances around L 4 in the elliptic restricted three-body problem

The size of the stable region around the Lagrangian point L ₄ in the elliptic restricted three-body problem is determined by numerical integration as a function of the mass parameter and eccentricity of the primaries. The size distribution of the stable regions in the mass parameter-eccentricity plane shows minima at certain places that are identified with resonances between the librational frequencies of motions around L ₄. These are computed from an approximate analytical equation of Rabe relating the frequency, mass parameter and eccentricity. Solutions of this equation are determined numerically and the global behaviour of the frequencies depending on the mass parameter and eccentricity is shown and discussed. The minimum sizes of the stable regions around L ₄ change along the resonances and the relative strength of the resonances is analysed. Applications to possible Trojan exoplanets are indicated. Escape from L ₄ is also investigated.     

Properties of voids in the 2dFGRS galaxy survey

A method for detecting voids in the galaxy distribution is presented. Using this method, we have identified 732 voids with a radius of the seed sphere R _seed > 4.0h ^?1 Mpc in a volume-limited sample of galaxies from the southern part of the 2dFGRS survey. 110 voids with R _seed > 9.0h ^?1 Mpc have a positive significance. The mean volume of such voids is ～19 × 10³ h ^?3 Mpc³. Voids with R _seed > 9.0h ^?1 Mpc occupy 55% of the sample volume. We construct a dependence of the volumes of all the identified voids on their ranks and determine parameters of the galaxy distribution. The dependence of the volume of voids on their rank is consistent with a fractal model (Zipf’s power law) of the galaxy distribution with a fractal dimension D ≈ 2.1 (given the uncertainty in determining the dimension using our method and the results of a correlation analysis) up to scales of ～25h ^?1 Mpc with the subsequent transition to homogeneity. The directions of the greatest elongations of voids and their ellipticities (oblateness) are determined from the parameters of equivalent ellipsoids. The directions of the greatest void elongations have an enhanced concentration to the directions perpendicular to the line of sight.     

Calculating Method and Characteristics of the Distribution of Neutron Exposures in the Radiative S-process Nucleosynthesis Model for AGB Stars

A study on the distribution of neutron exposures in a low-mass asymptotic giant branch (AGB) star is presented, according to the s-process nucleosynthesis model with the ¹²C(α, n)¹⁶O reaction occurred under radiative conditions in the interpulse phases. The model parameters, such as the over- lap factor r of two successive convective thermal pulses, the mass ratio q of the ¹³C shell with respect to the He intershell, and the effective mass of ¹³C in the ¹³C shell, vary with the pulse number. Considering these factors, a calculating method for the distribution of neutron exposures in the He intershell has been presented. This method has the features of simplicity and universality. Using this method, the exposure distribution for the stellar model of a star with the mass of 3 M_? and the solar metallicity has been calculated. The results suggest that under the reasonable assumption that the number density of neutrons is uniform in the ¹³C shell, the ?nal exposure distribution approaches to an exponential distribution. For a stellar model with the de?nite initial mass and metallicity, there is a de?nite relation between the mean neutron exposure τ₀ and the neutron exposure Δτ of each pulse, namely τ₀ = 0.434λ(q1, q2, …, qm_max +1, …, r₁, r₂, …, rm_max +1)Δτ, where m_max is the total number of thermal pulses with the third dredge-up episode, and the proportional coeffcient λ(q₁, q₂, …, qm_max +1, …, r₁, r₂, …, rm_max +1) can be determined by an exponential curve ?tting to the ?nal exposure distribution. This new formula quantitatively uni?es the classical model with the s-process nu- cleosynthesis model by means of neutron exposure distribution, and makes the classical model continue to offer guidance and constraints to the s-process nu- merical calculations of stellar models.     

The effects of the polytropic coefficient on plasma sheath in two cases isothermal and adiabatic ion thermal flow

Recently it has been shown that for finite and small values of the electron Debye length, the ion polytropic coefficient is approached to some constant value in the plasma sheath region by decreasing the plasma density. In this paper, using a plasma multi fluid model, the effect of ion polytropic coefficient γ _i on the plasma sheath structure have been examined. The numerical calculations of the basic equation of the model show that the polytropic coefficient strongly affects on the plasma sheath characteristics. The results show that by transition from an isothermal flow (γ _i =1) to an adiabatic flow (γ _i =3), the net current to the wall and the electric potential distribution increase and the sheath width decreases in a thermal plasma sheath.     

Atmospheric parameters and mass distribution of DA-white dwarfs

The method of effective temperatureT _eff and logg determination for DA-white dwarfs by KSW model atmospheres is analyzed. The existence of systematic errors in logg determination, leading to lower mass values forT _eff>15000 K, is demonstrated. With due account to logg corrections, masses for 355 DA-dwarfs were evaluated. The influence of the effects of observational selection on mass distribution has been considered. These effects are connected with the fact that such selection on effects favour discovery of white dwarfs of low masses. The distribution obtained is characterized by the average mass of ～0.75M _⊙ and the distribution width of ～0.20M _⊙.     

Dependence of the polar cap geometry on the IMF

The geometry of the open field line region in the polar region is computed for a variety of the interplanetary magnetic field (IMF) orientation. The open field line region can be identified as the area bounded by the auroral oval, namely the polar cap. The polar cap geometry varies considerably with the orientation of the IMF and magnitude, particularly when the IMF B_z component is positive and large. The corresponding exit points of the open field lines on the magnetopause are also examined. The results will be a useful guide in interpreting various upper atmospheric phenomena in the highest latitude region of the Earth and also in observing chemical releases outside the magnetopause.     

Source regions of low-latitude Pc1 pulsations and their relationship to the plasmapause

The polarization method of source location has been used on data from two low latitude stations (L = 1.9) to determine the exit region of structured Pc1 emissions from the magnetosphere into the ionosphere. Propagation directions in the ionospheric F₂ duct can be inferred from measurements of polarization parameters made at the low latitude recording station. Measurements on six events indicated an average source L value of 3.2, which represented the sources being on the average 1.0 ± 0.5 R_e inside the corresponding statistical plasmapause position.     

Computation of Jupiter interior models from gravitational inversion theory

A method for deriving a planetary interior model which exactly satisfies a set of N gravitational constraints is implemented. For Jupiter, recent spacecraft measurements provide the mass, radius at a standard pressure level, rotation law, multipole moments of the internal mass distribution, and constraints on the internal composition and temperature distribution. By appropriate iterations, interior models are found which exactly satisfy these constraints. The models are assumed to have constant chemical composition and constant specific entropy in the hydrogenic envelope. The derived pressure-density relation in the outer envelope depends sensitively on the observational uncertainty in the mass multipole moment J₄. Models are not forced to fit the more indirectly derived constraints, which are instead used as consistency checks. For a helium mass fraction in the envelope (Y) equal to 0.20, the inferred pressure at a mass density ≈ 0.2 g/cm³ is about a factor of 2 higher than would be indicated by experimental hydrogen shock compression data in the relevant pressure range of 10⁵ to 10⁶ bar. The inferred pressure distribution is in much better agreement with the shock data for a nominal Y = 0.30 ± 0.05. This value of Y is interpreted in terms of an enhancement in the envelope, by a factor of order 5 over solar abundance, of species primarily consisting of CH₄, NH₃, and possibly H₂O. The same method is applied to Saturn, but existing uncertainties in Saturn's gravitational parameters are still too large to allow useful conclusions about the composition of its envelope.     

Method of Modeling Atmospheric Optical Turbulence

The intensity and distribution of optical turbulence are important parameters to evaluate an observing station. A modeling method to obtain n atmospheric optical turbulence parameters, including the C2_n pro?le, coherent length, coherent time, seeing, isoplanatic angle, and scintillation index by using meteorological parameters are presented. The accomplishment of this method, the con?guration of the WRF model (Weather Research and Forecasting Model), and the veri?cation of calculated results are introduced. The reliability of the method is con?rmed preliminarily by comparing the calculated results with the DIMM (Differential Image Motion Monitor) measurements.     

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.     

Tidal Evolution of Low-mass Kepler Planets

The planets with a radius &lt; 4 R_⊕ observed by the Kepler mission exhibit a unique feature, and propose a challenge for current planetary formation models. The tidal effect between a planet and its host star plays an essential role in reconfiguring the final orbits of the short-period planets. In this work, based on various initial Rayleigh distributions of the orbital elements, the final semi-major axis distributions of the planets with a radius &lt; 4 R_⊕ after suffering tidal evolutions are investigated. Our simulations have qualitatively revealed some statistical properties: the semi-major axis and its peak value all increase with the increase of the initial semi-major axis and eccentricity. For the case that the initial mean semi-major axis is less than 0.1 au and the mean eccentricity is larger than 0.25, the results of numerical simulation are approximately consistent with the observation. In addition, the effects of other parameters, such as the tidal dissipation coefficient, stellar mass and planetary mass, etc., on the final semi-major axis distribution after tidal evolution are all relatively small. Based on the simulation results, we have tried to find some clues for the formation mechanism of low-mass planets. We speculate that these low-mass planets probably form in the far place of protoplanetary disk with a moderate eccentricity via the type I migration, and it is also possible to form in situ.     

On the spin distributions of ΛCDM haloes

We used merger trees realizations, predicted by the extended Press-Schechter theory, in order to study the growth of angular momentum of dark matter haloes. Our results showed that:

1. The spin parameter λ′ resulting from the above method, is an increasing function of the present day mass of the halo. The mean value of λ′ varies from 0.0343 to 0.0484 for haloes with present day masses in the range of 10⁹h^?1 M _⊙ to 10¹⁴h^?1 M _⊙.
2. The distribution of λ′ is close to a log-normal, but, as it is already found in the results of N-body simulations, the match is not satisfactory at the tails of the distribution. A new analytical formula that approximates the results much more satisfactorily is presented.
3. The distribution of the values of λ′ depends only weakly on the redshift.
4. The spin parameter of an halo depends on the number of recent major mergers. Specifically the spin parameter is an increasing function of this number.

     

Kinematics of the active region of the quasar 3C 345

The fine structure of the quasar 3C 345 in polarized emission at 7 mm and 2 cm has been investigated. The kinematics is shown to correspond to an anticentrifuge: the thermal plasma of the surrounding space accretes onto the disk, flows to the center, and is ejected in the form of a rotating bipolar outflow that carries away the excess angular momentum as it accumulates. The bipolar outflow consists of a high-velocity central jet surrounded by a low-velocity component. The low-velocity flows are the rotating hollow tubes ejected from the peripheral part of the disk with a diameter ～Ø₁ = 2.2 pc and from the region Ø₂ = 1 pc. The high-velocity jet with a diameter Ø₃ = 0.2 pc is ejected from the central part of the disk, while the remnant falls onto the forming central body. The ejection velocity of the high-velocity flow is v ? 0.06c. At a distance up to ～1 pc, the jet accelerates to an apparent velocity v ～ 8c. Further out, uniform motion is observed within ～2 pc following which deceleration occurs. The jet structure corresponding to a conical diverging helix with an increasing pitch is determined by gasdynamic instability. The counterjet structure is a mirror reflection of the nearby part of the jet. The brightness temperature of the fragment of the high-velocity flow at the exit from the counterjet nozzle is T _b ≈ (10¹²?10¹³) K. The disk inclined at an angle of 60° to the plane of the sky shadows the jet ejector region. Ring currents observed in the tangential directions as parallel chains of components are excited in the rotating flows. The magnetic fields of the rotating bipolar outflow and the disk are aligned and oriented along the rotation axis. The translational motions of the jet and counterjet are parallel and antiparallel to the magnetic field, which determines their acceleration or deceleration. The quasar core is surrounded by a thermal plasma. The sizes of the HII region reach ～30 pc. The electron density decreases with increasing distance from the center from N _e ≈ 10⁸ to ≈10⁵ cm^?3. The observed emission from the jet fragments at the exit from the nozzle is partially absorbed by the thermal plasma, is refracted with increasing distance—moves with an apparent superluminal velocity, and decelerates as it goes outside the HII region.     

Determination of the proton-to-helium ratio in cosmic rays at ultra-high energies from the tail of the Xmax distribution

We present a method to determine the proton-to-helium ratio in cosmic rays at ultra-high energies. It makes use of the exponential slope, Λ, of the tail of the X_max distribution measured by an air shower experiment. The method is quite robust with respect to uncertainties from modeling hadronic interactions and to systematic errors on X_max and energy, and to the possible presence of primary nuclei heavier than helium. Obtaining the proton-to-helium ratio with air shower experiments would be a remarkable achievement.To quantify the applicability of a particular mass-sensitive variable for mass composition analysis despite hadronic uncertainties we introduce as a metric the ‘analysis indicator’ and find an improved performance of the Λ method compared to other variables currently used in the literature. The fraction of events in the tail of the X_max distribution can provide additional information on the presence of nuclei heavier than helium in the primary beam.