Mass spectrum of giant molecular clouds in a coagulation model

Solutions of Smoluchovski’ equation, describing merging processes in a system of giant molecular clouds, are investigated in detail. Both the case of a constant spatial gas density in the clouds and the case of a constant radial gas density are considered. It is shown that the solution of the coagulation equation is not expressed by a power law that is the same for the entire mass range under consideration. It is also demonstrated that the form of the solution depends on the width of the mass range of the clouds. A comparison with observations shows that the Oort model and the coagulation mechanism can describe the observed cloud mass spectrum quite adequately. Ways of improving the Oort model are suggested.     

Stochastic coalescence model for terrestrial planetary accretion

A nonequilibrium stochastic coalescence model for terrestrial planetary accretion is developed by using an approximation to the Safronov-Golovin solution for the scalar transport equation with linear kernel. According to this model, formation of comparatively massive objects occurs quite rapidly during the early stages of accretive evolution in a given terrestrial planetesimal population, while during late growth stages, an increasingly substantial fraction of total population mass becomes incorporated into progressively fewer, relatively very large bodies. The model also implies that the (conservative) growth rate of the population's largest member varies directly as its mass, and further suggests that this growth rate may not decline significantly until very nearly final planetary mass is attained.     

Compact models with regular charge distributions

We model a compact relativistic body with anisotropic pressures in the presence of an electric field. The equation of state is barotropic, with a linear relationship between the radial pressure and the energy density. Simple exact models of the Einstein–Maxwell equations are generated. A graphical analysis indicates that the matter and electromagnetic variables are well behaved. In particular, the proper charge density is regular for certain parameter values at the stellar center unlike earlier anisotropic models in the presence of charge. We show that the electric field affects the mass of stellar objects and the observed mass for a particular binary pulsar is regained. Our models contain previous results of anisotropic charged matter with a linear equation of state for special parameter values.     

The maximum mass of ideal white dwarfs

The theory of thepolytropic gas spheres in conjunction with the equation of state of arelativislically degenerate electrongas leads to aunique value for the mass of a star built on this model. This mass (=_0.9I⊙) is interpreted as representing the upper limit to the mass of an ideal white dwarf.     

The Effect of Radiative Efficiency on the Growth of the Black Hole Mass

The effect of variation of radiative efficiency on the growth of the black hole mass is discussed. In the process of accretion, the black hole's angular momentum varies, resulting in a variation of the radiative efficiency, and the growth of the black hole mass is thereby affected. For the exponential growth model of back holes and taking into account the effect of a varying radiative efficiency, the equation for the growth of the black hole mass is solved numerically. Compared to the model that assumes a constant radiative efficiency, the result indicates that variation of radiative efficiency has a marked, retarding effect on the growth of the black hole mass. This model can explain quantitatively some recent observational results.     

Relativistic gravitational collapse of a cool white dwarf with allowance for the neutronization kinetics

We consider and numerically solve the problem of the relativistic gravitational collapse of a spherically symmetric cool nonrotating white dwarf with allowance for the neutronization kinetics. We propose a model equation of state and analyze the neutronization kinetics under simplifying assumptions. A comprehensive mathematical model is constructed for the phenomenon. The system of equations is integrated numerically. The gravitational collapse of a white dwarf that lost its stability is shown to lead to the envelope ejection and to the final state of a hot static neutron star. For comparison, we solve the problem with an equilibrium equation of state. We show that in this case, the entire mass ultimately goes under the gravitational radius to form a black hole.     

Electrostatic double layers and plasma evacuation in current-driven systems

After examining some of the background work relevant to double layers, the role constant current driven systems might play in the double layer formation is examined from two perspectives. First, a fluids analysis is considered via the method of characteristics. A density perturbation growth is predicted. Two model deficiencies, zero electron mass and lack of particle kinematics, suggest an improvement in the model via the Vlasov equation. This second model using the Vlasov equation still maintains a non-quasineutral posture. In addition to predicting the expected two-stream instability, the model also predicts a double layer-type electric field.     

辐射效率对黑洞质量增长的影响

考虑了在黑洞质量增长过程中,辐射效率的变化对黑洞质量增长的影响．随着吸积的进行,黑洞的角动量会发生变化,辐射效率也会随之发生变化,从而影响了质量增长．对于黑洞的指数增长模型,给出了考虑辐射效率对黑洞质量增长影响下的黑洞质量增长方程,用数值方法进行求解,并得到了黑洞质量随时间变化的曲线．与假定辐射效率为常数的模型对比,结果表明辐射效率的变化对黑洞质量的增长有较明显的影响,使黑洞的增长延迟．这个模型可以定量地说明最近的观测结果．     

On the 'coarse-grained' evolution of collisionless stellar systems

We have suggested in a previous article that the coarse-grained evolution of a collisionless stellar system could be viewed as a diffusion process in velocity space compensated by an appropriate friction. Using a quasi-linear theory, we calculate the diffusion coefficient associated with this evolution. This provides a new self-consistent relaxation equation for f , the locally averaged distribution function. This equation bears some resemblance to the conventional Fokker–Planck equation of collisional systems but the friction term is non-linear in f (accounting for degeneracy effects) and the relaxation time is much smaller (in agreement with the concept of 'violent relaxation'). Under the condition that the diffusion current vanishes identically at equilibrium, we recover Lynden-Bell's distribution function; but if we allow stars to escape from the system at a constant rate, we can derive a truncated model which coincides with Lynden-Bell's solution in the core but provides a depletion of high-energy stars in the halo. This distribution function has a finite mass and is the generalization of the Michie–King model to the case of (possibly degenerate) collisionless stellar systems.     

Mira变星拱星包层的温度结构

我们研究了Mira变星拱星包层的温度结构。假设Mira变星拱星包层由气体和尘埃颗粒两种成分组成,气体为理想气体,并有稳定的和球对称的径向向外流动;我们研究了拱星包层气体的加热机制和致冷原因,根据拱星包层气体的质量、动量和能量守恒方程及多方膨胀过程方程,通过计算得到了拱星包层气体温度所满足的温度方程。这个温度方程对于Mira变星拱星包层有普遍意义。对于典型的Mira变星我们进行了数值计算,得到了温度曲线。与观测得到的温度曲线比较表明,理论模型与观测事实相一致。     

视超光速运动的相对论超光速模型

从相对论出发，在视超光速源质心相对于观测者静止的条件下，推导出两个向相反方向运动的视超光速子源之间的视速度方程，这一方程包含了相对论射束模型的表现横向速度公式，且对高、低速不同条件均为适用。     

Effects of non-Newtonian gravity on the properties of strange stars

The properties of strange star matter are studied in the equivparticle model with inclusion of non-Newtonian gravity. It is found that the inclusion of non-Newtonian gravity makes the equation of state stiffer if Witten's conjecture is true. Correspondingly, the maximum mass of strange stars becomes as large as two times the solar mass, and the maximum radius also becomes bigger. The coupling to boson mass ratio has been constrained within the stability range of strange quark matter.     

Out-of-plane librations of spinning tethered satellite systems

We analyze the out-of-plane librations of a tethered satellite system that is nominally rotating in the orbit plane. To isolate the librational dynamics, the system is modeled as two point masses connected by a rigid rod with the system mass center constrained to an unperturbed circular orbit. For small out-of-plane librations, the in-plane motion is unaffected by the out-of-plane librations and a solution for the in-plane motion is determined in terms of Jacobi elliptic functions. This solution is used in the linearized equation for the out-of-plane librations, resulting in a Hill’s equation. Floquet theory is used to analyze the Hill’s equation, and we show that the out-of-plane librations are unstable for certain ranges of in-plane spin rate. For relatively high in-plane spin rates, the out-of-plane librations are stable, and the Hill’s equation can be approximated by a Mathieu’s equation. Approximate solutions to the Mathieu’s equation are determined, and we analyze the dominant characteristics of the out-of-plane librations for high in-plane spin rates. The results obtained from the analysis of the linearized equations of motion are compared to numerical simulations of the nonlinear equations of motion, as well as numerical simulations of a more realistic system model that accounts for tether flexibility. The instabilities discovered from the linear analysis are present in both the nonlinear system and the more realistic system model. The approximate solutions for the out-of-plane librations compare well to the nonlinear system for relatively high in-plane rotation rates, and also capture the significant qualitative behavior of the flexible system.     

Wave disturbances near the temperature jump in the transition region of the solar atmosphere

We theoretically analyzed the properties of surface waves near the temperature jump in the solar atmosphere whose dispersion relation is identical in form to the equation for waves on deep water. We found an exact solution to the model equation for the vertical velocity of the medium in such a wave. Based on the derived space-time dependence of the vertical velocity of the medium, we quantitatively explained one of the events recorded in the SOI/MDI experiment onboard the SOHO spacecraft that accompanied coronal mass ejection.     

Pseudo-Newtonian models for the equilibrium structures of rotating relativistic stars

We obtain equilibrium solutions for rotating compact stars, including special relativistic effects. The gravity is assumed to be Newtonian, but we use the active mass density, which takes into account all energies such as the motion of the fluid, internal energy and pressure energy in addition to the rest-mass energy, in computing the gravitational potential using Poisson's equation. Such a treatment could be applicable to neutron stars with relativistic motions or a relativistic equation of state. We applied Hachisu's self-consistent field (SCF) method to find spheroidal as well as toroidal sequences of equilibrium solutions. Our solutions show better agreement with general relativistic solutions than the Newtonian relativistic hydrodynamic approach, which does not take into account the active mass. Physical quantities such as the peak density and equatorial radii in our solutions agree with the general relativistic ones to within 5 per cent. Therefore our approach can be used as a simple alternative to the fully relativistic one when a large number of model calculations is necessary, as it requires much fewer computational resources.     

Moment of inertia of a neutron star. II. Relativistic corrections

In part I we suggested an approximate equation to determine the contribution of relativistic effects to the moment of inertia of a superdense star. In the present paper it is tested on model neutron stars with nine different variants of the equation of state of superdense matter. It is established that the approximation error does not exceed 5% for stable configurations. A more accurate version of the Ravenhall—Pethick equation [D. G. Ravenhall and C. J. Pethick, Astrophys. J., 424, 846 (1994)] for the moment of inertia as a function of the mass and radius of a neutron star is derived. Translated from Astrofizika, Vol. 40, No. 4, pp. 507–516, October–December, 1997.     

Dynamical evolution of two-component star clusters

The dynamical evolution of two-component star clusters, each of which is enclosed within a perfectly reflecting sphere, is investigated by numerically solving moment equations derived from the Boltzmann equation. One of the two adopted model clusters evolves, starting from a state of no mass segregation, toward an equilibrium state at a quite slow rate. The other one evolves away from an equilibrium state and its central density increases without limit. The different evolutionary behaviors of the two model clusters are explained by the fact that there exists no equilibrium state for such clusters if the total energy is less than a certain critical value. The critical value increases with increasing total mass fraction of the heavier stars. This is qualitatively the same as Spitzer's theorem (1969) expressed in another way.     

Suprathermal particle distributions in space physics: Kappa distributions and entropy

The energization of a charged test-particle of mass m in contact with a large ensemble of charged particles of mass M at equilibrium is studied with the Fokker-Planck equation for Coulomb collisions and a quasi-linear diffusion operator for wave-particle interactions. The features of the nonequilibrium steady state velocity distribution of the test-particle system is studied as a function of the mass ratio m/M, and the relative strengths of the wave-particle interactions and Coulomb collisions. It is shown that the steady distribution function is not necessarily a Kappa distribution. The temperature of heavy minor ions given by the model is shown to vary linearly with the mass ratio as observed in the solar wind. The time evolution of the distribution function with and without the energization by wave-particle interactions is calculated and it is demonstrated that the Kullback relative entropy rather than the Tsallis nonextensive entropy rationalizes the results obtained.     

Mass accretion by the nuclei of disk galaxies,II

Repeated explosions in the nuclei of galaxies are now accepted as observationally established phenomena. Each explosion leads to the ejection of gas from the central region of a galaxy with velocities depending on the strength of the explosive event. In the process the nucleus temporarily becomes gas-deficient. It is suggested that the mass los is replenished by the accretion of the mass which is shed by those evolved stars in the galactic bulge that possess relatively low rotational velocities. The gas to be accreted is assumed to be magnetized. In the present model, the accretion rate has been assumed to be a function of both radial distance and time. The cross-radial equation of motion has been solved to derive the expression for the rotational velocity which is found to bealmost linear with the radial distance from the centre. The radial equation has been solved to calculate the time-scale over which the nucleus accumulates sufficient mass to undergo instability and suffer explosion. The calculated time-scale range from few multiples of 10⁷ to a few multiples of 10⁸ yr. This range agrees very well with that as has been suggested on the basis of observation in the case of our own Galaxy.     

Constraining cold dark matter halo merger rates using the coagulation equations

We place additional constraints on the three parameters of the dark matter halo merger rate function recently proposed by Parkinson, Cole & Helly by utilizing Smoluchowski's coagulation equation, which must be obeyed by any binary merging process which conserves mass. We find that the constraints from Smoluchowski's equation are degenerate, limiting to a thin plane in the three-dimensional parameter space. This constraint is consistent with those obtained from fitting to N -body measures of progenitor mass functions, and provides a better match to the evolution of the overall dark matter halo mass function, particularly for the most massive haloes. We demonstrate that the proposed merger rate function does not permit an exact solution of Smoluchowski's equation and, therefore, the choice of parameters must reflect a compromise between fitting various parts of the mass function. The techniques described herein are applicable to more general merger rate functions, which may permit a more accurate solution of Smoluchowski's equation. The current merger rate solutions are most probably sufficiently accurate for the vast majority of applications.