Nonstationary Disk Research Articles

The effect of thermal winds on the outbursts evolution of LMXB systems

ABSTRACT Theoretical models of accretion discs and observational data indicate that the X-ray emission from the inner parts of an accretion disc can irradiate its outer regions and induce a thermal wind, which carries away the mass and angular momentum from the disc. Our aim is to investigate the influence of the thermal wind on the outburst light curves of black hole X-ray binary systems. We carry out numerical simulations of a non-stationary disc accretion with wind using upgraded open code freddi. We assume that the wind launches only from the ionized part of the disc and may turn off if the latter shrinks fast enough. Our estimates of the viscosity parameter α are shifted downward compared to a scenario without a wind. Generally, correction of α depends on the spectral hardness of central X-rays and the disc outer radius, but unlikely to exceed a factor of 10 in the case of a black hole low-mass X-ray binary (BH LMXB). We fit 2002 outburst of BH LMXB 4U 1543 − 47 taking into account the thermal wind. The mass-loss in the thermal wind is of order of the accretion rate on the central object at the peak of the outburst. New estimate of the viscosity parameter α for the accretion disc in this system is about two times lower than the previous one. Additionally, we calculate evolution of the number of hydrogen atoms towards 4U 1543 − 47 due to the thermal wind from the hot disc.

Investigation of the halo effect in the evolution of a nonstationary disk of spiral galaxies

Abstract In this article, we consider the problem of the evolution of the disk subsystem of galaxies, taking into account their halos. The global structure of the disk of galaxies strongly depends on the mass and shape of the halo. To this end, we have studied the evolution of nonradial oscillations of a nonstationary disk surrounded by a passive ellipsoidal halo with a uniform density. A system of equations for the evolution of a self-gravitating disk is obtained, taking into account the halo, in the form of matrix differential equations, and a method for its numerical analysis is developed to study the effect of the halo on disk formation. Numerical calculations were performed for various values of the system parameters, such as the initial perturbation, the circular speed of disk rotation, the ratio of the mass of the halo to the mass of the disk, and the time dependences of the major and minor semiaxes of the disk. The critical values of the system parameters are determined at which the halo stabilizes nonlinear and nonradial oscillations of the disk subsystem of galaxies at an early stage of their evolution.

Comparison of Instabilities of Annular Perturbations on the Background of Pulsating 2D and 3D Self-Gravitating Models

The problem of gravitational instability of the observed annular (ring-like) structural perturbation modes on the background of a nonlinearly pulsating spherical model based on the well-known equilibrium Camm ball is studied. Nonstationary analogues of dispersion relations for the perturbation modes under consideration within this model are obtained. Critical diagrams of the initial virial ratio versus the model rotation parameter are constructed for each case. A comparative analysis of the increments of gravitational instability of annular perturbation modes on the background of spherical and disk-shaped nonlinearly pulsating models is also performed. An analysis of the results shows that the annular perturbation modes are predominantly more unstable in a nonstationary disk than in a spherical nonequilibrium model, regardless of the rotation parameters and the initial virial ratio of the systems. The article is partly based on a report presented at the conference “Modern Stellar Astronomy-2022” held at the Caucasian Mountain Observatory of the Sternberg Astronomical Institute of Lomonosov Moscow State University, November 8–10, 2022.

Dependences of Characteristics of Bulges on the Mass of the Central Black Hole and Theoretical Aspects of Their Origin

To study the influence of the central black hole on the formation of the bulge of spiral galaxies, we analyzed the relationship between the masses of supermassive black holes (SMBHs) and the parameters of their bulges. Unlike other authors, we consider only spiral galaxies. In this paper, we present empirical formulas derived from observations of 54 spiral galaxies, establishing connections between the mass of the central black hole (MBH), the bulge stellar mass (Mbulge), and the velocity dispersion (σ) of stars in it. A non-linear non-stationary disk model with an anisotropic velocity diagram is constructed. Within this model, the instabilities of individual perturbation modes are studied. The increments of instability are calculated depending on the physical parameters of the model. These values are compared across three perturbation modes. The paper is partly based on the report presented at the conference “Modern Stellar Astronomy-2022,” held at the Caucasian Mountain Observatory of the Sternberg Astronomical Institute of Lomonosov Moscow State University, on November 8–10, 2022.

Nonlinear cosmogony of the spiral galaxy bulges

Abstract In this paper, we develop an early idea of one of the authors (Nuritdinov 1992a,b), who was the first to propose the mechanism of instability of the warp perturbation mode on the background of a nonstationary disk. For this aim, we have studied a model of a nonlinearly non-stationary self-gravitating disk with an anisotropic velocity diagram. The model has a composite nature, or rather, it is a superposition of isotropic and anisotropic states of the disk. In the general case, it is obtained a nonstationary analogue of the dispersion equation of this composite model. We have also investigated the behavior of the domed perturbation mode, the instability of which leads to the formation of a classical bulge in the central region of the disk. In addition, we considered the critical diagrams of the dependence of the virial ratio on the rotation rate of the system for various values of the superposition parameter and the corresponding diagrams for the increments of instability.

Instabilities in a nonstationary model of self-gravitating disks. IV. Generalization of the models and comparison of results

A generalized phase model of a radially nonstationary disk with an anisotropic velocity diagram is constructed which has an exact nonlinear nonstationarity law and is a nonequilibrium extension of the equilibrium disk of Bisnovatyi-Kogan and Zel’dovich. For a comparative analysis of the instabilities of the generalized model with respect to horizontal and vertical oscillatory modes, nonstationary analogs of the dispersion relations are obtained for these modes. An analysis of these results shows that the parameters characterizing the difference and degree of anisotropy of nonlinearly nonstationary models have opposite effects on the horizontal and vertical oscillations of a disk. We also compare the horizontal and vertical oscillatory modes against the background of nonstationary models with isotropic and anisotropic velocity diagrams. For small and moderate disk rotation parameters, it is found that the vertical modes dominate the horizontal modes, while the opposite picture is seen on approaching the maximum rotation.

Grain charging in protoplanetary discs

Recent work identified a growth barrier for dust coagulation that originates in the electric repulsion between colliding particles. Depending on its charge state, dust material may have the potential to control key processes towards planet formation such as MHD (magnetohydrodynamic) turbulence and grain growth which are coupled in a two-way process. We quantify the grain charging at different stages of disc evolution and differentiate between two very extreme cases: compact spherical grains and aggregates with fractal dimension D_f = 2. Applying a simple chemical network that accounts for collisional charging of grains, we provide a semi-analytical solution. This allowed us to calculate the equilibrium population of grain charges and the ionisation fraction efficiently. The grain charging was evaluated for different dynamical environments ranging from static to non-stationary disc configurations. The results show that the adsorption/desorption of neutral gas-phase heavy metals, such as magnesium, effects the charging state of grains. The greater the difference between the thermal velocities of the metal and the dominant molecular ion, the greater the change in the mean grain charge. Agglomerates have more negative excess charge on average than compact spherical particles of the same mass. The rise in the mean grain charge is proportional to N**(1/6) in the ion-dust limit. We find that grain charging in a non-stationary disc environment is expected to lead to similar results. The results indicate that the dust growth and settling in regions where the dust growth is limited by the so-called "electro-static barrier" do not prevent the dust material from remaining the dominant charge carrier.

Instabilities in a nonstationary model of self-gravitating disks. III. The phenomenon of lopsidedness and a comparison of perturbation modes

This is an examination of the gravitational instability of the major large-scale perturbation modes for a fixed value of the azimuthal wave number m = 1 in nonlinearly nonstationary disk models with isotropic and anisotropic velocity diagrams for the purpose of explaining the displacement of the nucleus away from the geometric center (lopsidedness) in spiral galaxies. Nonstationary analogs of the dispersion relations for these perturbation modes are obtained. Critical diagrams of the initial virial ratio are constructed from the rotation parameters for the models in each case. A comparative analysis is made of the instability growth rates for the major horizontal perturbation modes in terms of two models, and it is found that, on the average, the instability growth rate for the m = 1 mode with a radial wave number N = 3 almost always has a clear advantage relative to the other modes. An analysis of these results shows that if the initial total kinetic energy in an isotropic model is no more than 12.4% of the initial potential energy, then, regardless of the value of the rotation parameter Ω, an instability of the radial motions always occurs and causes the nucleus to shift away from the geometrical center. This instability is aperiodic when Ω = 0 and is oscillatory when Ω ≠ 0 . For the anisotropic model, this kind of structure involving the nucleus develops when the initial total kinetic energy in the model is no more than 30.6% of the initial potential energy.

Transient Optical Emission from a Nonstationary Accretion Disk: A Model for Optical Afterglow of Gamma Ray Bursts

We consider the time-dependent behavior of nonstationary accretion disk which is formed by the capture and disruption of a main-sequence star around a massive black hole. If an instability is developed in the inner edge of the nonstationary disk and produces a strong magnetic field, a large amount of the black hole rotational energy can be extracted via the Blandford-Znajek process, which results in a Gamma-Ray Burst (GRB) with a typical duration ∼ 10–102 s. Other parameters related to a typical GRB including burst energy, rise time of the burst, number of sub-burst etc are also estimated. The vertical structure and thermal stability properties of the disk are investigated in detail. In the early stage of forming transient accretion disk, the material supplied by the tidally disrupted star is clumped in the relatively cool disk. This eventually leads to a thermal instability, which results in an increase of the viscosity of the disk. As the instability propagates across the disk, the stability of a time-dependent disk and variability of the mass-deposition rate provide a possible explanation for transient optical emission. We speculate that this transient optical emission from a nonstationary accretion disk may relate to the behavior of GRB optical afterglow, and the transient optical afterglow can be reproduced if one takes into account the effect of an evolving viscous parameter, α.

Microlensing and the structure of active galactic nucleus accretion disks

Rapid variability has been reported in two of the four gravitationally lensed images of Q2237 + 0305, and this is attributed to microlensing caused by the intervening stars. The associated constraints on the source size and properties are studied and compared with a variety of stationary accretion disk models. The reported microlensing variation in Q2237 + 0305 requires the disk size to be over 3 times smaller than a blackbody disk of similar luminosity, implying that the optical emission is either nonthermal or optically tin. An exploration of nonstationary disk models including orbiting, transient hot spots leads to a similar conclusion. Implications for models of active galactic nucleus optical continua are briefly discussed.

General method describing self-similar regimes of nonstationary disc accretion. A possibility of self-organization

The hydrodinamic equations are used as a method of modelling nonstationary accretion discs. The obtained model equations are nonlinear and may be resolved with the help of numerical methods or by theoretical group methods. This work is based on model equation obtained under the assumption that viscosity and opacity laws are power functions of the local accretion disc parameters. The obtained self-similar solution provides a possibility of finding self-similar solutions from first and second gandre in dependence on the problem formulation. It is shown that if the accretiondisc mass varies with time resulting from secondary component flux variation, then the viscosity has apparent time dependence. The shape of this dependence in function of varying external flux is given. Using this result a criterion of self-organization occurence of quasi stationary toroidal type is given for the disc.

Self-similar processes in accretion discs

When considering transient X-ray sources and some types of cataclismic variables various kinds of problems may be resolved for nonstationary disc accretion. The evolution of viscous duscs is analytically studied within the frames of linear model equations [1]. The general nonlinear problem is condsidered only numerically [2,3,4]. This work illustrates the evolution of the disc as subdivided into several natural stages, each one of which is described by a self-similar solution of the initial equation. These solutions representing asimptotic of the real problems provide very important information, which does not follow nessesarily fromnumerical computations [5,6,7,8,9].

Non-stationary disc accretion

Based on large amount of observational data in the field of high energy astrophysics, and namely X- and Gamma-ray data, it is considered that most of the discrete sources are non-stationary. One of the mechanisms describing this phenomenon is the non-stationary disc accretion, of geometrically thin disc. Examples are given in proof on modelling of phenomena on the basis of non-stationary accretion disc under the assumption that a generalized formula of viscosity is used. It is shown that when the model describing the bursts is used we obtain in result of the substance flux variation a time dependant variation of the ‘α’ coefficient. We consider here the flux entering the accreation disc.