Effect Of Self-gravity Research Articles

Probing the role of self-gravity in clouds impacted by AGN-driven winds

ABSTRACT The impact of winds and jet-inflated bubbles driven by active galactic nuclei (AGN) are believed to significantly affect the host galaxy’s interstellar medium (ISM) and regulate star formation. To explore this scenario, we perform a suite of hydrodynamic simulations to model the interaction between turbulent star-forming clouds and highly pressurized AGN-driven outflows, focusing on the effects of self-gravity. Our results demonstrate that the cloudlets fragmented by the wind can become gravitationally bound, significantly increasing their survival time. While external pressurization leads to a global collapse of the clouds in cases of weaker winds ($10^{42}\!-\!10^{43}~{\rm erg\, s^{-1}}$), higher power winds ($10^{44}\!-\!10^{45}~{\rm erg\, s^{-1}}$) disperse the gas and cause localized collapse of the cloudlets. We also demonstrate that a kinetic energy-dominated wind is more efficient in accelerating and dispersing the gas than a thermal wind with the same power. The interaction can give rise to multiphase outflows with velocities ranging from a few 100 to several 1000 ${\rm km\, s^{-1}}$. The mass outflow rates are tightly correlated with the wind power, which we explain by an ablation-based mass-loss model. Moreover, the velocity dispersion and the virial parameter of the cloud material can increase by up to one order of magnitude through the effect of the wind. Even though the wind can suppress or quench star formation for about 1 Myr during the initial interaction, a substantial number of gravitationally bound dense cloudlets manage to shield themselves from the wind’s influence and subsequently undergo rapid gravitational collapse, leading to an enhanced star formation rate.

Self-gravity and Bekenstein-Hawking entropy

We study the effect of self-gravity on entropy by directly solving the 4D semi-classical Einstein equation. In particular, we focus on whether the Bekenstein-Hawking formula holds when self-gravity is extremely strong. As an example, we consider a simple spherically symmetric static configuration consisting of many quanta and construct a self-consistent non-perturbative solution for ħ in which the entropy exactly follows the area law for many local degrees of freedom of any kind. This can be a candidate for black holes in quantum theory. It represents a compact dense configuration with near-Planckian curvatures, and the interior typically behaves like a local thermal state due to particle creation inside. Here, the information content is stored in the interior bulk, and the self-gravity plays an essential role in changing the entropy from the volume law to the area law. We finally discuss implications to black holes in quantum gravity and a speculative view of entropy as a gravitational charge.

Viscous overstability in dense planetary rings – effect of vertical motions and dense packing

ABSTRACT We investigate the linear axisymmetric viscous overstability in dense planetary rings with typical values of the dynamical optical depth τ ≳ 0.5. We develop a granular flow model which accounts for the particulate nature of a planetary ring subjected to dissipative particle collisions. The model captures the dynamical evolution of the disc’s vertical thickness, temperature, and effects related to a finite volume filling factor of the ring fluid. We compute equilibrium states of self-gravitating and non-self-gravitating rings, which compare well with existing results from kinetic models and N-body simulations. Subsequently, we conduct a linear stability analysis of our model. We briefly discuss the different linear eigenmodes of the system and compare with existing literature by applying corresponding limiting approximations. We then focus on the viscous overstability, analysing the effect of temperature variations, radial and vertical self-gravity, and for the first time the effects of vertical motions on the instability. In addition, we perform local N-body simulations incorporating radial and vertical self-gravity. Critical values for the optical depth and the filling factor for the onset of instability resulting from our N-body simulations compare well with our model predictions under the neglect of radial self-gravity. When radial self-gravity is included, agreement with N-body simulations can be achieved by adopting enhanced values of the bulk viscous stress.

An improved dynamical Poisson equation solver for self-gravity

ABSTRACT Since self-gravity is crucial in the structure formation of the Universe, many hydrodynamics simulations with the effect of self-gravity have been conducted. The multigrid method is widely used as a solver for the Poisson equation of the self-gravity; however, the parallelization efficiency of the multigrid method becomes worse when we use a massively parallel computer, and it becomes inefficient with more than 104 cores, even for highly tuned codes. To perform large-scale parallel simulations (>104 cores), developing a new gravity solver with good parallelization efficiency is beneficial. In this article, we develop a new self-gravity solver using the telegraph equation with a damping coefficient, κ. Parallelization is much easier than the case of the elliptic Poisson equation since the telegraph equation is a hyperbolic partial differential equation. We analyse convergence tests of our telegraph equations solver and determine that the best non-dimensional damping coefficient of the telegraph equations is $\tilde{\kappa } \simeq 2.5$. We also show that our method can maintain high parallelization efficiency even for massively parallel computations due to the hyperbolic nature of the telegraphic equation by weak-scaling tests. If the time-step of the calculation is determined by heating/cooling or chemical reactions, rather than the Courant–Friedrichs–Lewy (CFL) condition, our method may provide the method for calculating self-gravity faster than other previously known methods such as the fast Fourier transform and multigrid iteration solvers because gravitational phase velocity determined by the CFL condition using these time-scales is much larger than the fluid velocity plus sound speed.

Self-gravitating collapsing star and black hole spin-up in long gamma ray bursts

Context. Long gamma ray bursts (GRBs) originate from the collapse of massive, rotating stars. Some of the GRBs exhibit much stronger variability patterns in the prompt GRB emission than the usual stochastic variations. We discuss the mechanisms able to account for this effect. Aims We aim to model the process of stellar collapse in the scenario of a self-gravitating collapsing star. We account for the changes in Kerr metric induced by the growth of the black hole; accretion of angular momentum; and the self-gravity effect due to a large mass of the collapsing stellar core falling onto black hole in a very short time. We also investigate the existence of accretion shocks in the collapsar, and the role of magnetic field in their propagation. Methods. We compute the time-dependent axially symmetric general relativistic magnetohydrodynamic model of a collapsing stellar core in the dynamical Kerr metric. We explore the influence of self-gravity in such a star, where the newly formed black hole is increasing the mass and changing its spin. The Kerr metric evolves according to the mass and angular momentum changes during the collapse. We parameterize the rotation inside the star, and account for the presence of large-scale poloidal magnetic field. For the set of the global parameters, such as the initial black hole spin and the initial content of specific angular momentum in the stellar envelope, we determine the evolution of black hole parameters (mass and spin) and quantify the strength of the gravitational instability. We then estimate the variability timescales and amplitudes. Results. We find that the role of the gravitational instability measured by the value of the Toomre parameter is relatively important in the innermost regions of the collapsing star. The character of accretion rate variability strongly depends on the assumption of self-gravity in the model, and is also affected by the magnetic field. Additional factors are initial spin and rotation of the stellar core. We find that for subcritical rotation of the precollapsed star, a centrifugally supported mini-disc is present at the equatorial plane, and it may be subject to fragmentation due to self-gravitating instability. We also find that self-gravity may play a role in the angular momentum transport and that it generally lowers the final mass and spin of the black hole, while the accretion-rate variability amplitude is much larger in self-gravitating objects. The effect of magnetic field is rather weak, while it seems to decrease the strength of accretion shocks. The magnetisation affects the global properties of the flow in a non-linear way, and is manifested mostly in models with moderate initial black hole spins but supercritical rotation of the collapsing star. Conclusions. Our computations confirm that gravitational instability can account for flaring activity in GRBs and the variations in their prompt emission. Rapid variability detected in the brightest GRBs (most likely powered by rapidly spinning black holes) is consistent with the self-gravitating collapsar model, where the transonic shocks are formed. The effect should be weakened by magnetic field.

Low frequency twisted waves in a self-gravitating nonextensive complex plasma

Abstract The effects of dust–dust self-gravitational force and nonextensive characteristics of plasma species on the low frequency twisted waves owing to the helical wave structure in complex (dusty) plasmas are analyzed. The electrons and ions of the plasma are modelled by nonextensive q-distribution function while massive dust particles are Maxwellian distributed. The self-gravitational effects are incorporated in the Vlasov equation of kinetic theory where perturbed distribution function, electrostatic and gravitational potentials are expressed with Laguerre–Gauss functions. The governing equations of kinetic theory are solved together under paraxial approximations. The dispersion relations and damping rates of twisted dust-acoustic waves (TDAWs) are obtained for two situations; (a) super-extensivity (q < 1) and (b) sub-extensivity (q > 1). The effects of self-gravity, nonextensivity and twist parameter significantly modified the basic features of dust-acoustic waves. This study contributes to our understanding of the complex dynamics of TDAWs in interstellar dust clouds, considering the interplay of self-gravity, nonextensivity, and helical phase structures. The obtained theoretical and numerical results provide valuable insights into the behavior of these waves and offer a foundation for further investigations in this field. However, understanding of the topic can be enhanced through a combination of theoretical models, numerical simulations and observational data.

Zonal Winds of Uranus and Neptune: Gravitational Harmonics, Dynamic Self-gravity, Shape, and Rotation

Uranus and Neptune exhibit fast surface zonal winds that can reach up to a few hundred meters per second. Previous studies on zonal gravitational harmonics and ohmic dissipation constraints suggest that the wind speeds diminish rapidly in relatively shallow depths within the planets. Through a case-by-case comparison between the missing dynamical gravitational harmonic from structure models, and with that expected from fluid perturbations, we put constraints on zonal wind decay in Uranus and Neptune. To this end, we generate polytropic empirical structure models of Uranus and Neptune using fourth-order theory of figures that leave hydrostatic J 4 as an open parameter. Allotting the missing dynamical contribution to density perturbations caused by zonal winds (and their dynamic self-gravity), we find that the maximum scale height of zonal winds are ∼2%–3% of the planetary radii for both planets. Allowing the models to have J 2 solutions in the ±5 × 10−6 range around the observed value has similar implications. The effect of self-gravity on is roughly a factor of ten lower than that of zonal winds, as expected. The decay scale heights are virtually insensitive to the proposed modifications to the bulk rotation periods of Uranus and Neptune in the literature. Additionally, we find that the dynamical density perturbations due to zonal winds have a measurable impact on the shape of the planet, and could potentially be used to infer wind decay and bulk rotation period via future observations.

Modified geodesic equations of motion for compact bodies in alternative theories gravity

We derive exact, modified geodesic equations for a system of non-spinning, self-gravitating interacting bodies in a class of alternative theories of gravity to general relativity. We use a prescription proposed by Eardley for incorporating the effects of self-gravity within gravitationally bound bodies, in which their masses may depend on invariant quantities constructed from the auxiliary scalar, vector or tensor fields introduced by such theories, evaluated in the vicinity of each body. The forms of the equations are independent of the field equations of the chosen theory. In the case where the masses are strictly constant, the equations reduce to the conventional geodesic equations of general relativity. These equations may be useful tools for deriving equations of motion for compact bodies to high post-Newtonian orders in alternative theories of gravity.

Testing gravitational self-interaction via matter-wave interferometry

The Schrodinger-Newton equation has frequently been studied as a nonlinear modification of the Schrodinger equation incorporating gravitational self-interaction. However, there is no evidence yet as to whether nature actually behaves this way. This work investigates a possible way to experimentally test gravitational self-interaction. The effect of self-gravity on interference of massive particles is studied by numerically solving the Schrodinger-Newton equation for a particle passing through a double-slit. The results show that the presence of gravitational self-interaction has an effect on the fringe width of the interference that can be tested in matter-wave interferometry experiments. Notably, this approach can distinguish between gravitational self-interaction and environment induced decoherence, as the latter does not affect the fringe width. This result will also provide a way to test if gravity requires to be quantized on the scale of ordinary quantum mechanics.

Non-resonant relaxation of anisotropic globular clusters

ABSTRACT Globular clusters are dense stellar systems whose core slowly contracts under the effect of self-gravity. The rate of this process was recently found to be directly linked to the initial amount of velocity anisotropy: tangentially anisotropic clusters contract faster than radially anisotropic ones. Furthermore, initially anisotropic clusters are found to generically tend towards more isotropic distributions during the onset of contraction. Chandrasekhar’s ‘non-resonant’ (NR) theory of diffusion describes this relaxation as being driven by a sequence of local two-body deflections along each star’s orbit. We explicitly tailor this NR prediction to anisotropic clusters, and compare it with N-body realizations of Plummer spheres with varying degrees of anisotropy. The NR theory is shown to recover remarkably well the detailed shape of the orbital diffusion and the associated initial isotropization, up to a global multiplicative prefactor which increases with anisotropy. Strikingly, a simple effective isotropic prescription provides almost as good a fit, as long as the cluster’s anisotropy is not too strong. For these more extreme clusters, accounting for long-range resonant relaxation may be necessary to capture these clusters’ long-term evolution.

The velocity statistics of turbulent clouds in the presence of gravity, magnetic fields, radiation, and outflow feedback

ABSTRACTThe interaction of turbulence, magnetic fields, self-gravity, and stellar feedback within molecular clouds is crucial for understanding star formation. We study the effects of self-gravity and outflow feedback on the properties of the turbulent velocity via the SF over length-scales from ∼0.01 to 2 pc. We analyse a series of three-dimensional, magnetohydrodynamical (MHD) simulations of star cluster formation. We find outflow feedback can change the scaling of velocity fluctuations but still roughly being in between Kolmogorov and Burgers turbulence. We observe that self-gravity and protostellar outflows increase the velocity fluctuations over all length-scales. Outflows can amplify the velocity fluctuations by up to a factor of ∼7 on scales ∼0.01–0.2 pc and drive turbulence up to a scale of ∼1 pc. The amplified velocity fluctuations provide more support against gravity and enhance fragmentation on small scales. The self-gravity’s effect is more significant on smaller dense clumps and it increases the fraction of the compressive velocity component up to a scale of ∼0.2 pc. However, outflow feedback drives both solenoidal and compressive modes, but it induces a higher fraction of solenoidal modes relative to compressive modes. Thus, with outflows, the dense core ends up with a slightly higher fraction of solenoidal modes. We find that the compressible fraction is fairly constant with about 1/3 on scales ∼0.1–0.2 pc. The combined effect of enhanced velocity dispersion and reduced compressive fraction contributes to a reduction in the star formation rate.

Effects of Self-gravity on Mass-loss of the Post-impact Super-Earths

Kepler’s observations show most of the exoplanets are super-Earths. The formation of a super-Earth is generally related to the atmospheric mass loss that is crucial in the planetary structure and evolution. The shock driven by the giant impact will heat the planet, resulting in the atmosphere escape. We focus on whether self-gravity changes the efficiency of mass loss. Without self-gravity, if the impactor mass is comparable to the envelope mass, there is a significant mass-loss. The radiative-convective boundary will shift inward by self-gravity. As the temperature and envelope mass increase, the situation becomes more prominent, resulting in a heavier envelope. Therefore, the impactor mass will increase to motivate the significant mass loss, as the self-gravity is included. With the increase of envelope mass, the self-gravity is particularly important.

Laser transmission welding of PMMA to alumina ceramic

In this paper, a method of laser transmission welding on ceramic surface after pulse laser microtexture pretreatment was proposed to address the problem that welding ceramics with high transparency polymers is demanded but difficult to be performed. In this method, the polymer flows into the micro-texture of the blind hole on the surface to form mechanical riveting to enhance the welding strength. The formation characteristics and welding mechanism of PMMA welded joint with micro-texture alumina ceramics were studied experimentally and simulatively. The effects of blind hole microtexture size, continuous laser power and continuous laser scanning rate on solution flow and welding strength were studied. The results showed that the air bubbles formed in the welded seam by entering the micro-texture blind hole and trapped air in the blind hole were the key factors affecting the strength of the joint. A 3D finite element model of the transient temperature field and flow field of polymer during laser welding was established. The simulation results showed that the polymer on the left side of the blind hole melted first when heated and inflowed along the wall due to the effects of self-gravity and buoyancy caused by temperature differences. The gas expanded and extruded upward to the left, forming bubbles in the polymer melt pool and pushing the polymer melt into the blind pore microtexture. Finally, a complete molten pool was formed. The flow of polymer melt, the formation of bubbles and the formation of joint were revealed.

The “Maggie” filament: Physical properties of a giant atomic cloud

Context. The atomic phase of the interstellar medium plays a key role in the formation process of molecular clouds. Due to the line-of-sight confusion in the Galactic plane that is associated with its ubiquity, atomic hydrogen emission has been challenging to study. Aims. We investigate the physical properties of the “Maggie” filament, a large-scale filament identified in H I emission at line-of-sight velocities, vLSR ~−54 km s−1. Methods. Employing the high-angular resolution data from The H I/OH Recombination line survey of the inner Milky Way (THOR), we have been able to study H I emission features at negative vLSR velocities without any line-of-sight confusion due to the kinematic distance ambiguity in the first Galactic quadrant. In order to investigate the kinematic structure, we decomposed the emission spectra using the automated Gaussian fitting algorithm GAUSSPY+. Results. We identify one of the largest, coherent, mostly atomic H I filaments in the Milky Way. The giant atomic filament Maggie, with a total length of 1.2 ± 0.1 kpc, is not detected in most other tracers, and it does not show signs of active star formation. At a kinematic distance of 17 kpc, Maggie is situated below (by ≈500 pc), but parallel to, the Galactic H I disk and is trailing the predicted location of the Outer Arm by 5−10 km s−1 in longitude-velocity space. The centroid velocity exhibits a smooth gradient of less than ±3 km s−1 (10 pc)−1 and a coherent structure to within ±6 km s−1. The line widths of ~10 km s−1 along the spine of the filament are dominated by nonthermal effects. After correcting for optical depth effects, the mass of Maggie’s dense spine is estimated to be 7.2−1.9+2.5 × 105 M⊙. The mean number density of the filament is ~4 cm−3, which is best explained by the filament being a mix of cold and warm neutral gas. In contrast to molecular filaments, the turbulent Mach number and velocity structure function suggest that Maggie is driven by transonic to moderately supersonic velocities that are likely associated with the Galactic potential rather than being subject to the effects of self-gravity or stellar feedback. The probability density function of the column density displays a log-normal shape around a mean of ⟨NH I⟩ = 4.8 × 1020 cm−2, thus reflecting the absence of dominating effects of gravitational contraction. Conclusions. While Maggie’s origin remains unclear, we hypothesize that Maggie could be the first in a class of atomic clouds that are the precursors of giant molecular filaments.

Survival of planet-induced vortices in 2D disks

Context. Several observations of protoplanetary disks reveal non-axisymmetric features, which are often interpreted as vortices. Numerical modeling has repeatedly shown that gap-opening planets are capable of producing large and long-lasting vortices at their outer gap edge, making massive planets popular candidates as the source of such features. Aims. We explore the lifetime of vortices generated by Jupiter-sized planets as a function of the thermal relaxation timescale, the level of turbulence, and the effect of disk self-gravity. Methods. We conduct 2D numerical simulations using the hydrodynamics codes PLUTO and FARGO, scanning through several physical and numerical parameters. Vortex properties are automatically extracted from thousands of simulation snapshots. Results. We find that vortices that spawn at the outer gap edge can survive for about 100–3000 planetary orbits, with the shortest lifetimes occurring for moderately efficient dissipation and cooling. However, we also observe a different regime of long-lasting vortices with lifetimes of at least 15 000 orbits for very low viscosity and very short thermal relaxation timescales. Disk self-gravity significantly shortens the lifetime of regular vortices but still allows long-lived ones to survive. Conclusions. Our results suggest that the cooling timescale plays an important role in vortex formation and lifetime and that planet-generated vortices should be observable at large distances from the star for typical thermal relaxation timescales and low turbulence levels.

Acceleration and clustering of cosmic dust in a gravoturbulent gas I. Numerical simulation of the nearly Jeans-unstable case

ABSTRACT We investigate the dynamics of interstellar dust particles in moderately high resolution (5123 grid points) simulations of forced compressible transonic turbulence including self-gravity of the gas. Turbulence is induced by stochastic compressive forcing which is delta-correlated in time. By considering the nearly Jeans-unstable case, where the scaling of the simulation is such that a statistical steady state without any irreversible collapses is obtained, we obtain a randomly varying potential, acting as a second stochastic forcing. We show that, in this setting, low-inertia grains follow the gas flow and cluster in much the same way as in a case of statistical steady-state turbulence without self-gravity. Large, high-inertia grains, however, are accelerated to much higher mean velocities in the presence of self-gravity. Grains of intermediate size also show an increased degree of clustering. We conclude that self-gravity effects can play an important role for aggregation/coagulation of dust even in a turbulent system which is not Jeans-unstable. In particular, the collision rate of large grains in the interstellar medium can be much higher than predicted by previous work.

Nonlinear dynamics of structure formation in protoplanetary disks

A nonlinear nonideal generalized magnetohydrodynamic (MHD) model is developed to explore the evolutionary dynamics of nonlinear wave-structural patterns naturalistically excitable in inhomogeneous protoplanetary disks (PPDs). A local nonlinear perturbation theory (multiscale analysis) over the magnetohydrostatic homogeneous equilibrium of the axisymmetric disk yields a second-order nonlinear partial differential equation in the perturbed gravitational potential curvature with a unique set of multiparametric coefficients. A numerical illustrative platform demonstrates the excitation of nonlinear coherent structures in the form of solitary lump waves (SLWs). The atypical SLW-characteristics are explored geometrically with the phase space trajectories. The SLW amplitude increases in magnitude with the Alfvenic Mach number, and vice-versa. It is interestingly inferred that the Mach number (reference frame velocity and density) acts as a destabilizing (stabilizing) agency to the PPD-dynamics against the nonlocal self-gravity effects, and so forth. It enlightens the long-standing gravitational Laplace 1796 conjecture having a real astronomic significance. At the last, the nontrivial applicability of our findings in the SLW-driven bounded planetary structure formation in varied astroenvirons is actualized.

Formation of Massive Star Clusters by Fast H i Gas Collision

Abstract Young massive clusters (YMCs) are dense aggregates of young stars, which are essential to galaxy evolution, owing to their ultraviolet radiation, stellar winds, and supernovae. The typical mass and radius of YMCs are M ∼ 104 M ⊙ and R ∼ 1 pc, respectively, indicating that many stars are located in a small region. The formation of YMC precursor clouds may be difficult because a very compact massive cloud should be formed before stellar feedback blows off the cloud. Recent observational studies suggest that YMCs can be formed as a consequence of the fast H i gas collision with a velocity of ∼100 km s−1, which is the typical velocity of the galaxy–galaxy interaction. In this study, we examine whether the fast H i gas collision triggers YMC formation using three-dimensional magnetohydrodynamics simulations, which includes the effects of self-gravity, radiative cooling/heating, and chemistry. We demonstrate that massive gravitationally bound gas clumps with M > 104 M ⊙ and L ∼ 4 pc are formed in the shock compressed region induced by the fast H i gas collision, in which massive gas clumps can evolve into YMCs. Our results show that the YMC precursors are formed by the global gravitational collapse of molecular clouds, and YMCs can be formed even in low-metal environments, such as the Magellanic Clouds. Additionally, the very massive YMC precursor cloud, with M > 105 M ⊙, can be created when we consider the fast collision of H i clouds, which may explain the origin of the very massive stellar cluster R136 system in the Large Magellanic Cloud.

Formation of an Accretion Flow

After a star has been tidally disrupted by a black hole, the debris forms an elongated stream. We start by studying the evolution of this gas before its bound part returns to the original stellar pericenter. While the axial motion is entirely ballistic, the transverse directions of the stream are usually thinner due to the confining effects of self-gravity. This basic picture may also be influenced by additional physical effects such as clump formation, hydrogen recombination, magnetic fields and the interaction with the ambient medium. We then examine the fate of this stream when it comes back to the vicinity of the black hole to form an accretion flow. Despite recent progress, the hydrodynamics of this phase remains uncertain due to computational limitations that have so far prevented us from performing a fully self-consistent simulation. Most of the initial energy dissipation appears to be provided by a self-crossing shock that results from an intersection of the stream with itself. The debris evolution during this collision depends on relativistic apsidal precession, expansion of the stream from pericenter, and nodal precession induced by the black hole spin. Although the combined influence of these effects is not fully understood, current works suggest that this interaction is typically too weak to significantly circularize the trajectories, with its main consequence being an expansion of the shocked gas. Global simulations of disc formation performed for simplified initial conditions find that the debris experiences additional collisions that cause its orbits to become more circular until eventually settling into a thick and extended structure. These works suggest that this process completes faster for more relativistic encounters due to the stronger shocks involved. It is instead significantly delayed if weaker shocks take place, allowing the gas to retain large eccentricities during multiple orbits. Radiation produced as the matter gets heated by circularizing shocks may leave the system through photon diffusion and participate in the emerging luminosity. This current picture of accretion flow formation results from recent theoretical works synthesizing the interplay between different aspects of physics. In comparison, early analytical works correctly identified the essential processes involved in disc formation, but had difficulty developing analytic frameworks that accurately combined non-linear hydrodynamical processes with the underlying relativistic dynamics. However, important aspects still remain to be understood at the time of writing, due to numerical challenges and the complexity of this process.

Study of the structure of the inflow/outflow region in the self-gravitating standard accretion disks

The structure of self-gravitating accretion disks is investigated. In order to describe this, we establish the quantitative changes in the θ direction by solving a set of ordinary differential equations in the spherical coordinates (r, θ, φ). The use of a spherical coordinate system causes a positive radial velocity to indicate the presence of an outflow region and a negative radial velocity to indicate an inflow region. In order to discuss the regions of inflow and outflow of self-gravitating disks, we assume that the disk is axisymmetric, that is ∂/∂ϕ=0. We also consider the disk to be steady and uniform. We use self-similar solution in the radial direction. By inserting the advection factor in the energy equation, we can distinguish standard disks from inefficient irradiation accretion disks. The effect of self-gravity of the disk is considered both in the radial and angular direction in the momentum equation. After solving the equations, the results show that the self-gravity decreases the disk’s inflow/outflow region which is observed both in gas-pressure-dominated and radiation-pressure-dominated standard accretion disks. The self-gravity can affect the angular and vertical structure and thickness of the disks. The results show that by increasing the mass of the disk, the thickness of the disk decreases. In radial direction, the self-gravity force reduces the outflow region of the disk.