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On the global warping of a thin self-gravitating near Keplerian gaseous disk with application to the disk in NGC 4258  [PDF]
John C. B. Papaloizou,Caroline Terquem,Doug N. C. Lin
Physics , 1997, DOI: 10.1086/305436
Abstract: On the global warping of a thin self-gravitating near Keplerian gaseous disk with application to the disk in NGC 4258
Evolution of superbubbles in a self-gravitating disk  [PDF]
L. Zaninetti
Physics , 2012, DOI: 10.1111/j.1365-2966.2012.21649.x
Abstract: The expansion of a superbubble is investigated both analytically and numerically. Our model implements the thin layer approximation in a vertical profile of density as given by an isothermal self-gravitating disk. A precise comparison with the results of numerical hydro-dynamics is given. Analogies are drawn with the Kompaneets equation that includes the quadratic hyperbolic-secant law in the list of the plane-parallel stratified media. An astrophysical application is made to the superbubble connected with the two worms 46.4+5.5 and 39.7+5.7. The effects of the rotation of the galaxy on the simulated radius and on the velocity are introduced. The worms with their strong limb-brightening visible on astronomical maps are explained in the framework of image theory.
Self-Similar Collapse of a Self-Gravitating Viscous Disk  [PDF]
Shin Mineshige,Masayuki Umemura
Physics , 1997, DOI: 10.1086/303964
Abstract: A self-similar solution for time evolution of isothermal, self-gravitating viscous disks is found under the condition that $\alpha' \equiv \alpha (H/r)$ is constant in space (where $\alpha$ is the viscosity parameter and $H/r$ is the ratio of a half-thickness to radius of the disk). This solution describes a homologous collapse of a disk via self-gravity and viscosity. The disk structure and evolution is distinct in the inner and outer parts. There is a constant mass inflow in the outer portions so that the disk has flat rotation velocity, constant accretion velocity, and surface density decreasing outward as $\Sigma \propto r^{-1}$. In the inner portions, in contrast, mass is accumulated near the center owing to the boundary condition of no radial velocity at the origin, thereby a strong central concentration being produced; surface density varies as $\Sigma \propto r^{-5/3}$. Moreover, the transition radius separating the inner and outer portions increases linearly with time. The consequence of such a high condensation is briefly discussed in the context of formation of a quasar black hole.
Viscous accretion of a polytropic self-gravitating disk in the presence of wind  [PDF]
Shahram Abbassi,Erfan Nourbakhsh,Mohsen Shadmehri
Physics , 2012, DOI: 10.1088/0004-637X/765/2/96
Abstract: Self-similar and semi-analytical solutions are found for the height-averaged equations govern the dynamical behavior of a polytropic, self-gravitating disk under the effects of winds, around the nascent object. In order to describe time evolution of the system, we adopt a radius dependent mass loss rate, then highlight its importance on both the traditional $\alpha$ and innovative $\beta$ models of viscosity prescription. In agreement with some other studies, our solutions represent that Toomre parameter is less than one in most regions on the $\beta$-disk which indicate that in such disks gravitational instabilities can occur in various distances from the central accretor and so the $\beta$-disk model might provide a good explanation of how the planetary systems form. The purpose of the present work is twofold. First, examining the structure of disk with wind in comparison to no-wind solution; and second, to see if the adopted viscosity prescription affects significantly the dynamical behavior of the disk-wind system. We also considered the temperature distribution in our disk by a polytropic condition. The solutions imply that, under our boundary conditions, the radial velocity is larger for $\alpha$-disks and increases as wind becomes stronger in both viscosity models. Also, we noticed that the disk thickness increases by amplifying the wind or adopting larger values for polytropic exponent $\gamma$. It also may globally decrease if one prescribe $\beta$-model for the viscosity. Moreover, in both viscosity models, surface density and mass accretion rate reduce as wind gets stronger or $\gamma$ increases.
Instabilities in a Self-Gravitating Magnetized Gas Disk  [PDF]
Sang Min Lee,Seung Soo Hong
Physics , 1999,
Abstract: A linear stability analysis has been performed onto a self-gravitating magnetized gas disk bounded by external pressure. The resulting dispersion relation is fully explained by three kinds of instability: a Parker-type instability driven by self-gravity, usual Jeans gravitational instability and convection. In the direction parallel to the magnetic fields, the magnetic tension completely suppresses the convection. If the adiabatic index $\gamma$ is less than a certain critical value, the perturbations trigger the Parker as well as the Jeans instability in the disk. Consequently, the growth rate curve has two maxima: one at small wavenumber due to a combination of the Parker and Jeans instabilities, and the other at somewhat larger wavenumber mostly due to the Parker instability. In the horizontal direction perpendicular to the fields, the convection makes the growth rate increase monotonically upto a limiting value as the perturbation wavenumber gets large. However, at small wavenumbers, the Jeans instability becomes effective and develops a peak in the growth rate curve. Depending on the system parameters, the maximum growth rate of the convection may or may not be higher than the peak due to the Jeans-Parker instability. Therefore, a cooperative action of the Jeans and Parker instabilities can have chances to over-ride the convection and may develop large scale structures of cylindrical shape in non-linear stage. In thick disks the cylinder is expected to align its axis perpendicular to the field, while in thin ones parallel to it.
Gap formation in a self-gravitating disk and the associated migration of the embedded giant planet  [PDF]
Hui Zhang,Huigen Liu,Ji-Lin Zhou,Robert A. Wittenmyer
Physics , 2013, DOI: 10.1088/1674-4527/14/4/006
Abstract: We present the results of our recent study on the interactions between a giant planet and a self-gravitating gas disk. We investigate how the disk's self-gravity affects the gap formation process and the migration of the giant planet. Two series of 1-D and 2-D hydrodynamic simulations are performed. We select several surface densities and focus on the gravitationally stable region. To obtain more reliable gravity torques exerted on the planet, a refined treatment of disk's gravity is adopted in the vicinity of the planet. Our results indicate that the net effect of the disk's self-gravity on the gap formation process depends on the surface density of the disk. We notice that there are two critical values, \Sigma_I and \Sigma_II. When the surface density of the disk is lower than the first one, \Sigma_0 < \Sigma_I, the effect of self-gravity suppresses the formation of a gap. When \Sigma_0 > \Sigma_I, the self-gravity of the gas tends to benefit the gap formation process and enlarge the width/depth of the gap. According to our 1-D and 2-D simulations, we estimate the first critical surface density \Sigma_I \approx 0.8MMSN. This effect increases until the surface density reaches the second critical value \Sigma_II. When \Sigma_0 > \Sigma_II, the gravitational turbulence in the disk becomes dominant and the gap formation process is suppressed again. Our 2-D simulations show that this critical surface density is around 3.5MMSN. We also study the associated orbital evolution of a giant planet. Under the effect of the disk's self-gravity, the migration rate of the giant planet increases when the disk is dominated by gravitational turbulence. We show that the migration timescale associates with the effective viscosity and can be up to 10^4 yr.
The Global Structure and Evolution of a Self-Gravitating Multi-phase Interstellar Medium in a Galactic Disk  [PDF]
Keiichi Wada,C. A. Norman
Physics , 1999, DOI: 10.1086/311987
Abstract: Using high resolution, two-dimensional hydrodynamical simulations, we investigate the evolution of a self-gravitating multi-phase interstellar medium in the central kiloparsec region of a galactic disk. We find that a gravitationally and thermally unstable disk evolves, in a self-stabilizing manner, into a globally quasi-stable disk that consists of cold (T < 100 K), dense clumps and filaments surrounded by hot (T > 10^4 K), diffuse medium. The quasi-stationary, filamentary structure of the cold gas is remarkable. The hot gas, characterized by low-density holes and voids, is produced by shock heating. The shocks derive their energy from differential rotation and gravitational perturbations due to the formation of cold dense clumps. In the quasi-stable phase where cold and dense clouds are formed, the effective stability parameter, Q, has a value in the range 2-5. The dynamic range of our multi-phase calculations is 10^6 - 10^7 in both density and temperature. Phase diagrams for this turbulent medium are analyzed and discussed.
The Role of the Cooling Prescription for Disk Fragmentation: Numerical Convergence & Critical Cooling Parameter in Self-Gravitating Disks  [PDF]
Hans Baehr,Hubert Klahr
Physics , 2015, DOI: 10.1088/0004-637X/814/2/155
Abstract: Protoplanetary disks fragment due to gravitational instability when there is enough mass for self-gravitation, described by the Toomre parameter, and when heat can be lost at a rate comparable to the local dynamical timescale, described by t_c=beta Omega^-1. Simulations of self-gravitating disks show that the cooling parameter has a rough critical value at beta_crit=3. When below beta_crit, gas overdensities will contract under their own gravity and fragment into bound objects while otherwise maintaining a steady state of gravitoturbulence. However, previous studies of the critical cooling parameter have found dependence on simulation resolution, indicating that the simulation of self-gravitating protoplanetary disks is not so straightforward. In particular, the simplicity of the cooling timescale t_c prevents fragments from being disrupted by pressure support as temperatures rise. We alter the cooling law so that the cooling timescale is dependent on local surface density fluctuations, a means of incorporating optical depth effects into the local cooling of an object. For lower resolution simulations, this results in a lower critical cooling parameter and a disk more stable to gravitational stresses suggesting the formation of large gas giants planets in large, cool disks is generally suppressed by more realistic cooling. At our highest resolution however, the model becomes unstable to fragmentation for cooling timescales up to beta = 10.
The Relativistic Three-Dimensional Evolution of SN 1987A  [PDF]
Lorenzo Zaninetti
International Journal of Astronomy and Astrophysics (IJAA) , 2014, DOI: 10.4236/ijaa.2014.42030

The high velocities observed in supernovae require a relativistic treatment for the equation of motion in the presence of gradients in the density of the interstellar medium. The adopted theory is that of the thin layer approximation. The chosen medium is auto-gravitating with respect to an equatorial plane. The differential equation which governs the relativistic conservation of momentum is solved numerically and by recursion. The asymmetric field of relativistic velocities as well the time dilation is plotted at the age of 1 yr for SN 1987A.

The Structure of a Self-Gravitating Protoplanetary Disk and its Implications to Direct Imaging Observations  [PDF]
Takayuki Muto
Physics , 2011, DOI: 10.1088/0004-637X/739/1/10
Abstract: We consider the effects of self-gravity on the hydrostatic balance in the vertical direction of a gaseous disk and discuss the possible signature of the self-gravity that may be captured by the direct imaging observations of protoplanetary disks in future. In this paper, we consider a vertically isothermal disk in order to isolate the effects of self-gravity. The specific disk model we consider in this paper is the one with a radial surface density gap, at which the Toomre's $Q$-parameter of the disk varies rapidly in the radial direction. We calculate the vertical structure of the disk including the effects of self-gravity. We then calculate the scattered light and the dust thermal emission. We find that if the disk is massive enough and the effects of self-gravity come into play, a weak bump-like structure at the gap edge appears in the near-infrared (NIR) scattered light, while no such bump-like structure is seen in the sub-mm dust continuum image. The appearance of the bump is caused by the variation of the height of the surface in the NIR wavelength. If such bump-like feature is detected in future direct imaging observations, with the combination of sub-mm observations, it will bring us useful information about the physical states of the disk.
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