Mohsen Shadmehri

Analytical solution for the structure of ADAFs

The standard Advection-Dominated Accretion Flow (ADAF) is studied using a set of self-similar analytical solutions in the spherical coordinates. Our new solutions are useful for studying ADAFs without dealing with the usual mathematical complexity. We assume the rϕ component of the stress tensor dominates and the latitudinal component of the velocity is negligible. Moreover, the fluid is incompressible and the solutions are radially self-similar. We show that our analytical solutions display most of the important properties of ADAFs which have already been obtained by the detailed numerical solutions. According to our solutions, the density and the pressure of the flow decreases from the equator to the polar regions and this reduction depends on the amount of the advected energy. We also show analytically that an ADAF tends to a quasi-spherical configuration as more energy is advected with the radial flow.

Multicomponent theory of buoyancy instabilities in magnetized plasmas: the case of magnetic field parallel to gravity

We investigate electromagnetic buoyancy instabilities of the electron-ion plasma with the heat flux based on not the magnetohydrodynamic (MHD) equations, but using the multicomponent plasma approach when the momentum equations are solved for each species. We consider a geometry in which the background magnetic field, gravity, and stratification are directed along one axis. The nonzero background electron thermal flux is taken into account. Collisions between electrons and ions are included in the momentum equations. No simplifications usual for the one-fluid MHD-approach in studying these instabilities are used. We derive a simple dispersion relation, which shows that the thermal flux perturbation generally stabilizes an instability for the geometry under consideration. This result contradicts to conclusion obtained in the MHD-approach. We show that the reason of this contradiction is the simplified assumptions used in the MHD analysis of buoyancy instabilities and the role of the longitudinal electric field perturbation which is not captured by the ideal MHD equations. Our dispersion relation also shows that the medium with the electron thermal flux can be unstable, if the temperature gradients of ions and electrons have the opposite signs. The results obtained can be applied to the weakly collisional magnetized plasma objects in laboratory and astrophysics.

Viscous Accretion of a Polytropic Self-gravitating Disk in the Presence of Wind

Self-similar and semi-analytical solutions are found for the height-averaged equations governing the dynamical behavior of a polytropic, self-gravitating disk under the effects of winds around the nascent object. In order to describe the time evolution of the system, we adopt a radius-dependent mass loss rate, then highlight its importance on both the traditional α and innovative β models of viscosity prescription. In agreement with some other studies, our solutions represent that the Toomre parameter is less than one in most regions on the β-disk, which indicates that in such disks gravitational instabilities can occur at various distances from the central accretor. So, the β-disk model might provide a good explanation of how the planetary systems form. The purpose of the present work is twofold: examining the structure of a disk with wind in comparison to a no-wind solution and seeing whether the adopted viscosity prescription significantly affects 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 α-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 the polytropic exponent γ. It also may globally decrease if one prescribes a β-model for the viscosity. Moreover, in both viscosity models, the surface density and mass accretion rate diminish as the wind gets stronger or γ increases.

STREAMING COLD COSMIC-RAY BACK-REACTION AND THERMAL INSTABILITIES ALONG THE BACKGROUND MAGNETIC FIELD

We investigate the streaming and thermal instabilities of the electron-ion plasma with homogeneous cold cosmic rays drifting perpendicular to the background magnetic field in the multi-fluid approach. One-dimensional perturbations along the magnetic field are considered. The induced return current of the background plasma and back-reaction of cosmic rays are taken into account. It is shown that the cosmic ray back-reaction results in the streaming instability having considerably larger growth rates than that due to the return current of the background plasma. This increase is by a factor of the square root of the ratio of the background plasma mass density to the cosmic ray mass density. The maximal growth rates and corresponding wave numbers are found. The thermal instability is shown to be not subject to the action of cosmic rays in the model under consideration. The dispersion relation for the thermal instability includes ion inertia. In the limit of fast thermal energy exchange between electrons and ions, the isobaric and isochoric growth rates are derived. The results obtained can be useful for the investigation of the electron-ion astrophysical objects such as galaxy clusters including the dynamics of streaming cosmic rays.

Structure of radiation dominated gravitoturbulent quasar discs

Self-gravitating accretion discs in a gravitoturbulent state, including radiation and gas pressures, are studied using a set of new analytical solutions. While the Toomre parameter of the disc remains close to its critical value for the onset of gravitational instability, the dimensionless stress parameter is uniquely determined from the thermal energy reservoir of the disc and its cooling rate. Our solutions are applicable to the accretion discs with dynamically important radiation pressure like in the quasars discs. We show that physical quantities of a gravitoturbulent disc in the presence of radiation are significantly modified compared to solutions with only gas pressure. We show that the dimensionless stress parameter is an increasing function of the radial distance so that its steepness strongly depends on the accretion rate. In a disc without radiation its slope is 4.5, however, we show that in the presence of radiation, it varies between 2 and 4.5 depending on the accretion rate and the central mass. As for the surface density, we find a shallower profile with an exponent -2 in a disc with sub-Eddington accretion rate compared to a similar disc, but without radiation, where its surface density slope is -3 independent of the accretion rate. We then investigate gravitational stability of the disc when the stress parameter reaches to its critical value. In order to self-consistently determine the fragmentation boundary, however, it is shown that the critical value of the stress parameter is a power-law function of the ratio of gas pressure and the total pressure and its exponent is around 1.7. We also estimate the maximum mass of the central black hole using our analytical solutions.

On the location of the ice line in circumbinary discs

Position of the ice line in a circumbinary disc is determined using a simplified and illustrative model. Main sources of the heat in the energy balance of the disc, i.e. heating by the turbulence, irradiation by the components of the binary and the tidal heating are considered. Our goal is to clarify role of the tidal heating in the position of the ice line. When viscous heating and irradiation of the binary are considered, ice line lies interior to the inner radius of the disc in most of the binaries represented by our parameter survey. But tidal heating significantly extends position of the ice line to a larger radius, so that a smaller fraction of the circumbinaries population may have ice lines interior to the inner radius of the disc.

Rayleigh–Taylor instability in an ionized medium

We study the linear theory of the magnetized Rayleigh–Taylor instability in a system consisting of ions and neutrals. Both components are affected by a uniform vertical gravitational field. We consider ions and neutrals as two separate fluid systems that can exchange momentum through collisions. However, ions have a direct interaction with the magnetic field lines but neutrals are not affected by the field directly. The equations of our two-fluid model are linearized and by applying a set of proper boundary conditions, a general dispersion relation is derived for our two superposed fluids separated by a horizontal boundary. We found two unstable modes for a range of wavenumbers. It seems that one of the unstable modes corresponds to the ions and the other one is for the neutrals. Both modes are reduced with increasing particle collision rate and ionization fraction. We show that if the two-fluid nature is considered, the RT instability would not be suppressed and we also show that the growth time of the perturbations increases. As an example, we apply our analysis to the Local Clouds which seem to have arisen because of the RT instability. Assuming that the clouds are partially ionized, we find that the growth rate of these clouds increases in comparison to the fully ionized case.

Vertically self-gravitating ADAFs in the presence of toroidal magnetic field

Force due to the self-gravity of the disc in the vertical direction is considered to study its possible effects on the structure of a magnetized advection-dominated accretion disc. We present steady-sate self similar solutions for the dynamical structure of such a type of the accretion flows. Our solutions imply reduced thickness of the disc because of the self-gravity. It also imply that the thickness of the disc will increase by adding the magnetic field strength.

Exact analytical solutions for ADAFs

We obtain two-dimensional exact analytic solutions for the structure of the hot accretion flows without wind. We assume that the only non-zero component of the stress tensor is

Role of thermal conduction in an advective accretion with bipolar outflows

T_{rvarphi}