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 $r\varphi$ 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.Comment: Accepted for publication in MNRA

Thermal instability with the effect of cosmic-ray diffusion

We study dynamical effects of cosmics rays (CRs) on the thermal instability in the linear regime. CRs and the thermal plasma are treated as two different interacting fluids, in which CRs can diffuse along the magnetic field lines. We show that growth rate of the magnetothermal condensation mode is reduced because of the existence of CRs and this stabilizing effect depends on the diffusion coefficient and the ratio of the CRs pressure to gas pressure. Thus, a slower rate of structure formation via thermal instability is predicted when CRs are considered.Comment: accepted by MNRA

Magneto-thermal condensation modes including the effects of charged dust particles

We study thermal instability in a magnetized and partially ionized plasma with charged dust particles. Our linear analysis shows that the growth rate of the unstable modes in the presence of dust particles strongly depends on the ratio of the cooling rate and the modified dust-cyclotron frequency. If the cooling rate is less than the modified dust-cyclotron frequency, then growth rate of the condensation modes does not modify due to the existence of the charged dust particles. But when the cooling rate is greater than (or comparable to) the modified dust-cyclotron frequency, the growth rate of unstable modes increases because of the dust particles. Also, wavenumber of the perturbations corresponding to the maximum growth rate shifts to the smaller values (larger wavelengths) as the cooling rate becomes larger than the modified dust-cyclotron frequency. We show that growth rate of the condensation modes increases with the electrical charge of the dust particles.Comment: accepted by MNRA