Time dependence of accretion flow with a toroidal magnetic field

Abstract

In this paper, we investigate the time evolution of quasi-spherical polytropic accretion flow with a toroidal magnetic field. We focus in particular on the astrophysically important case in which the adiabatic exponent γ = 5/3. In this scenario, we have assumed that the angular momentum transport is a result of viscous turbulence and we have used the α-prescription for the kinematic coefficient of viscosity. The equations of accretion flow are solved in a simplified one-dimensional model that neglects the latitudinal dependence of the flow. In order to solve the integrated equations that govern the dynamical behaviour of the accretion flow, we have used a self-similar solution. The solution provides some insight into the dynamics of quasi-spherical accretion flow and avoids many of the strictures of the steady self-similar solution. The effect of the toroidal magnetic field is considered with an additional variable β[= p mag /p gas ], where p mag and p gas are the magnetic pressure and gas pressure, respectively. The solution indicates a transonic point in the accretion flow, that this point approaches the central object by adding the strength of the magnetic field. Also, by adding the strength of the magnetic field, the radial thickness of the disc decreases and the disc compresses. We indicate analytically that the radial velocity is only a function of Alfvén velocity. The model implies that the flow has differential rotation and is sub-Keplerian at all radii.

Self‐similar evolutionary solutions for an accreting magneto‐fluid around a compact object with finite electrical conductivity

“…Also, these relations show p 0 (t) and b 0 (t) are dependent on the behaviour of ρ 0 (t). Our results are in agreement with the previous findings for such time-dependent systems (Ogilvie 1999;Khesali & Faghei 2008, 2009. Moreover, self-similar solutions indicate that electrical conductivity is scaled with time as t −1/3 .…”

Viscous and resistive accretion flows with radially self-similar outflows

“…Because we apply a steady self‐similar method to solve the system equation, Π is constant throughout the disc. In fact, Π is a function of position and time (Machida, Nakamura & Matsumoto 2006; Oda et al 2007; Khesali & Faghei 2008, 2009). Studies of hot accretion flows have found that the typical value of Π is in the range 0.01–1 (De Villiers, Hawley & Krolik 2003; Beckwith, Hawley & Krolik 2008).…”

Dynamics of hot accretion flow with thermal conduction

“…Thus, we introduce a similarity variable ξ and assume that each physical quantity is given by the following form: where is a constant and its value can be obtained from typical values of the system. In addition, we assumed that under similarity transformations is a function of ξ only (Khesali & Faghei 2008, 2009). Substitution of the above transformations into the basic equations ()– (4) yields the dimensionless equations below: These equations provide a fourth‐order system of non‐linear ordinary differential equations that must be solved numerically.…”