  In the present study time evolution of quasi-spherical polytropic accretion
flow with toroidal magnetic field is investigated. The study especially focused
the astrophysically important case in which the adiabatic exponent
$\gamma=5/3$. In this scenario, it was assumed that the angular momentum
transport is due to viscous turbulence and used $\alpha$-prescription for
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 which govern the
dynamical behavior of the accretion flow, self-similar solution was used. 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 additional variable
$\beta[=p_{mag}/p_{gas}]$, where $p_{mag}$ and $p_{gas}$ are the magnetic and
gas pressure, respectively. The solution indicates a transonic point in the
accretion flow, that this point approaches to central object by adding strength
of the magnetic field. Also, by adding strength of the magnetic field, the
radial-thickness of the disk decreases and the disk compresses. It was
analytically indicated that the radial velocity is only a function of Alfv'en
velocity. The model implies that the flow has differential rotation and is
sub-Keplerian at all radii.
