We have carried out and analyzed a set of axisymmetric MHD simulations of the evolution of a turbulent/diffusive accretion disc around an initially unmagnetized star .
The disc is initially threaded by a weak magnetic field where the magnetic pressure is significantly less than the kinetic pressure in the disc .
The viscosity and magnetic diffusivity are modeled by two “ alpha ” parameters , while the coronal region above the disc is treated using ideal MHD .
The initial magnetic field is taken to consist of three poloidal field loops threading the disc .
The motivation for this study is to understand the advection of disc matter and magnetic field by the turbulent/diffusive disc .
At early times ( \lesssim 400 orbits of the inner disc ) , the innermost field loop twists and its field lines become open .
The twisting of the opened field lines leads to the formation of both an inner collimated , magnetically-dominated jet , and at larger distances from the axis a matter dominated uncollimated wind .
For later times ( > 1000 ) , the strength of the magnetic field decreases owing to field reconnection and annihilation in the disc .
For the early times , we have derived from the simulations both the matter accretion speed in the disc u _ { m } and the accretion speed of the magnetic field u _ { B } which is determined by measuring the speed of the inward motion of the inner O-point of the magnetic field in the equatorial plane .
We show that the derived u _ { m } agrees approximately with the predictions of a model where the accretion speed is the sum of two terms , one due to the disc ’ s viscosity ( which gives a radial outflow of angular momentum in the disc ) , and a second due to the twisted magnetic field at the disc ’ s surface ( which gives a vertical outflow of angular momentum ) .
At later times the magnetic contribution to u _ { m } becomes small compared to the viscous contribution .
For early times we find that u _ { m } is larger than the magnetic field accretion speed u _ { B } by a factor of \sim 2 for the case where the alpha parameters are both equal to 0.1 .