Dynamics of magnetized accretion disks of young stars

We investigate the dynamics of the accretion disks of young stars with fossil large-scale magnetic field. The author's magnetohydrodynamic (MHD) model of the accretion disks is generalized to consider the dynamical influence of the magnetic field on gas rotation speed and vertical structure of the disks. With the help of the developed MHD model, the structure of an accretion disk of a solar mass T Tauri star is simulated for different accretion rates $\dot{M}$ and dust grain sizes $a_d$. The simulations of the radial structure of the disk show that the magnetic field in the disk is kinematic, and the electromagnetic force does not affect the rotation speed of the gas for typical values $\dot{M}=10^{-8}\,M_\odot\,\mbox{yr}^{-1}$ and $a_d=0.1 \mu$m. In the case of large dust grains, $a_d\geq 1$ mm, the magnetic field is frozen into the gas and a dynamically strong magnetic field is generated at radial distances from the star $r\gtrsim 30$ au, the tensions of which slow down the rotation speed by $\lesssim 1.5$ % of the Keplerian velocity. This effect is comparable to the contribution of the radial gradient of gas pressure and can lead to the increase in the radial drift velocity of dust grains in the accretion disks. In the case of high accretion rate, $\dot{M}\geq 10^{-7}\,M_\odot\,\mbox{yr}^{-1}$, the magnetic field is also dynamically strong in the inner region of the disk, $r<0.2$ au. The simulations of the vertical structure of the disk show that, depending on the conditions on the surface of the disk, the vertical gradient of magnetic pressure can lead to both decrease and increase in the characteristic thickness of the disk as compared to the hydrostatic one by 5-20 %. The change in the thickness of the disk occurs outside the region of low ionization fraction and effective magnetic diffusion (`dead' zone), which extends from $r=0.3$ to $20$ au at typical parameters.