Abstract
We investigate dynamics of accretion discs of young stars with fossil large-scale magnetic field. Our magneto-gas-dynamic (MHD) model of the accretion discs includes equations of Shakura and Sunyaev, induction equation, equations of thermal and collisional ionization. Induction equation takes into account Ohmic and magnetic ambipolar diffusion, magnetic buoyancy. We also consider the influence of Ohmic and ambipolar heating on thermal structure of the accretion discs. We analyse the influence of considered dissipative MHD effects on the temperature of the accretion discs around classical T Tauri star. The simulations show that Ohmic and ambipolar heating operate near the borders of the region with low ionization fraction (`dead' zone). Temperature grows by $\sim 1000$ K near the inner boundary of the `dead' zone, $r\approx (0.5-1)$ au, and by $\sim 100$ K near its outer boundary, $r\approx (30-50)$ au.
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