Structure Of Thin Accretion Discs Research Articles

Analytical model for the local vertical structure of thin accretion discs

ABSTRACT We derive several analytical relations and approximate solutions for the local vertical structure of viscous thin accretion discs. Under the alpha prescription, when the viscous heating is proportional to the gas pressure p, we derive the analytical relation between the radiative flux F and the radiation pressure P: (F/F0)2 = [1 − (P/Pc)5/4]/[1 − (P0/Pc)5/4], where the subscript 0 means the value at the surface and the subscript c is the value at the disc centre. Both F and P are approximately integrated to yield the well-known uniform heating model. In this case, furthermore, the height z and density ρ are approximately fitted as a function of the optical depth τ. When the viscous heating is proportional to the radiation pressure P and the disc is almost isothermal, the flux F is proportional to z as F = (3/2)αΩPz, where α and Ω are the alpha parameter and angular speed, respectively. In this case, moreover, the height and density are analytically solved and expressed as $z=(\sqrt{2}c_{\rm T}/\Omega) {\rm erf}^{-1}(1-\tau /\tau _{\rm c})$ and ρ = ρcexp { − [erf−1(1 − τ/τc)]2}, cT being the isothermal sound speed, and erf−1 the inverse of the error function.

The structure of thin accretion discs around magnetised stars

Aims. We determine the steady-state of an axisymmetric thin accretion disc with an internal dynamo around a magnetised star. Methods. Starting from the vertically integrated equations of magnetohydrodynamics we derive a single ordinary differential equation for a thin accretion disc around a massive magnetic dipole and integrate this equation numerically from the outside inwards. Results. Our numerical solution shows that the torque between the star and the accretion disc is dominated by the contribution from the dynamo in the disc. The location of the inner edge of the accretion disc varies between RA and 10 RA depending mainly on the strength and direction of the magnetic field generated by the dynamo in the disc

The magnetic geometry of magnetic-dominated thin accretion disks

The presence of an imposed external magnetic field drastically influences the structure of thin accretion disks. The magnetic field energy is assumed to be in balance with the thermal energy of the accretion flow, and a diusion approximation simulates the (vertical) energy transport. Our main result is that inside the corotation radius the resulting radial inclination i of the magnetic field lines from the rotation axis easily exceeds the critical value 30 (required to launch cold jets) even for mag- netic Prandtl numbers of order unity. The self-consistent consideration of both magnetic field and accretion flow demonstrates only a weak dependence of the inclination angle on the magnetic Prandtl number. The surface values of the toroidal magnetic fields necessary to induce considerably high values for the radial inclination are much smaller than expected. As the innermost part of the disk produces the largest B tor , the largest radial inclination can also be expected there. The idea is therefore supported that the cold jets are basically launched in the central disk area.

Magnetic field dragging and the vertical structure of thin accretion discs

ABSTRA C T The presence of an imposed vertical magnetic field may drastically influence the structure of thin accretion discs. If the field is sufficiently strong, the rotation law can depart from the Keplerian one. We consider the structure of a disc for a given eddy magnetic diffusivity but neglect details of the energy transport. The magnetic field is assumed to be in balance with the internal energy of the accretion flow. The thickness of the disc as well as the turbulent magnetic Prandtl number and the viscosity, a , are the key parameters of our model. The calculations show that the radial velocity can reach the sound speed for a magnetic disc if the thickness is comparable to that of a non-magnetic one. This leads to a strong amplification of the accretion rate for a given surface density. The inclination angle of the magnetic field lines can exceed the critical value 308 (required to launch cold jets) even for a relatively small magnetic Prandtl number of order unity. The toroidal magnetic fields induced at the disc surface are smaller than predicted in previous studies.