Linear Two-Dimensional MHD of Accretion Disks: Crystalline structure and Nernst coe cient

We analyse the two-dimensional MHD con gurations characterising the steady state of the accretion disk on a highly magnetised neutron star. The model we describe has a local character and represents the extension of the crystalline structure outlined in [1], dealing with a local model too, when a speci c accretion rate is taken into account. We limit our attention to the linearised MHD formulation of the electromagnetic back-reaction characterising the equilibrium, by xing the structure of the radial, vertical and azimuthal pro les. Since we deal with toroidal currents only, the consistency of the model is ensured by the presence of a small collisional e ect, phenomenologically described by a non-zero constant Nernst coe cient (thermal power of the plasma). Such an e ect provides a proper balance of the electron force equation via non zero temperature gradients, related directly to the radial and vertical velocity components. We show that the obtained pro le has the typical oscillating feature of the crystalline structure, reconciled with the presence of viscosity, associated to the di erential rotation of the disk, and with a net accretion rate. In fact, we provide a direct relation between the electromagnetic reaction of the disk and the (no longer zero) increasing of its mass per unit time. The radial accretion component of the velocity results to be few orders of magnitude 1 ar X iv :0 90 9. 03 71 v1 [ as tr oph .H E ] 2 S ep 2 00 9 below the equatorial sound velocity. Its oscillating-like character does not allow a real matter in-fall to the central object (an e ect to be searched into non-linear MHD corrections), but it accounts for the out-coming of steady uxes, favourable to the ring-like morphology of the disk. keywords: Accretion disks; Plasma physics; Nernst coe cient PACS Nos.: 97.10.Gz, 52.30.-q