Importance of Finite Thermal Energy Density and Singular Modes for the Transport of Angular Momentum in Accretion Disks

Abstract

In thin accretion disks the electromagnetic modes that can transport angular momentum (in the outward direction as needed for accretion to occur) are shown to require, for their excitation, the combined effects of the finite plasma temperature and of the gradient of the rotation frequency Ω(R) in the realistic case where the disk magnetic field has a toroidal component. In particular, the contribution of finite plasma compressibility (▿ · v≠0) is shown to play a key role. Accordingly, the relevant instabilities would not grow out of a cold plasma disk and pre-heating becomes necessary for the occurrence of momentum transport and accretion. The new kind of modes that are found are singular when described by the ideal MHD approximation, corotate with the plasma at the radius where their amplitude is maximum, are non-axisymmetric, and are strongly affected by the gradient of the relevant Doppler shifted frequency ω=ω−n0Ω (n0= toroidal mode number ≠0). The case where a toroidal and a vertical component of the magnetic field are present is considered. Then the minimum value of the parallel, to the field, component of the relevant wave vector is not bound by the height of the disk and the bending of the magnetic field lines by the modes can be optimized to minimize the instability threshold. The ideal MHD equation for the radial amplitude is characterized by two singularities: one corresponds to the radii where ω equals the “slow” magnetosonic mode frequency, that vanishes if the plasma temperature vanishes, and the other to the radii where ω equals the shear-Alfvén frequency. The key role is played by the first kind of resonance and the presence of a very small and locally enhanced rate of dissipation (e.g., finite thermal conductivity) is required to “remove” the relevant singularities and produce meaningful growth rates. By contrast, axisymmetric (n0=0) modes, that are shown to acquire a vertical ballooning structure, in a thin disk, are considerably more difficult to excite. The importance of finite compressibility is demonstrated also for this kind of modes.