Twisted accretion disks. I - Derivation of the basic equations

A twisted accretion disk is defined as a set of rings of different radii lying in different planes and for which the variation of the planes occurs smoothly with radius, viscosity being the smoothing mechanism. The basic equations governing the twist structure of a disk are derived, assuming the presence of some unspecified twisting force. A twisted coordinate system is introduced, five conditions are given for a stationary twisted thin accretion disk, and the hydrodynamic equations through which the twist structure of such a disk can be completely determined are formulated in the twisted coordinates. It is shown that if the angles between the planes of different rings are not greater than about 10 deg, the difference between a twisted and a flat accretion disk can be described completely (to a lowest order) by a single time-independent partial differential 'twist' equation, which governs the global structure of the disk. The twist equation obtained is then decomposed into a set of two coupled ordinary differential equations.