Warped accretion disk with power-law models for viscosities

In this paper, we investigate a thin accretion disk that is warped due to the Black hole spin using numerical methods. We assume that the two viscosity coefficients vary with radius according to a power-law model, each with different power indices. Additionally, we consider the contribution of the inner disk by applying the appropriate boundary condition. Our results indicate that the alignment of the disk is influenced by the power indices of the viscosities (n and α₁). Specifically, the vertical viscosity index is more influential than the azimuthal viscosity index. An increase in the vertical viscosity index leads to greater misalignment of the disk concerning the spin axis of the black hole. These findings suggest that, contrary to previous studies, the inner regions of the disk can remain tilted relative to the rotation axis of the black hole, even for rotating black holes with a larger Kerr parameter, specifically, a = 0.3. Our results help explain the observed quasi-periodic oscillation features in X-ray emissions and the Fe Kα line, which may arise from the precession of a warped inner accretion disk. This research could be valuable for exploring regions of strong gravitational fields.