Emission Line Profiles of Warped Disks in the Kerr Spacetime

The calculations of emission line profiles of a warped disk in the Kerr spacetime have been discussed in this paper. The main content consists of two parts. In the first part, the geodesic motion in the Kerr spacetime and the equations of motion in integral form, as well as the method to obtain the solution with the Weierstrass’ elliptic functions are presented. Using the Weierstrass’ elliptic functions, the Boyer-Lindquist (B-L) coordinates and the affine parameter o are semi-analytically expressed as the functions of a parameter p. Then a code named ynogk (Yunnan Observatory Geodesic Kerr) is introduced based on the above discussions to calculate very fast the null geodesic in the Kerr spacetime. As an application of ynogk, the emission line profiles of warped disks are investigated in detail in the second part of this paper. Here the structure model of warped disks is based on the results of Bardeen and Petterson in 1975, and the line profiles are computed with the ray tracing method. Finally, the discussions and conclusions of the calculated results are presented. It is indicated that the line profiles are dependent mainly on the inclination and azimuthal angles of the observer, as well as the index of emissivity, and that they may have a triple-peaked even multi-peaked structure, different from the double-peaked structure in the line profiles of a standard thin accretion disk.