Relativistic emission lines from accretion discs around black holes

The next generation of X-ray satellites will provide high-resolution line profiles from active galactic nuclei, which are nowadays considered to be born in an accretion disc around a supermassive black hole. In order to allow theoretical models to be fitted to observational data, powerful computational tools are required. We present new, fast and accurate methods that use integrated geodesic equations in terms of Jacobian elliptic functions, in both the Schwarzschild and the Kerr metrics, to produce accretion disc images and line profiles. Two different codes were designed in order to make maximal use of the symmetries of the Schwarzschild and Kerr solutions. In the Schwarzschild case, one can analytically map any point of the disc - even a warped one - into the image plane, which makes the calculations accurate and fast. In the Kerr case, the analytic form of the integrated geodesic equations is not as simple, so that some numerical interpolations are required in calculating line profiles, and the case of warped discs cannot be treated as easily. Both codes are able to calculate lines produced by material extending below the marginally stable orbit and can handle various emissivity and illumination laws. The codes are freely available to the community.