Black holes are found at the centres of galaxies which are similar in size to our own Milky Way Galaxy or larger. When black holes collide and merge they form supermassive black holes which are events among the most powerful in the universe. Supermassive black holes have a mass range between 7 and 10 orders of magnitude greater than our Sun.
Active Galactic Nuclei form in the accretion disks of supermassive black holes and have unusually large luminosities which can be 4 orders of magnitude greater than that of 'ordinary' galaxies. The increased luminosity is largely due to energy release by matter accreting towards and falling into the centre, hence extracting gravitational potential energy and converting it to radiation. Observations of the Fe K-alpha emission from the Seyfert 1 galaxy MCG-6-30-15 allow measurements of its spectral line profile at energies of 6.4keV (X-Rays). Such line profiles have a characteristic narrow bright blue-shifted peak and also a wide faint gravitationally red-shifted peak. The blue shift results from the Doppler motion of the matter in the disk as it rotates around the rotating black hole (Kerr metric). The red shifted peak results from increased wavelengths as the radiation escapes from the gravitational potential well about the supermassive black hole, thus losing energy. The red peak has energies which correspond to one-third the speed of light which indicates emission with relativistic velocities. Such line profile structures tell us a great deal about plasma conditions and dynamics as well as the space-time geometry around a supermassive black hole.
In this paper the authors use numerical simulations to model emission from accretion disks around such supermassive black holes using a ray tracer method which accounts for any photon trajectories reaching the observer. They calculate the energy flux emitted and and the flux observed, as well as emissivity, to calculate the distribution of red to blue shifting summed over all angles between the observed accretion disk, with an inclination of 35 degrees. This calculation had to account for energy shifted due to relativistic effects which is given by the ratio of the observed energy to the emitted energy flux.
They simulated a synthetic spectral line profile for Fe K-alpha based on the observational data and considered the possible changes in the profile for different angles of inclination, supermassive black hole masses (gravitational forces), inner accretion disk radii and outer accretion disk radii (calculated to be some multiple of the gravitational radius of the supermassive black hole). The model for the accretion disk in this scenario was taken from the Shakura-Sunyaev disk model which is characteristically optically thick and geometrically
thin.
As a result, their simulations showed that through increasing the relative radii of the inner and outer regions of the accretion disk, the peak in the red shift became substantially stronger but with a lower velocity, as well as numerous other effects. So in conclusion, the changing shape of the spectral profiles imply that the dynamics of the black hole angular momentum and mass and the dimensions of the surrounding accretion disk have an important influence on the emission rates and shifts in the plasma, with particular importance due to the Fe K-alpha emission.
Link/reference:
Jovanovic P., Popovic L.C., 2008, Fortschr. Phys. Vol. 55, No. 1, pages 1-5, 'Observational Effects of Strong Gravity in Vicinity of Supermassive Black Holes'