Emission Line Formation in a Relativistic Accretion Disk

The observed profile of spectral lines from a relativistic accretion disk can constrain parameters such as the disk geometry and the rotation of the central black hole. The formation of the spectral line in a disk generally has been modeled with simple assumptions such as local isotropy of emission. Here we consider line formation in the presence of velocity gradients induced by the differential flow in the disk. In this case the emission can have anisotropy in the form of an azimuthal dependence relative to the local principle axes of shear. Since the physical conditions in a disk are uncertain in detail, we investigate this effect with simple parameterized models based on Sobolev theory to highlight the overall character of the changes in the line profile. We find that velocity gradients generally cause a relative increase of flux in the red wing, hence the inner radius of the disk would be underestimated if the effect were not taken into consideration. If the inner radius is used as a signature of black hole rotation, as when the disk is not emissive within the marginally stable circular orbit, then the inferred rotation would be overestimated in cases where the emissivity of the disk has fairly shallow fall-off with radius. If the disk were emissive even within the marginally stable orbit, then the local azimuthal anisotropy of emission produces features in the line profile which distinguish rotating from nonrotating black holes.