Most of the SR effects relevant to the EW of the iron line can be studied within a scenario in which the iron line originates from a stationary slab of cold matter.
Suppose we have a semi-infinite slab of cold gas filling the half-space z<0. Let this cold slab be stationary with respect to a distant observer who views it at an inclination i with respect to the upward normal to the slab. Furthermore, suppose this cold slab is illuminated by an X-ray source which is at some distance h above the face of the slab. We make the following assumptions about the X-ray source:
From simple vector geometry, we can calculate two other important angles.
First, for a given point on the slab
, the angle that the
source velocity makes with the line joining the source with that point,
, is given by
Secondly, the angle between the observers line of sight and the source
velocity,
, is
The question we wish to address is this: how does the relative slab-source motion influence the strength of the iron fluorescence line that will result from the illumination. There will be two relevant effects. First, the Doppler shifts and aberration of the source emission will influence both the number and average direction of primary photons that fall above the iron photoelectric threshold. This will change the absolute line photon emission rate as compared with the static source case. Secondly, the fact that the primary emission suffers relativistic aberration whereas the line emission does not will affect the observed ratio of these two emissions and, hence, the EW of the iron line. We will now discuss these two effects in turn.