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A stationary slab illuminated by a moving source

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:

  1. the source is pointlike.
  2. the X-ray emission is isotropic in the rest-frame of the source.
  3. the spectrum of the emission, when viewed in the rest frame, is a power-law with photon index tex2html_wrap_inline574 for all energies relevant to this discussion. This choice of photon index is observationally motivated (e.g. Nandra & Pounds 1994; Reynolds 1997).
We further assume that the source is moving at velocity v relative to the slab. We define tex2html_wrap_inline526 to be the angle this velocity vector makes with the downward normal (thus tex2html_wrap_inline506 corresponds to motion directly towards the slab). We also define tex2html_wrap_inline582 to be the azimuthal direction of the source in the slab plane relative to some reference line on the slab. We choose the projection of the observers line of sight to be this reference line. Finally, we construct a standard 2-d polar co-ordinate system tex2html_wrap_inline584 on the slab taking the point that is (instantaneous) below the source to be the origin, and using same reference direction used to define tex2html_wrap_inline582 .

From simple vector geometry, we can calculate two other important angles. First, for a given point on the slab tex2html_wrap_inline584 , the angle that the source velocity makes with the line joining the source with that point, tex2html_wrap_inline590 , is given by

equation126

Secondly, the angle between the observers line of sight and the source velocity, tex2html_wrap_inline592 , is

equation130

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.




next up previous
Next: Influence of the motion Up: Special relativistic effects on Previous: Introduction

Chris Reynolds
Wed Jun 25 19:56:55 MDT 1997