*Astron. Astrophys. 357, L25-L28 (2000)*
## 2. Delays of scattered radiation
According to Fig. 1 light travels either along the direct path
between the X-ray source *S* and the observer *O* (distance
*d*) or can take a `detour' via a dust grain *G* (by
scattering). *x* denotes the fractional distance where the
scattering takes place, the angle of
observation and the scattering angle.
For details on X-ray scattering on interstellar dust, the related
physics and the observational aspects and limits we refer to the work
done by Hayakawa (1970), Mathis & Lee (1991), and Predehl &
Klose (1996). For the purpose here it is only relevant to note that
the differential scattering cross section depends on the scattering
angle or the observing angle
, respectively, the photon energy
*E*, and the grain size *a* according to
with given in arcmin, *a* in
*µ*m, E in keV. The total scattering cross section depends
on the photon energy according to
The optical depth in scattering is
defined as the product of and the
grain column density along the line of sight *N*. The relative
halo strength is given by
The time delay *dt* of a scattered photon with respect to an
unscattered one is given by (see Fig. 1):
if *d* is given in kpc and in
arcsec (*c* is the speed of light).
The halo radiation is composed of scattering anywhere along the
line of sight, thereby producing different time delays (Eq. 4).
Since the scattering is generally a strong function of the scattering
angle (Eq. 1), the halo is produced preferentially by grains
close to the observer. However, for the observing angles
relevant for this study
(10 arcsec, see below) together
with a mean grain size
*a* = 0.1m and photon energies
below 2 keV, the differential cross section is constant over
about 95% of the line of sight. Therefore, we can handle the delay
effects within the scattering halo using Eq. 4 alone.
© European Southern Observatory (ESO) 2000
Online publication: May 3, 2000
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