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Astron. Astrophys. 357, L25-L28 (2000)

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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, [FORMULA] the angle of observation and [FORMULA] 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 [FORMULA] or the observing angle [FORMULA], respectively, the photon energy E, and the grain size a according to

[EQUATION]

with [FORMULA] given in arcmin, a in µm, E in keV. The total scattering cross section depends on the photon energy according to

[EQUATION]

[FIGURE] Fig. 1. Scattering geometry

The optical depth in scattering [FORMULA] is defined as the product of [FORMULA] and the grain column density along the line of sight N. The relative halo strength is given by

[EQUATION]

The time delay dt of a scattered photon with respect to an unscattered one is given by (see Fig. 1):

[EQUATION]

if d is given in kpc and [FORMULA] 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 [FORMULA] relevant for this study ([FORMULA]10 arcsec, see below) together with a mean grain size a = 0.1[FORMULA]m 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.

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© European Southern Observatory (ESO) 2000

Online publication: May 3, 2000
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