Master thesis - UBC Physics & Astronomy

14 M. Alexandersen : Master thesis
As mentioned earlier θ ≪ 1, so cos θ ≃ 1 − 1 2 θ2 . From this, Eq. (8)
becomes
D d = ct ( 1 − 1 2 θ2)
1
2 θ2 . (9)
With θ ≪ 1 we now apply that 1 − 1 2 θ2 ≃ 1, so finally we get
D d = 2ct
θ 2 . (10)
Writing this in typical units for dust scattered X-ray haloes, the above
equation becomes
D d ≃ 827 pc t 1 arcsec 2
. (11)
1 s θ 2
As h ds ≃ D ds , the X-rays hitting the dust are moving almost parallel
to each other. Therefore θ ≃ the scattering angle, and will be referred to
as the scattering angle in this thesis.
3.4. Scattering of X-rays by dust
In order to see this kind of halo, the dominant scattering process must be
small angle scattering and not Rayleigh scattering or other physical processes.
For Rayleigh scattering light is scattered in all directions, whereas
small angle scattering only scatters radiation within a fairly small interval
of angles, in the forward direction. Rayleigh scattering applies when
the wavelength of the radiation is larger than or similar to the scattering
particles (Whittet 1992). In the case of interstellar dust of typical
size 0.2 µm (Vaughan et al. 2004), in order for the wavelength to be
much smaller than the dust size, thereby making small angle scattering
the dominant process, the radiation has to be γ-rays, X-rays or the
high energy end of Ultra Violet (UV). The upper boundary on the X-
ray wavelength is 10 nm, which safely satisfies the condition that the
wavelength should be much smaller than the dust grain.
Small angle scattering depends on the principle of total internal reflection.
When radiation hits a surface between two media at an angle of