Master thesis - UBC Physics & Astronomy

28 M. Alexandersen : Master thesis
Figure 13. The DDD for the XMM PN observation of GRB031203,
binned in bins of 20 pc, using fplot. It is clear that this form of binning
cannot be good across the entire range in distances.
way to Earth. The distance to the point of scattering, D i , for each event,
can then be calculated using equation Eq. (11) rewritten as
D i = 827 pc t i
1 s
1 arcsec 2
, (14)
where t i is the time since burst, and θ i is the scattering angle (the angle
between the source GRB and the event, on the sky).
These distances are then binned into bins of equal number of counts,
rather than equal widths. This is done because the distances span over
several orders of magnitude, from 10 1 pc to 10 4 pc. Constant bin size
would give very few bins with a lot of counts at low distances, and very
many bins, most of which would be empty, at high distances, as for example
in Fig. 13. Binning instead with a constant number of counts in
θ 2 i