Master thesis - UBC Physics & Astronomy

32 M. Alexandersen : Master thesis
Fourier analysis successfully. The periodicity should repeat at least 10
times over the data. If the dynamical image is binned with 10 time bins,
that will, for good data as for GRB070524, leave just 50-150 counts per
time interval. A large part of these are then in the background, and not
in the actual expanding halo. So not very many counts are available for
each peak.
Furthermore, the halo fades as it expands. This would also be a problem
for the Fourier analysis method, as the periodicity is not really periodic
then.
Last, but not least, the Swift data is full of holes. The size of the
holes vary, but for most observation, more than half of every ∼ 5400 s
orbit of the Swift satellite is unobservable, because the Earth blocks the
view. These holes destroys the periodicity of the one dimensional data
strip in that there are holes where there should have been a peak. One
cannot simply ignore and leave out the time interval where there is no
observation, because then there will not be a constant increase in θ 2 from
one bin to the next 3 . The only way to get around this problem would be
to use time intervals so large that there are always counts in every time
interval. The Swift orbital period, 5400 s, would be good. This, however,
limits the usefulness, as very few Swift GRB observations stretch much
more than 3-5 orbits, and even good haloes as GRB050724 are faded
significantly by then.
Fig. 16 demonstrates well why even good Swift data, as GRB050724, is
not suited for this method. The fading of the peaks is very large, and by
the 5th time interval the peak cannot be seen. If the data in Fig. 16 was
to be split to produce 10 peaks, most of the peaks would be vanishingly
faint. Depending on where the intervals are put, and their size, some of
the intervals would be empty or nearly empty, because of the unobserved
periods.
So, in the end, there are many reasons why this method cannot be
used on Swift data. XMM data, such as the observation of GRB031203
that revealed two expanding rings, have a much higher count rate, and
3 Imagine the dynamical image in Fig. 23 without the holes. The expanding
ring would not be a straight line. In the same way, the one dimensional data
would not be periodic.