Master thesis - UBC Physics & Astronomy

30 M. Alexandersen : Master thesis
distribution to be spread out. In most cases, most of the width of the
Lorentz peak is due to the PSF, and not due to the thickness of the dust
sheets. Unless the peak is significantly wider than the width caused by
the PSF, little information is therefore available about the dust sheets
thickness. In the analysis of GRB061019 in Vianello et al. (2007) they
find that the peak is significantly wider than what would be caused by the
PSF alone, and can therefore conclude that the dust layer has a thickness
of 150 pc. However, this is generally not possible.
The background can be roughly estimated synthetically, as we know
the size of the CCD, the co-ordinates of the GRB, and the time intervals
that the observation covers. I have made an IDL procedure, called
loglogmerebaggrund.pro that can do this (see Sec. 6.5.9), and subtract it
from the observed DDD, thereby making a flatter and lower background,
allowing any peaks to be seen clearer.
5.4. Fourier transform method
Studying the dynamical image, I saw that the area of high counts, due
to the expanding halo, moves upwards a little bit from one time bin to
the next. The amount by which it moves upwards from one time bin to
the next is constant. Using larger time bins, the dynamical image can be
cut up into columns, each one time bin wide, thereby producing several
plots of counts versus θ 2 , in which the peak moves a little from one to
the next. If these plots are then laid end to end, then one is left with a
long strip with periodic peaks, as seen in Fig. 15.
My idea was that I could then Fourier transform this function, which
would now be only one dimensional. The Fourier transform should have a
clear peak at a period (with units arcsec 2 ) of the height of the dynamical
image plus the amount the halo moved outwards from one time bin to
the next. The period given by the Fourier transform would thereby give
the rate of expansion of the halo, and from that the distance of the scattering
layer could be calculated. Data sets with no expanding halo should
equivalently show no significant peaks anywhere when transformed.