In most evaluations of for individual GRBs, it has been
assumed that it equals
where
is the
minimum detectable count rate and
is the count rate at
the maximum amplitude of the burst. This may not be correct. If we
remove the source to the largest distance at which it is just still
detectable, it is likely that the detection of the burst will occur
later, and therefore that
will include some burst signal.
Also, in some cases the part of the burst containing
will
not cause a trigger when we remove the burst. Due to
these inescapable effects,
will be larger than follows
from the values of
and
at detection. This
situation was encountered by Higdon & Schmidt (1990) in their
discussion of GRBs from the Venera 11 and 12 KONUS experiments.
We have derived the euclidean value of for each GRB
as follows. Upon detection, we derive the burst time profile by
subtracting the background (interpolated between the two background
stretches, see Fig. 1) from the counts. We multiply this original
time profile by a factor of X and add it to the background. Next we
apply the search algorithm to see whether we detect a burst. If so,
we repeat the process with a smaller value of X, until we do not
detect a burst anymore. This represents the situation (as best we can)
when the source has been removed
in distance by a factor X-1/2 in euclidean
space. Therefore
for the source is X3/2. Application
of this process to all bursts in the sample produces
.
Acknowledgements
During the many years in which this work came to fruition, I have had much appreciated help from or discussions with D. Chakrabarty, M. Finger, G. Fishman, J. Gunn, J. Higdon, J. Horack, C. Meegan, T. Prince, and B. Vaughan.
Copyright The European Southern Observatory (ESO)