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Let the sky be observed with a detector having a pencil beam diagram across. The number of stars per frequency decade that is swept by the detector is a function of celestial coordinates (say, galactic coordinates l,b):
For a homogeneous distribution of stars over the sky this number is coordinate independent:
Here is defined as
All sky ( steradian) corresponds to , and for small this is just the halfwidth of the beam.
The transparency of the background begins once ; this inequality provides us with the critical angular resolution the detector should have in order not to ``notice'' the background. To obtain rough estimates we can use a ``homogeneous'' galaxy to find
(below the dependence () will be omitted). Obviously, the red part is of no interest (unless one observes a region of the sky very poor in stars), and for the blue part one finds a critical frequency, , above which no stars occur in the region of the sky subtended by the detector's beam. The function is shown in Figure 41.
Figure 41: The regions of transparency of the GWB from different
objects in the angular resolution of the detector - critical frequency
diagram. The GWB from a homogeneous model of our Galaxy (the total number
of stars is
) is transparent below the line ``Our Galaxy''. The line marked ``sample
galaxy'' shows the transparency boundary for a Milky Way-type galaxy with
observed angular size
. The break at 0.05 Hz is caused by the continuity limit of coalescing
binary WD at a rate of 1 per 100 year. The bottom curve shows the transparency
boundary for the GWB from
external galaxies. The upper horizontal line corresponds to the all-sky
). The hatched region corresponds to ``absolutely hopeless'' (Lipunov et
It is clear from the figure that for an all-sky detector the Galaxy becomes transparent above the frequency Hz. For a realistic LIGO detector network angular resolution of about this frequency reduces to 2 Hz.
The isolines of the critical frequency on the (l,b) sky map are presented in Figure 42 for the realistic galactic model described above and 10 percent of the mass of the corona consisting of stars, seen by the -detector.
Figure 42: Isolines of the critical frequency on the (l,b)-sky
map for the model of the Galaxy described in the text (Lipunov et al.,