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To get rid of the extragalactic GWB produced by binaries, one can use the above considerations to find the optimal detector halfwidth and frequency for observations. Again, for simple estimates we can suppose the stars in the Universe to be distributed homogeneously. Assuming an average galaxy to consist of stars and the total number of galaxies in the Universe to be , we get the average number of stars per decade falling into the detector's beam to be
for the flat red end of the GWB, and
for the blue end of the GWB formed by the coalescing binaries. Equating to unity, one finds the critical detector halfwidth
One immediately notes that observations at low frequencies ( ) are always contaminated by the stochastic binary GWB. In contrast, by observing the sky with a GW detector with a narrow enough halfwidth , one will not ``see'' the extragalactic GWB at frequencies .
Alternatively, if one uses a GW-detector with a fixed halfwidth of the beam, equation (15.8.1) gives the answer to the question at what frequency one should make observations so that they do not include any binary-produced stochastic noise. In fact, the transparency of the extragalactic GWB occurs at frequencies above 1 Hz, that is in the part of the spectrum produced by coalescing binary neutron stars. Taking for their rate , one finds that the extragalactic GWB begins being transparent above the frequency
as shown in Figure 41.