next up previous contents index
Next: A Gravitational Wave Map Previous: Critical Frequencies and Gravitational


Amplitude Distribution

In this section we consider the GWB spectrum as such, that is, we study how dimensionless strain metric amplitude h is dependent on frequency. For a sample of N independent binaries emitting GW at a given frequency tex2html_wrap_inline12262 the net result is


If one uses the frequency interval tex2html_wrap_inline12264 , the result will be




is the familiar amplitude produced by an individual binary,


are, respectively, effective distance to the sample and effective mass of the binaries (in solar units) producing the GW radiation at the frequency tex2html_wrap_inline12262 . For example, for a homogeneous sample (which is a good approximation to extragalactic binaries)  one obtains tex2html_wrap_inline12270 , where tex2html_wrap_inline12272 is the outer boundary of the sample.

Making use of expressions (15.3.2), (15.3.3) and (15.9.3) yields


for the red end of the spectrum ( tex2html_wrap_inline12249 ) and


for the blue end.

One may be interested in how the GWB from the external object relates to that from our Galaxy, providing that the observations are being performed with a detector of angular resolution tex2html_wrap_inline8929 such that the Galaxy is still not transparent at the frequency of observations, and the object is inside the detector's beam, tex2html_wrap_inline12278 . In this case


Here n is the number of stars within the object, tex2html_wrap_inline12284 is an effective ``radius'' of the Galaxy tex2html_wrap_inline12286 kpc. Some specific examples are shown in Table 13.


It can be seen from Table gif that only the closest stellar systems (such as Magellanic Clouds  and M31) can noticeably affect the galactic binary background. The level of the cosmological binary GWB is always an order of magnitude below the galactic level. Indeed, in analogy with expressions (15.9.4) and (15.9.5) one obtains for the red (flat) and blue (decreasing) parts of the spectrum, respectively: $$ .h|_r =2.1 10^-17 n_11^1/2N_11^1/2^2/3 C_4/3^1/2(3500 Mpcr),

Their comparison with expressions (15.9.4) and (15.9.5) yields


for both ends of the spectrum.

The GW noise produced by extragalactic binary systems  is still considerably higher than the expected amplitudes of relic gravitational waves produced in well-known inflationary models (Rubakov et al., 1982[169]): displaymath12306, even if one conducts observations at the galactic poles which are poor in stars.

Figure 43: Distribution of galaxies from Tully's Catalog by distance. 

next up previous contents index
Next: A Gravitational Wave Map Previous: Critical Frequencies and Gravitational

Mike E. Prokhorov
Sat Feb 22 18:38:13 MSK 1997