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Detection rate of binary compact star merging

 

Under the assumptions made above, we can calculate the binary merging rates in the Galaxy R. The results are presented in Fig. gif and gif.

   figure196
Figure: The dependence of different compact binary merging rates in a model ``elliptical'' galaxy (where all the stars were formed simultaneously at the moment t=0) with mass tex2html_wrap_inline948 M tex2html_wrap_inline874 . The horizontal line shows the mean merging rate of binary NS in a spiral galaxy of the same mass with a stationary star formation.

   figure203
Figure: The dependence of different compact binary merging rates in a spiral galaxy with tex2html_wrap_inline952 M tex2html_wrap_inline874 on the characteristic kick velocity tex2html_wrap_inline910 .

After having found the merging rates R in a typical galaxy, we need to go over the event rate D at the detector. Applying the optimal filtering technique [21], the signal-to-noise ratio S/N at the spiral-in stage is

displaymath964

Here tex2html_wrap_inline966 is ``chorp''-mass of the binary system. This means that for a given S/N our detector can register more massive BH from larger distances than NS. The volume within which BH or NS is to be detected should be proportional tex2html_wrap_inline970 . Then the ratio of detection rates of BH and NS can be written as

displaymath972

   figure226
Figure: The total merging rate of NS+NS, NS+BH, and BH+BH binaries as would be detected by a laser interferometer with tex2html_wrap_inline974 for Lyne-Lorimer kick velocity distribution with tex2html_wrap_inline976 -400 km/s and BH progenitor's masses tex2html_wrap_inline978 -50M tex2html_wrap_inline874 , for different scenarios of binary star evolution as a function of tex2html_wrap_inline982 . NS+NS mergings are shown separately. In all cases BH+BH mergings contribute more than tex2html_wrap_inline984 to the total rate. The filled ``Loch-Ness-monster-head''-like region corresponds to BH formation parameters tex2html_wrap_inline986 M tex2html_wrap_inline874 and tex2html_wrap_inline990 .

Let us make a simple estimate. Take a GW detector with tex2html_wrap_inline974 and S/N=1 (as for the initial LIGO or VIRGO interferometer). Let the mass of NS and BH be 1.4M tex2html_wrap_inline874 (the typical value well justified experimentally) and 8.5M tex2html_wrap_inline874 (the mean mass of the BH candidates, see Table gif). Let us also assume that any star with the initial mass M(NS)>10M tex2html_wrap_inline874 yields NS (the typical value confirmed theoretically), and the threshold mass for BH formation is the maximal from the estimates given above, tex2html_wrap_inline1004 M tex2html_wrap_inline870 . Hence using Salpeter mass function we find

displaymath1008

and then

displaymath1010

This estimate is, of course, very rough, but the precise calculation gives essentially the same result. Fig. gif shows the calculated absolute registration rate of mergings D by the detector with tex2html_wrap_inline974 and S/N=1, as a function of tex2html_wrap_inline926 . The calculations have been done for Lyne-Lorimer kick velocity distribution with the parameter tex2html_wrap_inline912  /. The vertical dispersion is due to the dependence of D on tex2html_wrap_inline914 . It is seen that binary NS mergings occur with a rate of about 1 event per year. In the same time, the total detection rate (except for tex2html_wrap_inline1026 ) can exceed that of binary NS mergings by 2-3 orders. The filled region shows the region of the ``most probable parameters'', for which the calculations meet both the upper limit to the number of BH with radiopulsars (less than 1 per 700 single pulsars) and the number of BH candidates of Cyg X-1 type (from 1 to 10 in the Galaxy). In this region, from 10 to 100 mergings per year must be detected, with the majority of them being binary BH mergings.




next up previous
Next: Discussion Up: No Title Previous: Parameters of binary compact

Lipunov V.M.
Fri Nov 28 17:12:56 MSK 1997