6.2 Note on realistic calculation of the detection rates of binary mergings

Now we shall briefly discuss how the detection rates of binary mergings can be calculated for a given gravitational wave detector. For a secure detection, the S ∕N ratio is usually raised up to 7 – 8 to avoid false alarms over a period of a year (assuming Gaussian noise)8. This requirement determines the maximum distance from which an event can be detected by a given interferometer. The distance ranges of LIGO I/VIRGO (LIGO II) interferometers for relativistic binary inspirals are given in [71]: 20(300) Mpc for NS + NS (1.4M ⊙ + 1.4 M ⊙), 43(650) Mpc for NS + BH (1.4 M ⊙ + 10 M ⊙) Note that the distances increase for a network of detectors.

To calculate a realistic detection rate of binary mergers the distribution of galaxies should be taken into account within the volume bounded by the distance range of the detector (see, for example, the earlier attempt to take into account only bright galaxies from Tully’s catalog of nearby galaxies in [223], and the use of LEDA database of galaxies to estimate the detection rate of supernova explosions [19]). However, not only the mass and type of a given galaxy, but also the star formation rate and, better, the history of the star formation rate in that galaxy (since the binary merger rate in galaxies strongly evolves with time [231]) are needed to estimate the expected detection rate 𝒟. But this is a tremendous problem – even the sample of galaxies (mostly, dwarfs) within the Local Volume (< 8 Mpc) is only 70% – 80% complete [187], and the number of new nearby galaxies continues to increase. So to assess the merger rate from a large volume based on the Galactic values, the best one can do at present appears to be using formulas like Equation (4View Equation) given earlier in Section 2.2. This, however, adds another factor two of uncertainty in the estimates. Clearly, a more accurate treatment of the transition from Galactic rates to larger volumes with an account of the galaxy distribution is required.

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