G. Corvino, V. Ferrari, S. Marassi, R. Schneider
In this paper we perform a detailed analysis of the effect of various approximations that have been adopted in the literature to compute the detection rates of compact binary coalescences for first, second and third generation gravitational wave detectors. In particular, we compute the detection rates for the coalescence of BH-BH, NS-NS, and BH-NS systems taking into account their specific statistical properties obtained from population synthesis models (distributions of masses and delay times), the cosmic star formation rate history and the effects of redshift on the emitted gravitational wave signals. We then compare our findings with procedures adopted in the literature that are based on different levels of approximations, such as using averaged values for the total mass and symmetric mass ratio for all the systems of a binary population, using these to compute the horizon distance for individual detectors, or estimating the coalescence rate density within this distance by its local value. We find that most of these approximations are adequate to estimate the detection rates of first generation interferometers, because these are sensitive only to very low redshifts (even for BH-BH systems, the maximum detectable redshift for LIGO/VIRGO is $z \le 0.02$). However, for second generation interferometers, such as Advanced LIGO/VIRGO, the adopted approximations can lead to a factor $\gtrsim3$ error in the estimated detection rates, and can not be applied to third generation detectors, such as the Einstein Telescope for which we give the estimated detection rate using no approximations.
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http://arxiv.org/abs/1203.5110
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