Astron. Astrophys. 346, 91-100 (1999)

4. Conclusions

We have modeled the evolution of binary systems using a Monte Carlo code. The results of the simulations are consistent with the results of other codes (Portegies Zwart & Yungelson, 1998; Lipunov et al., 1997; Portegies Zwart & Verbunt, 1996). Using this code we find that the merger rate of compact object binaries and consequently the detection rate in gravitational wave detectors falls approximately exponentially with the width of kick velocity distribution. While the code that we use is far from describing all the details of binary stellar evolution we must emphasize that it produces similar results to the ones obtained elsewhere and in this work we only concentrate on the relative scaling of the resultant merger rate with the kick velocity in a supernova explosion.

The exact shape of the kick velocity distribution is very difficult to measure. Cordes & Chernoff (1997) and Bethe & Brown (1998) use a distribution which is a weighted sum of two Gaussian distributions: 80 percent with the width 175 km s^-1, 20 percent with 700 km s^-1; Portegies Zwart & Spreeuw (1996) use a Gaussian with the width of 450 km s^-1. On the other hand Iben & Tutukov (1996) argue that no velocity kicks are required at all, however the lack of pulsars in wide binaries suggests that at least a small kick of a few tens of km s^-1 must be present (Portegies Zwart et al., 1997). Thus, the velocity kick determination remains uncertain. Consequently the detection rate estimates in gravitational wave detectors may be uncertain by this amount. Approximating the kick velocity distribution by a single Gaussian profile and changing its dispersion, we calculated the merger rate for a wide range of velocity kicks. Changing the width of the assumed profile within the values proposed by other authors, namely from to km s^-1 results in decrease of the merger rate by a factor of 30. The expected number of compact object mergers varies by more than an order of magnitude when the kick velocity goes from 200 km s^-1 (the value preferred in population studies) to 500 km s^-1 (the measured in the observed population of pulsars).

The measurements of gravitational wave signals may thus allow some determination of the kick velocities. The rates and also perhaps measurements of the "chirp" masses, , where µ and M are the reduced and total mass of binary system - Chernoff & Finn (1993), and their distribution will pose yet another constraint on the stellar evolution.

© European Southern Observatory (ESO) 1999

Online publication: May 6, 1999
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