Presently, there are several population synthesis codes used for massive binary system studies, which
take into account with different degree of completeness various aspects of binary stellar evolution (e.g., the
codes by Portegies Zwart et al. [329, 469], Bethe and Brown [33], Hurley, Tout, and Pols [156], Belczynski
et al. [24], Yungelson and Tutukov [423
]). A review of applications of the population synthesis method to
various types of astrophysical sources and further references can be found in [326, 467]. Some results of
population synthesis calculations of compact binary mergers carried out by different groups are presented in
Table 4.
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Authors | Ref. | NS + NS | NS + BH | BH + BH |
[yr–1]
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[yr–1]
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[yr–1]
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Tutukov and Yungelson (1993) | [420![]() |
3 × 10–4 | 2 × 10–5 | 1 × 10–6 |
Lipunov et al. (1997) | [228![]() |
3 × 10–5 | 2 × 10–6 | 3 × 10–7 |
Portegies Zwart and Yungelson (1998) | [329![]() |
2 × 10–5 | 10–6 | |
Nelemans et al. (2001) | [286![]() |
2 × 10–5 | 4 × 10–6 | |
Voss and Tauris (2003) | [437![]() |
2 × 10–6 | 6 × 10–7 | 10–5 |
O’Shaughnessy et al. (2005) | [298![]() |
7 × 10–6 | 1 × 10–6 | 1 × 10–6 |
de Freitas Pacheco et al. (2006) | [72] | 2 × 10–5 | ||
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Actually, the authors of the studies mentioned in Table 4 make their simulations for a range of
parameters. We list in the table the rates for the models which the authors themselves consider as
“standard” or “preferred” or “most probable”. Generally, for the NS + NS merger rate Table 4 shows the
scatter within a factor 4, which may be considered quite reasonable, having in mind the uncertainties
in input parameters. There are two clear outliers, [420
] and [437
]. The high rate in [420
] is due to the
assumption that kicks to nascent neutron stars are absent. The low rate in [437
] is due to the fact
that these authors apply in the common envelope equation an evolutionary-stage-dependent
structural constant
. Their range for
is 0.006 – 0.4, to be compared with the “standard”
applied in most of the other studies. A low
favours mergers in the first critical lobe
overflow episode and later mergers of the first-born neutron stars with their non-relativistic
companions7.
A considerable scatter in the rates of mergers of systems with BH companions is due, mainly, to
uncertainties in stellar wind mass loss for the most massive stars. For instance, the implementation of winds
in the code used in [329, 286
] resulted in the absence of merging BH + BH systems, while a rather low
assumed in [437] produced a high merger rate of BH + BH systems.
A word of caution should be said here. It is hardly possible to trace a detailed evolution of each binary, so one usually invokes the approximate approach to describe the change of evolutionary stages of the binary components (the so-called evolutionary track), their interaction, effects of supernovae, etc. Thus, fundamental uncertainties of stellar evolution mentioned above are complemented with (i) uncertainties of the scenario and (ii) uncertainties in the normalization of the calculations to the real galaxy (such as the fraction of binaries among allstars, the star formation history, etc.). The intrinsic uncertainties in the population synthesis results (for example, in the computed event rates of binary mergers etc.) are in the best case not less than of the order of factor two or three. This should always be born in mind when using the population synthesis calculations. However, we emphasize again the fact that the double NS merger rate, as inferred from binary pulsar statistics with account for the double pulsar observations [49, 182], is very close to the population syntheses estimates with a kick of about (250 – 300) kms.
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