2.2 How frequent are double NS coalescences?

As it is seen from Table 3, only six double NS systems presently known will coalesce over a time interval shorter than ≈ 10 Gyr: J0737–3039A, B1534+12, J1756–2251, J1906+0746, B1913+16, and B2127+11C. Of these six systems, one (PSR B2127+11C) is located in the globular cluster M15. This system may have a different formation history, so usually it is not included in the analysis of the coalescence rate of Galactic double compact binaries. The formation and evolution of relativistic binaries in dense stellar systems is reviewed elsewhere [27Jump To The Next Citation Point]. For a recent general review of pulsars in globular clusters see also [52].

The ordinary way of estimating the double NS merger rate from binary pulsar statistics is based on the following extrapolation [272314Jump To The Next Citation Point]. Suppose we observe i classes of Galactic binary pulsars. Taking into account various selection effects of pulsar surveys (see, e.g., [271191Jump To The Next Citation Point]), the Galactic number of pulsars N i in each class can be evaluated. To compute the Galactic merger rate of double NS binaries, we need to know the time since the birth of the NS observed as a pulsar in the given binary system. This time is the sum of the observed characteristic pulsar age τc and the time required for the binary system to merge due to GW orbit decay τGW. With the exception of PSR J0737–3039B and the recently discovered PSR J1906+0746, pulsars that we observe in binary NS systems are old recycled pulsars which were spun-up by accretion from the secondary companion to the period of several tens of ms (see Table 2). Thus their characteristic ages can be estimated as the time since termination of spin-up by accretion (for the younger pulsar PSR J0737–3039B this time can be also computed as the dynamical age of the pulsar, P ∕(2P˙), which gives essentially the same result).

Then the merger rate ℛi can be calculated as ℛi ∼ Ni∕ (τc + τGW ) (summed over all binary pulsars). The detailed analysis [191] indicates that the Galactic merger rate of double NSs is mostly determined by pulsars with faint radio luminosity and short orbital periods. Presently, it is the nearby (600 pc) double-pulsar system PSR J0737–3039 with a short orbital period of 2.4 hr [49Jump To The Next Citation Point] that mostly determines the empirical estimate of the merger rate. According to Kim et al. [192Jump To The Next Citation Point], “the most likely values of DNS merger rate lie in the range 3 – 190 per Myr depending on different pulsar models”. The estimates by population synthesis codes are still plagued by uncertainties in statistics of binaries, in modeling binary evolution and supernovae. The most optimistic “theoretical” predictions amount to ≃ 300 Myr–1 [420Jump To The Next Citation Point23Jump To The Next Citation Point].

Recently, the bursting radio source GCRT J1745–3009 in the direction to the Galactic centre was proposed to be a possible double NS binary [407]. The source was found to emit a series of radio bursts with high brightness temperature, of typical duration ∼ 10 min, with an apparent periodic pattern of ∼ 77 min [158]. Confirmation of the binary NS nature of transient radio sources like GCRT J1745–3009 would be important to get a more precise estimate of the Galactic coalescence rate of double NS.

The extrapolation beyond the Galaxy is usually done by scaling the Galactic merger rate to the volume from which the merger events can be detected with given GW detector’s sensitivity. The scaling factor widely used is the ratio between the B-band luminosity density in the local Universe, correlating with the star-formation rate, and the B-band luminosity of the Galaxy [314184]. One can also use for this purpose the direct ratio of the Galactic star formation rate SFRG ≃ 3M ⊙ yr−1 [257Jump To The Next Citation Point401Jump To The Next Citation Point] to the star formation rate on the local Universe −1 SFRloc ≃ 0.03M ⊙ yr [307372]. These estimates yield the relation

−3 ℛV ≈ 0.01ℛG [Mpc ]. (4 )
So for the Galactic merger rate ℛG ∼ 10−4 yr−1 a very optimistic detection rate for binary NSs of about once per 1 – 2 years of observations by the first-generation GW detectors is predicted [49Jump To The Next Citation Point]. This estimate is still uncertain, mostly due to poor knowledge of the luminosity function for faint radio pulsars [192].

Recently, the first results of the search for GWs from coalescing binary systems in the Milky Way and the Magellanic Clouds using data taken by two of the three LIGO interferometers [2Jump To The Next Citation Point] established an observational upper limit to the Galactic binary NS coalescence rate of 2 −1 ℛG < 1.7 × 10 yr. With increasing sensitivity of GW detectors, this limit will be much improved in the nearest future.

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