Of key importance here is the rate of NS-NS mergers in the Galaxy which can then be extrapolated to more distant galaxies to provide event rate predictions for gravity wave detectors . Statistical studies of the Galactic population of NS-NS systems are, however, hampered by small number statistics. The present sample summarised in Table 1 includes only three systems which have merging times significantly smaller than a Hubble time-scale viz: B1913+16 , B1534+12 , which are in the disk of our Galaxy, and B2127+11C which is located in the Globular Cluster M15 .
Early estimates indicated a Galactic rate as high as yr . These rather optimistic estimates had to be reduced by a factor of 30 [117, 125] following revised scale factor calculations based on the surveys that discovered PSRs B1534+12 and B2127+11C. These estimates implied that many new NS-NS systems should be found by the all-sky millisecond pulsar surveys . This was surprisingly not the case; the only discovery being PSR J1518+4904 -- a mildly relativistic binary system that will merge on a time-scale of yr . The most recent estimates of the NS-NS population, which take into account the lack of detections by the all-sky surveys, place a lower limit on the Galactic NS-NS population of and a merging rate of yr [50, 160].
It is important to stress that these estimates are insensitive to systems fainter than some defined luminosity limit and therefore only provide a lower limit to . Bailes  proposed a means of estimating an upper bound on . Bailes postulates that the birth rates of normal pulsars in NS-NS systems must be equal to those of recycled pulsars in NS-NS systems. We know of only one NS-NS system in which the normal pulsar is visible: B2303+46 (see Table 1). This system will, however, not merge within a Hubble time-scale. In this case, cannot be larger than , where is the number of observed normal pulsars and is their birth rate. Inserting the most recent numbers into this equation ( ; yr ) yields an upper limit of the formation rate of merging NS-NS binaries of yr .
An independent method of estimating can be made via population syntheses of binary stars [89, 55, 132, 158]. The essence of this approach is to follow the orbital and stellar evolution of a large number () of binary star systems of varying mass and orbital separation. Based on a number of plausible physical arguments it is possible to predict the relative fractions of the various types of binary systems containing neutron stars. The most recent estimates using this method [92, 127] find yr . Given the uncertainties involved, we conclude that both methods yield consistent results i.e. :
Extrapolations including Galaxies out to Mpc suggest that the rate of NS-NS mergers will be high enough to yield detection rates of several sources per year. Ultimately, the detection statistics from the gravity wave detectors should provide far tighter constraints on the NS-NS merging rate.
|Binary and Millisecond Pulsars
D. R. Lorimer (firstname.lastname@example.org)
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