Mpc, it is hoped that merging NS-NS binaries will prove numerous
enough to make a detection likely by the present and future
generation of gravitational wave detectors [153,
139].
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 [125
]. 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 [78], B1534+12 [166], which are in the disk of our Galaxy, and B2127+11C which is
located in the Globular Cluster M15 [128].
Early estimates indicated a Galactic rate as high as
yr
[45]. 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 [50]. 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 [120]. 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 [22] 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 (dunc@mpifr-bonn.mpg.de) http://www.livingreviews.org/lrr-1998-10 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |
