In addition to tests of strong-field gravity through observations of relativistic binary systems (see Section 4.4), estimates of their Galactic population and merger rate are of great interest as one of the prime sources for current gravitational wave detectors such as GEO600 [124], LIGO [208], VIRGO [375] and TAMA [352]. In the following, we review empirical determinations of the population sizes and merging rates of binaries where at least one component is visible as a radio pulsar.
As discussed in Section 2.2, double neutron star (DNS) binaries are expected to be rare. This is certainly
the case; as summarized in Table 1, only around ten DNS binaries are currently known. Although we only
see both neutron stars as pulsars in J0737–3039 [242], we are “certain” of the
identification in five other systems from precise component mass measurements from pulsar timing
observations (see Section 4.4). The other systems listed in Table 1 have eccentric orbits, mass functions
and periastron advance measurements that are consistent with a DNS identification, but for which there is
presently not sufficient component mass information to confirm their nature. One further DNS candidate,
the 95-ms pulsar J1753–2243 (see Table 3), has recently been discovered [189
].
Although the mass function for this pulsar is lower than the DNS systems listed in Table 1, a
neutron star companion cannot be ruled out in this case. Further observations should soon
clarify the nature of this system. We note, however, that the 13.6-day orbital period of this
system means that it will not contribute to gravitational wave inspiral rate calculations discussed
below.
J0737–3039 | J1518+4904 | B1534+12 | J1756–2251 | J1811–1736 | |
![]() |
22.7/2770 | 40.9 | 37.9 | 28.5 | 104.2 |
![]() |
0.102 | 8.6 | 0.4 | 0.32 | 18.8 |
![]() |
0.088 | 0.25 | 0.27 | 0.18 | 0.83 |
![]() ![]() |
8.3/7.7 | 10.3 | 8.4 | 8.6 | 9.0 |
![]() ![]() |
7.9 | 12.4 | 9.4 | 10.2 | 13.0 |
Masses measured? | Yes | No | Yes | Yes | Yes |
B1820–11 | J1829+2456 | J1906+0746 | B1913+16 | B2127+11C | |
![]() |
279.8 | 41.0 | 144.1 | 59.0 | 30.5 |
![]() |
357.8 | 1.18 | 0.17 | 0.3 | 0.3 |
![]() |
0.79 | 0.14 | 0.085 | 0.62 | 0.68 |
![]() ![]() |
6.5 | 10.1 | 5.1 | 8.0 | 8.0 |
![]() ![]() |
15.8 | 10.8 | 8.5 | 8.5 | 8.3 |
Masses measured? | No | No | Yes | Yes | Yes |
Despite the uncertainties in identifying DNS binaries, for the purposes of determining the Galactic
merger rate, the systems for which is less than
(i.e. PSRs J0737–3039,
B1534+12, J1756–2251, J1906+0746,
B1913+16 and B2127+11C) are primarily of interest. Of these
PSR B2127+11C is in the process of being ejected from the globular cluster
M15 [295, 290] and is thought to make only a negligible contribution to the merger rate [286
]. The
general approach with the remaining systems is to derive scale factors for each object, construct the
probability density function of their total population (as outlined in Section 3.2.1) and then divide these by
a reasonable estimate for the lifetime. Getting such estimates is, however, difficult. It has been
proposed [181] that the observable lifetimes for these systems are determined by the timescale on which the
current orbital period is reduced by a factor of two [10]. Below this point, the orbital smearing selection
effect discussed in Section 3.1.3 will render the binary undetectable by current surveys. More recent
work [76
] has suggested that a significant population of highly eccentric binary systems could easily evade
detection due to their short lifetimes before gravitational wave inspiral. If this selection effect is significant,
then the merger rate estimates quoted below could easily be underestimated by a factor of a
few.
The results of the most recent DNS merger rate estimates of this kind [191] are summarised in the left
panel of Figure 19
. The combined Galactic merger rate, dominated by the double pulsar and
J1906+0746 is found to be
, where the uncertainties reflect the 95%
confidence level using the techniques summarised in Section 3.2.2. Extrapolating this number to include
DNS binaries detectable by LIGO in other galaxies [286], the expected event rate is
for
initial LIGO and
for advanced LIGO. Future prospects for detecting gravitational wave
emission from binary neutron star inspirals are therefore very encouraging, especially if the population of
highly eccentric systems is significant [76]. Since much of the uncertainty in the rate estimates
is due to our ignorance of the underlying distribution of double neutron star systems, future
gravitational wave detection could ultimately constrain the properties of this exciting binary
species.
Although the double pulsar system J0737–3039 will not be important for ground-based
detectors until its final coalescence in another 85 Myr, it may be a useful calibration source for the future
space-based detector LISA [215]. It is calculated [178
] that a 1-yr observation with LISA would detect
(albeit with
) the continuous emission at a frequency of 0.2 mHz based on the current
orbital parameters. Although there is the prospect of using LISA to detect similar systems
through their continuous emission, current calculations [178] suggest that significant (
)
detections are not likely. Despite these limitations, it is likely that LISA observations will be able to
place independent constraints on the Galactic DNS binary population after several years of
operation.
Although the population of white dwarf–neutron star (WDNS) binaries in general is substantial, the
fraction which will merge due to gravitational wave emission is small. Like the DNS binaries, the observed
WDNS sample suffers from small-number statistics. From Figure 18, we note that only three WDNS
systems are currently known that will merge within
, PSRs J0751+1807 [238
],
J1757–5322 [103
] and J1141–6545 [186
]. Applying the same techniques as
used for the DNS population, the merging rate contributions of the three systems can be calculated [193
]
and are shown in Figure 19
. The combined Galactic coalescence rate is
(at 68% confidence
interval). This result is not corrected for beaming and therefore should be regarded as a lower
limit on the total event rate. Although the orbital frequencies of these objects at coalescence
are too low to be detected by LIGO, they do fall within the band planned for LISA [215].
Unfortunately, an extrapolation of the Galactic event rate out to distances at which such events
would be detectable by LISA does not suggest that these systems will be a major source of
detection [193
]. Similar conclusions were reached by considering the statistics of low-mass X-ray
binaries [81].
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