Merging NS-NS and BH-NS binaries, i.e., those for which the merger timescale is smaller than the Hubble
time, are typically formed through similar evolutionary channels in stellar field populations of galaxies [37]
(both may also be formed through dynamical processes in the high-density cores of some star clusters, but
the overall populations are smaller and more poorly constrained; see [258] for a review). It is difficult to
describe the evolutionary pathways that form NS-NS binaries without discussing BH-NS binaries as well,
and it is important to note that the joint distribution of parameters such as merger rates and component
masses that we could derive from simultaneous GW and EM observations will constrain the
underlying physics of binary stellar evolution much more tightly than observing either source
alone.
Population synthesis calculations for both merging NS-NS and BH-NS binaries typically favor the
standard channel in which the first-born compact object goes through a common-envelope (CE)
phase, although other models have been proposed, including recent ones where the progenitor
binary is assumed to have very nearly-equal mass components that leave the main sequence and
enter a CE phase prior to either undergoing a supernova [42, 54]. Simulations of this latter
process have shown that close NS-NS systems could indeed be produced by twin giant stars with
core masses
, though twin main sequence stars typically merge during the contact
phase [176].
In the standard channel (see, e.g., [44, 178], and Figure 1
for an illustration of the process), the
progenitor system is a high-mass binary (with both stars of mass
to ensure a pair of
supernovae). The more massive primary evolves over just a few million years before it leaves the main
sequence, passes through its giant phase, and undergoes a Type Ib, Ic, or II supernova, leaving behind what
will become the heavier compact object (CO): the BH in a BH-NS binary or the more massive NS in an
NS-NS binary. The secondary then evolves off the main sequence in turn, triggering a CE phase when it
reaches the giant phase and overflows its Roche lobe. Dynamical friction shrinks the binary separation
dramatically, until sufficient energy is released to expel the envelope. Without this step, binaries would
remain too wide to merge through the emission of GWs within a Hubble time. Eventually, the
exposed, Helium-rich core of the secondary undergoes a supernova, either unbinding the system or
leaving behind a tight binary, depending on the magnitude and orientation of the supernova
kick.
This evolutionary pathway has important effects on the physical parameters of NS-NS and BH-NS binaries, leading to preferred regions in phase space. The primary, which can accrete some matter during the CE phase, or during an episode of stable mass transfer from the companion Helium star, should be spun up to rapid rotation (see [178] for a review). In NS-NS binaries, we expect that this process will also reduce the magnetic field of the primary down to levels seen in “recycled” pulsars, typically up to four orders of magnitude lower than for young pulsars [180, 73]. The secondary NS, which never undergoes accretion, is likely to spin down rapidly from its nascent value, but is likelier to maintain a stronger magnetic field.
While this evolutionary scenario has been well studied for several decades, many aspects remain highly uncertain. In particular:
Given all these uncertainties, it is reassuring that most estimates of the NS-NS and BH-NS merger rate,
expressed either as a rate of mergers per Myr per “Milky Way equivalent galaxy” or as a predicted
detection rate for LIGO (the Laser Interferometer Gravitational-Wave Observatory) and Virgo (see
Section 5.5 below), agree to within 1 – 2 orders of magnitude, which is comparable to the typical
uncertainties that remain once all possible sources of error are folded into a population synthesis model. In
Table 1, we show the predicted detection rates of NS-NS and BH-NS mergers for both the first generation
LIGO detectors (“LIGO”), which ran at essentially their design specifications [2], and the Advanced LIGO
(“AdLIGO”) configuration due to go online in 2015 [292]. We note that the methods used to generate these
results varied widely. In [143], the authors used the observed parameters of close binary pulsar systems to
estimate the Galactic NS-NS merger rate empirically (such results do not constrain the BH-NS merger
rate). In [198
, 128
], the two groups independently estimated the binary merger rate from the observed
statistics of SGRBs. In these cases, one does not get an independent prediction for the NS-NS and
BH-NS merger rate, but rather some linear combination of the two. In both cases, the authors
estimated that, if NS-NS and BH-NS mergers are roughly equal contributors to the observed
SGRB sample, LIGO will detect about an order of magnitude more BH-NS mergers since their
higher mass allows them to be seen over a much larger volume of the Universe. As they both
noted, should either type of system dominate the SGRB sample, we would expect a doubling of
LIGO detections for that class, and lose our ability to constrain the rate of the other using this
method. Many population synthesis models have attempted to understand binary evolution
within our galaxy by starting from a basic parameter survey of the various assumptions made
about CE evolution, supernova kick distributions, and other free parameters. In [323
, 79
],
population synthesis models are normalized by estimates of the star formation history of the
Milky Way. In [140
, 218
], parameter choices are judged based on their ability to reproduce the
observed Galactic binary pulsar sample, which allows posterior probabilities to be applied to each
model in a Bayesian framework. A review by the LIGO collaboration of this issue may be found
in [1
].
Author |
NS-NS
|
BH-NS
|
Method | ||
LIGO | AdLIGO | LIGO | AdLIGO | ||
Kim et al. [143] | 5e-3 | 27 | Empirical | ||
Nakar et al. [198] | ![]() |
![]() |
SGRBs | ||
Guetta & Stella [128] | 7.0e-3 | 22 | 7.0e-2 | 220 | SGRBs |
Voss & Tauris [323] | 6.0e-4 | 2.0 | 1.2e-3 | 4.0 | Pop. Synth. – SFR |
de Freitas Pacheco et al. [79] | 8.0e-4 | 6.0 | Pop. Synth. – SFR | ||
Kalogera et al. [140] | 1.0e-2 | 35 | 4.0e-3 | 20 | Pop. Synth. – NS-NS |
O’Shaughnessy et al. [218] | 1.0e-2 | 10 | 1.0e-2 | 10 | Pop. Synth. – NS-NS |
Should the next generation of GW interferometers begin to detect a statistically significant number of merger events including NSs, it should be possible to constrain several astrophysical parameters describing binary evolution much more accurately. These include
While Advanced LIGO or another interferometer will likely be required to make the first direct
observations of NS-NS mergers and their immediate aftermath, it is possible that more than just the
high-energy prompt emission from mergers may be observable using EM telescopes. Although the particular
candidate source they identified resulted from a pointing error [110], Nakar and Piran suggest that the mass
ejection from mergers should yield an observable radio afterglow [200], although the afterglows may be too
faint to be seen by current telescopes at the observed distances of existing localized SGRBs [190]. While
such outbursts could also result from a supernova, the luminosity required would be an order of magnitude
larger than those previously observed. Given the length and timescales characterizing radio bursts, no
NS-NS simulation has been able to address the model directly, but it certainly seems plausible
that the time-variable magnetic fields within a stable hypermassive remnant could generate
enough EM energy to power the resulting radio burst [280]. If mergers produce sufficiently
large ejecta masses,
, r-process nuclear reactions may produce a “kilonova”
afterglow one day after a merger with a V-band optical luminosity
(roughly
1000 times brighter than a classical nova) [191]. These potential EM observations of mergers
are likely to spur further research into the amount and velocity of merger ejecta, which could
then be coupled to a larger-scale astrophysical simulation of the potential optical and radio
afterglows.
http://www.livingreviews.org/lrr-2012-8 |
Living Rev. Relativity 15, (2012), 8
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