2 Evolutionary Channels and Population Estimates

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 [37Jump To The Next Citation Point] (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 [42Jump To The Next Citation Point, 54]. Simulations of this latter process have shown that close NS-NS systems could indeed be produced by twin giant stars with core masses ≳ 0.15M ⊙, though twin main sequence stars typically merge during the contact phase [176].

In the standard channel (see, e.g., [44, 178Jump To The Next Citation Point], and Figure 1View Image for an illustration of the process), the progenitor system is a high-mass binary (with both stars of mass M ≳ 8 –10M ⊙ 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.

View Image

Figure 1: Cartoon showing standard formation channels for close NS-NS binaries through binary stellar evolution. Image reproduced from [178Jump To The Next Citation Point].

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 [143Jump To The Next Citation Point], 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 [198Jump To The Next Citation Point, 128Jump To The Next Citation Point], 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 [323Jump To The Next Citation Point, 79Jump To The Next Citation Point], population synthesis models are normalized by estimates of the star formation history of the Milky Way. In [140Jump To The Next Citation Point, 218Jump To The Next Citation Point], 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 [1Jump To The Next Citation Point].

Table 1: Estimated initial and advanced LIGO rates for BH-NS and NS-NS mergers from population synthesis calculations and other methods. The methods used are, in order, empirical constraints from the observed sample of binary pulsars (‘Empirical’), constraints on the combined NS-NS/BH-NS merger rate assuming that they are the progenitors of short-hard gamma-ray bursts (‘SGRBs’), population synthesis models calibrated to the star formation rate in the Milky Way (‘Pop. Synth. – SFR’), and population synthesis calibrated against the observed Galactic binary pulsar sample (‘Pop. Synth. – NS-NS’). We note that observations of binary pulsars do not yield constraints for BH-NS binaries. SGRB observations may produce constraints on NS-NS merger rates, BH-NS, merger rates, or both, depending on which sources are the true progenitors, but this remains unclear. Therefore, the table quotes results assuming a roughly equal split between the two. The official review of these results and their implications by the LIGO/Virgo Scientific Collaborations may be found in [1].
Kim et al. [143] 5e-3 27 Empirical
Nakar et al. [198] ∼ 2 ∼ 20.0 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 [280Jump To The Next Citation Point]. If mergers produce sufficiently large ejecta masses, − 3 Mej ≳ 10 M ⊙, r-process nuclear reactions may produce a “kilonova” afterglow one day after a merger with a V-band optical luminosity 41 νx ν ≈ 10 erg∕s (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.

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