Thunderball (about binary neutron-star mergers)

The richest Einstein's laboratory?
Up to now my August holiday series of posts has (not expressly) turned around the ICHEP 2016, reporting glowingly the absence of a sign of any new particle beyond the Standard Model list. I carry on the series today shifting my interest to a subject more exciting because its experimental side is still in its child-birth while its phenomenological side has already entered its exuberant teenage years as one can read in the following review: 
Neutron stars are believed to be born in supernova explosions triggered by the collapse of the iron core in massive stars. Many astronomical observations have revealed that binary neutron stars (BNSs) indeed exist [1] ... Despite this observational evidence of existence, the formation mechanism of a BNS system is not known in detail. The general picture is that in a binary system made of two massive main-sequence stars, the more massive one undergoes a supernova explosion and becomes a neutron star. This is followed by a very uncertain phase in which the neutron star and the main-sequence star evolve in a “common envelope”, that is, with the neutron star orbiting in the extended outer layers of the secondary star [2, 3]. At the end of this stage, also the second main-sequence star undergoes a supernova explosion and, if the stars are still bound after the explosions, a BNS system is formed. The common-envelope phase, though brief, is crucial because in that phase the distance between the stars becomes much smaller as a result of drag, and this allows the birth of BNS systems that are compact enough to merge within a Hubble time, following the dissipation of their angular momentum through the emission of gravitational radiation.
This is undoubtedly an exciting and dynamical time for research on BNS mergers, when many accomplishments have been achieved (especially since 2008), while many more need to be achieved in order to describe such fascinating objects and the related physical phenomena. The first direct detection through the advanced interferometric LIGO detectors [7] of the gravitational-wave signal from what has been interpreted as the inspiral, merger and ringdown of a binary system of black holes [8] marks, in many respects, the beginning of gravitational-wave astronomy. Additional advanced detectors, such as Virgo [9] and KAGRA [10], are going to become operational in the next few years, and we are likely to witness soon also signals from the inspiral and post-merger of neutron-star binaries or neutron-star–black-hole binaries, with a detection rate that has an uncertainty of three orders of magnitude, but is expected to be of several events per year [11].
BNS mergers are rather unique objects in the landscape of relativistic astrophysics as they are expected to be at the origin of several and diverse physical processes, namely: (i) to be significant sources of gravitational radiation, not only during the inspiral, but also during and after the merger; (ii) to be possible progenitors for short-gamma-ray bursts (SGRBs); (iii) to be the possible sources of other electromagnetic and neutrino emission; (iv) to be responsible for the production of a good portion of the very heavy elements in the Universe. When viewed in this light, BNS mergers naturally appear as Einstein’s richest laboratory, where highly nonlinear gravitational effects blend with complex microphysical processes and yield astonishing astrophysical phenomena...
FIG. 1. Schematic diagram illustrating the various stages in the evolution of an equal-mass binary system of neutron stars and indicating how the dynamics changes in time as a function of the initial mass of the binary. Depending on the initial mass, the binary can either collapse promptly to a black hole surrounded by a torus, or give rise to a hypermassive neutron star (HMNS) which ultimately collapses to a black hole and torus, or lead to a HMNS which eventually yields a supramassive neutron star. Also indicated in red are the typical frequencies at which gravitational waves are expected to be emitted [Adapted from Ref. [34]].
Research on the post-merger phase has been undergoing intense development over the last few years because of its importance for linking numerical simulations and astrophysical observations. The (early) post-merger is also the phase in which most of the energy in gravitational waves is emitted, as pointed out in Ref. [222], even though the gravitational waves emitted in this stage are not those that give the largest signal-to-noise ratio, because their frequency range is not in the best sensitivity zone of current interferometric detectors. The numerical description of this stage is far more challenging than the inspiral one because of the highly nonlinear dynamics and of the development of strong, large-scale shocks that inevitably reduce the convergence order, thus requiring far higher resolutions than the ones normally employed. As a result, the accuracy of some quantities computed after the merger is sometimes only marginal. The most notable example of these quantities is the lifetime of the remnant before its collapse to black hole; since this object is only in metastable equilibrium, even small differences in resolution or even grid setup are sufficient to change its dynamical behaviour, accelerating or slowing down its collapse to a black hole. Fortunately, other quantities, such as the spectral properties of the gravitational-wave post-merger emission appear far more robust and insensitive to the numerical details... Since the first general-relativistic simulations of BNS mergers, several works have studied the nature (neutron star or black hole) of the objects resulting from the mergers [14, 15, 43, 170, 177, 223–225]. It is of course important to establish whether a black hole forms promptly after the merger or instead a HMNS forms and lives for long times (more than 0.1 s), because the post-merger gravitational-wave signal in the two cases is clearly different...

... many researchers have taken up the challenge of studying the properties of the binary-merger product, because this may give indications on the ultra-high density EOS, the origin of SGRBs, and even the correct theory of gravity... While detectable differences between simulations that employed different EOSs already appear during the inspiral..., the post-merger phase depends more markedly on the EOS [132, 189, 190, 237–240]. A note of caution is necessary here to say that post-merger waveforms are at rather high frequencies and thus probably only marginally measurable by detectors like Advanced LIGO. Third-generation detectors, such has Einstein Telescope [182], may provide the first realistic opportunity to use gravitational waves to decipher the stellar structure and EOS [241].
In addition to simulating BNS mergers with various EOSs, it is important to find ways to connect future gravitational-wave observation with the EOS of the neutron stars. Recently there have been several suggestions on how to achieve this, based either on the signature represented by the tidal corrections to the orbital phase or on the power spectral density (PSD) of the post-merger gravitational waveforms or on the frequency evolution of the same. 
... there is a widespread consensus that: (i) the post-merger gravitational-wave signal possesses spectral features that are robust and that emerge irrespective of the EOS or the mass ratio; (ii) the frequencies of the peaks in the post-merger PSD can be used to obtain important information on the stellar properties (i.e., mass and radius) and hence represent a very good proxy to deduce the EOS. This is summarised in Fig. 9, which shows the PSDs for the equal-mass binaries with nuclear-physics EOSs reported in Fig. 8. Solid lines of different colours refer to the high-passed waveforms, while the dashed lines refer to the full waveforms. Indicated with coloured circles are the various contact frequencies fcont, while the curves of Advanced LIGO and ET are shown as green and light-blue lines, respectively [190]. The first detailed description of a method for extracting information about the EOS of nuclear matter by carefully investigating the spectral properties of the post-merger signal was provided by Bauswein et al. [268, 269]. After performing a large number of simulations... 
FIG. 8. Gravitational waveforms for equal-mass binaries with nucleonic equations of states, shown in different colours. Each column refers to a given initial gravitational mass. [Reprinted with permission from Ref. [190]. c (2015) by the American Physical Society.]

FIG. 9. Power spectral densities ... for the equal-mass binaries with nucleonic EOSs shown in Fig. 8. Solid lines of different colours refer to the high-passed waveforms, while the dashed lines refer to the full waveforms... the curves of Advanced LIGO and Einstein Telescope are shown as green and light-blue lines, respectively [Reprinted with permission from Ref. [190]. © (2015) by the American Physical Society.]
... the typical scenario leading to short gamma ray bursts (GRBs) assumes that a system composed of a rotating black hole and a surrounding massive torus is formed after the merger [12, 13]. A large number of numerical simulations [14–18] have confirmed that this scenario can be attained through BNS mergers unless the progenitor stars have very small masses [smaller than half of the maximum allowed mass for neutron stars with a given equation of state (EOS)]. Furthermore, if sufficiently massive, the torus could provide the large amount of energy observed in SGRBs, either through neutrino processes or by extracting the rotational energy of the black hole via magnetic fields [13, 19]. Furthermore, if the neutron stars in the binary have relatively large magnetic fields and extended magnetospheres, the inspiral could also be accompanied by a precursor electromagnetic signal [20], while after the merger magnetically confined jet structures may form once a torus is present around the black hole [21–24]. Possible evidence that a BNS merger can be behind the phenomenology associated with SGRBs has emerged recently from the infrared excess in the afterglow curve of Swift’s short gamma-ray burst SGRB 130603B [25, 26], which has been interpreted as a “macronova” emission [27, 28] (sometimes also referred to as “kilonova” [29]), i.e., as due to the radioactive decay of by-products of the r-processed matter from the material ejected in the merger [... r (or rapid) processes are nucleosynthetic processes involving the rapid capture of neutrons.] The observations of the infrared transient in the afterglow of SGRB 130603B [25, 26] is important not only because it provides a potential observational link between two distinct phenomena (i.e., a SGRB explosion and a radioactive decay), but also because it suggests that BNSs can be the site of active and intense nucleosynthesis. Additional evidence in this direction is offered by the Solar system abundance of 244Pu [30, 31] and recent observations of r-process enriched stars in a metal-poor ultra-faint dwarf galaxy [32]. Both of these observations suggest that r-process elements might be preferentially produced in rare/high-yield events such as mergers instead of common/low-yield occurrences such as core-collapse supernovae...
Figure 29. Schematic summary of potential electromagnetic counterparts of binary neutron star mergers, as a function of the observer angle, θobs. Following the merger, a centrifugally supported disc (blue) remains around the central compact object (usually a black hole). Rapid accretion lasting ∼ 1 s powers a collimated relativistic jet, which produces a short gamma ray burst. Due to relativistic beaming, the gamma-ray emission is restricted to observers at small viewing angles. Non-thermal afterglow emission results from the interaction of the jet with the surrounding circum-burst medium (pink). Optical afterglow emission is observable on timescales up to days/weeks by observers with larger viewing angles. Radio afterglow emission is observable from all viewing angles (isotropic) once the jet decelerates to mildly relativistic speeds on a timescale of weeks/months, and can also be produced on timescales of years from sub-relativistic ejecta. Short-lived isotropic optical emission lasting a few days (kilonova/macronova; yellow) can also accompany the merger, powered by the radioactive decay of heavy elements synthesised in the ejecta. [Reproduced from Ref. [421] with permission by the authors.]
... The huge progress accomplished over the last ten years has helped trace a broadbrush picture of BNS mergers that has several sound aspects, among which the most robust in our opinion are the following ones:
• Independently of the fine details of the EOS, of the mass ratio or of the presence of magnetic fields, the merger of a binary system of neutron stars eventually leads to a rapidly rotating black hole with dimensionless spin J/M^2 
 0.7 − 0.8 surrounded by a hot accretion torus with mass Mtorus ∼ 0.01 − 0.1 M . Only very low-mass progenitors whose total mass is below the maximum mass of a (nonrotating) neutron star would not produce a black hole. It is unclear whether such progenitors are statistically important.
The complete gravitational-wave signal from inspiralling and merging BNSs can be computed numerically with precision that is smaller but overall comparable with that available for black holes.
• When considering the inspiral-only part of the gravitational-wave signal, semi-analytical approximations either in the post-Newtonian or EOB approximation, can reproduce the results of numerical-relativity calculations essentially up to the merger.
The gravitational-wave spectrum is marked by precise frequencies, either during the inspiral or after the merger that exhibit a “quasi-universal” behaviour, that is, a behaviour that is only mildly dependent on the EOS.
The result of the merger, i.e., the binary-merger product, is a highly massive and differentially rotating neutron star. The lifetime of the binary-merger product depends on a number of factors, including the mass of the progenitors, their mass ratio and EOS, as well as the role played by magnetic fields and neutrino losses. While sufficiently large initial masses can yield a prompt collapse at the merger, smaller masses can lead to a binary-merger product surviving hundreds of seconds and possibly more.
• When considering magnetic fields of realistic strengths endowing the stars prior to the merger, the correction imprinted by them on the gravitational-wave signal during the inspiral are too small to be detected from advanced gravitational-wave detectors. Electromagnetic signals could be produced before the merger, but these are probably too weak to be detected from cosmological distances.
Magnetic fields are expected to be amplified both at the merger (via Kelvin-Helmholtz instability), after it and before the collapse and after the formation of a black-hole–torus system (in all cases via a magneto-rotational instability or a dynamo action converting small-scale fields into large-scale ones). The final and effective amplification of the resulting magnetic fields is still uncertain, although it should be of at least two-three orders of magnitude.
• The interaction of amplified magnetic fields and accretion in the black-hole–torus system leads to the formation of a magnetically confined plasma along the polar directions of the black hole. Under suitable conditions, the plasma in this funnel may be launched to relativistic speeds (still unobserved in simulations).
Matter is expected to be ejected both at the merger and subsequently as a result of a combination of processes: tidal and dynamical mass ejection, magnetically driven winds, neutrinodriven winds, shock-heating winds. Overall, the matter ejected from binaries in quasi-circular orbits amounts to Mejected ∼ 0.001 − 0.01 M , while binaries in eccentric orbits can yield up to one order of magnitude more.
The ejected and unbound matter is expected to undergo nuclear transformations that are mediated by the emission and absorption of neutrinos. Rapid neutron-capture processes (r-processes) will then lead to nucleosynthetic yields that are insensitive to input physics or merger type in the regions of the second and third r-process peaks, matching the Solar abundances surprisingly well. However, first-peak elements are difficult to explain without invoking contributions from either neutrino and viscously-driven winds operating on longer timescales after the merger, or from core-collapse supernovae.
• The radioactive decay of the ejected matter or its interaction with the interstellar medium are likely to yield afterglows in the infrared or radio bands that are expected to follow the merger after timescales that go from several days to years


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