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Binary Neutron Star Merger GW170817: Shedding Light on the Interior of Neutron Stars
Debades Bandyopadhyay
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DOI: 10.22661/AAPPSBL.2019.29.4.04

Binary Neutron Star Merger GW170817: Shedding Light on the Interior of Neutron Stars

DEBADES BANDYOPADHYAY1
ASTROPARTICLE PHYSICS AND COSMOLOGY DIVISION,
SAHA INSTITUTE OF NUCLEAR PHYSICS, 1/AF
BIDHANNAGAR, KOLKATA-700064, INDIA

1 E-mail address: debades.bandyopadhyay@saha.ac.in

ABSTRACT

The outstanding discovery of the first binary neutron star merger event GW170817 opens up a new window to probe the interior of neutron stars. The multi-messenger nature of this event is exploited to understand the properties of neutron star matter. In particular, we discuss how the tidal deformabilty extracted from the gravitational wave signal puts constraints on the equation of the state of dense matter. Furthermore, an upper bound on the maximum mass of non-rotating neutron stars can be determined if the massive remnant has collapsed to form a black hole.

INTRODUCTION

It took one hundred years following the publication of Einstein's theory of general relativity in 1915 for the existence of gravitational waves to be confirmed. In the course of this journey, many interesting astrophysical discoveries were made. One of the most important discoveries was the first detection of a pulsar by A. Hewish and Jocelyn Bell in 1967 [1]. This detection paved the way for the discovery of first binary pulsar, PSR1916+13, by R. Hulse and J. Taylor in 1974 [2]. Pulsars, which are rotating neutron stars with strong surface magnetic fields, are unique laboratories for testing Einstein's theory of strong gravity. The Hulse-Taylor binary pulsar provided the first evidence of indirect detection of gravitational waves. But there were more surprises in store for us in the golden jubilee year of the first pulsar discovery when gravitational waves were detected from two colliding neutron stars on August 17, 2017 [3]. Once again, Einstein's theory of general relativity came out with flying colors.

The first neutron star merger event, GW170817, was discovered both through gravitational waves and light. The gravitational wave signal was observed by LIGO detectors at Hanford and Livingstone, USA as well as the VIRGO detector at Pisa [3]. A short gamma ray burst (sGRB) was recorded 1.7 s after the merger by the Fermi-GBM [4]. This conclusively demonstrated the link between a neutron star merger event and sGRB. Later, electromagnetic signals in ultraviolet (UV), optical and infrared (IR) bands were detected from the 'kilonova' which was made of the ejected matter.

The discovery of GW170817 and its detection in gravitational waves and across the electromagnetic spectrum resulted in vast amount of information about the sGRB, binary chirp mass, tidal deformability, speed of gravitational waves and the Hubble constant [3, 4]. GW170817 was a shot in the arm for nuclear astrophysics communities around the world because of compositions and the dense matter equation of state (EoS); in neutron stars and r-process nucleosynthesis in the ejected neutron rich matter could be probed [5-7]. The merger event provided crucial information about the remnant and the neutron stars in the binary. The chirp mass was estimated to be . Assuming low spins as found from the observations of neutron stars in our Galaxy, individual neutron star masses in the binary ranges are 1.17-1.60 M. The massive remnant formed in the merger had a mass [3].

We have learned many lessons from the binary neutron star (BNS) merger event GW1790817. It was inferred that a hypermassive neutron star (HMNS) was born and survived for a short duration of time. If the HMNS collapsed to a black hole, this could lead to an upper limit on the maximum mass of non-rotating neutron stars [9]. We know the lower bound on the maximum mass of neutron stars (2.01짹0.04 M) from the galactic pulsar observations [8]. Both bounds on the maximum neutron star mass together put strong constraints on the EoS of dense matter [7, 9, 10]. It has been possible to extract the tidal deformability parameter from gravitational wave data of GW170817 [3]. This gives another opportunity to constrain the EoS. It was shown that too soft or too stiff EoS is ruled out by this parameter [10]. Furthermore, radii of neutron stars were estimated from the tidal deformability parameter [11, 12].

FATE OF MERGER REMNANTS

Binary neutron star mergers might leave behind compact remnants that emit gravitational waves at a few kilohertz. However, no postmerger signal was observed by LIGO and VIRGO detectors due to the lack of sensitivity of the detectors at such high frequencies [3]. In this context, what happened to the compact remnant formed in GW170817 is an important question to ask. A binary neutron star merger event could lead to four possibilities: (a) prompt collapse to a black hole, (b) formation of a hypermassive neutron star (HMNS) that ultimately collapses to a BH in a second or so, (c) birth of a supramassive neutron star (SMNS) that survives for ~ 104 s before collapsing to a BH and (d) a long lived neutron star. The observation of electromagnetic counterparts in GW170817 might hold clues to this riddle.

Electromagnetic Observation and Kilonova

An aggressive electromagnetic observation campaign was launched using various telescopes from around the world as well as space based telescopes following the detection of gravitational waves from GW170817 [13]. The first electromagnetic (EM) counterpart was observed almost 11 hours after the merger event. The early blue emission in UV observations faded away in two days. This was followed by the detection of redder optical and near-IR emissions that lasted for 2-3 weeks. Finally X-ray and radio emissions were reported on the 9th and 16th days, respectively. These observations in UV/Optical/IR bands demanded two separate components in the ejected material. The spectral energy distribution of early fading UV and blue emission is nicely described by a blackbody with a bolometric luminosity ~ 5 횞 1041 erg s-1. This clearly indicates that these features of an EM counterpart associated with GW170817 are best exhibited by the kilonova (KN) model [5]. A KN is powered by the decays of r-process radioactive nuclei synthesized in the ejected matter in a BNS merger.

In a BNS merger, matter is dynamically ejected in the polar direction as well as on the equatorial plane. The faster moving matter ejected in the polar direction originated at the interface of two colliding neutron stars due to the shock heating. This matter was again reprocessed by neutrinos coming from the HMNS. Consequently, this ejecta was neutron-poor and had low opacity. In this case, the electron fraction could be ~ 0.2-0.3. This matter might also originate from the accretion disk. Light nuclei were synthesized in this ejecta through the r-process. A blue kilonova was made of this matter, which could explain the early UV and blue emissions. On the other hand, the dynamically ejected matter due to tidal stripping resided on the equatorial plane. It had a low electron fraction < 0.2 and high opacity due to the presence of heavy elements that were synthesized in the r-process. This neutron-rich ejecta was responsible for red kilonova and longer lasting redder emission. The blue KN accounted for an ejected mass of ~ 10-2 M, whereas the amount of ejected matter in the red KN was ~ 5 횞 10-2 M. The total kinetic energy of the blue and red ejecta was ~ 1051 ergs [6].

It is amply clear that a prompt collapse to a BH could not be compatible with the amount of blue KN ejecta with a high electron fraction as observed in GW170817. Furthermore, a relativistic jet launched in a prompt collapse with negligible delay would encounter almost no material in the polar direction. On the other hand, a HMNS becomes a SMNS after losing its differential rotation completely. A SMNS might have huge rotational energy; ~ 1053 ergs. If it were a long lived SMNS, it would have pumped a significant portion of this rotational energy into the merger surroundings [6, 14], but this is not evident from the energy budget of the GRB and the KN in the case of GW170817. All of these findings demonstrated that the merger remnant was short lived and collapsed to a BH in the end.

In the delayed collapse to a BH, the relativistic jet ploughs through the blue eject, slows down and becomes part of a cocoon. As the jet breaks free of the ejecta, the prompt gamma ray emission happens due to internal dissipation. This could be a plausible explanation for the delay in observing the sGRB after the merger. In this scenario, more matter is ejected from the accretion torus into the equatorial plane.

 

Fig. 1: Mass-radius relations for different EoSs are plotted here. Grey horizontal lines indicate the lower and upper mass limits of millisecond pulsar PSR0740+6620 at 68 % credibility.

UPPER LIMITS ON A NEUTRON STAR'S MAXIMUM MASS

In all possibilities, the compact merger remnant in GW170817 collapsed into a BH in a sec or so [14] from the time of coalescence. If it was so, it would be possible to determine the upper limit on the maximum mass of the non-rotating neutron star .

The HMNS produced in the merger was differentially rotating. As it survived for a second or so, it spinned down emitting gravitational waves. As the HMNS became a uniformly rotating SMNS, it collapsed close to the mass-shedding limit. The maximum mass at the mass shedding limit is related to that of nonrotating . This follows from the universal relation, [18]

(1)

The total binary mass of GW170817 for low spin prior was accurately determined from the chirp mass as ~ 2.74 M. The mass loss due to gravitational waves [3], ejected matter [6, 13] and neutrinos might amount to ~ 0.15 짹0.03 M [16]. The mass of the merger remnant was ~ 2.6 M at the time of collapse to the black hole. If we assume this is the mass of , the upper limit on the maximum mass of the corresponding nonrotating star is obtained from the Eq. (1). The upper limit comes out to be ~ 2.16 M.

The upper limit was also estimated using input from EM observations and numerical simulations following GW170817 by different groups [6, 9, 15, 16]. All those results point to an upper limit on the maximum neutron star mass ≃ 2.17 M. On the other hand, a massive neutron star of at 68% credibility has been reported from observations of millisecond pulsar PSR J0740+6620 by North American Nanohertz Observatory for Gravitational waves (NANOGrav) [17]. This value is very close to the estimated value of the upper limit as extracted from binary neutron star merger GW170817 and its EM counterpart. The pulsar observations along with results of the binary neutron star mergers put strong constraints on the EoS of dense matter in neutron stars.

TIDAL DEFORMABILITY

It was predicted that tidal effects during the late inspiralling phase of binary neutron star merger would be so significant that it could be detectable in gravitational wave detectors [19-21]. The binary neutron star merger event GW170817 provided a great opportunity to extract the combined tidal deformability parameter from gravitational wave signals. The dimensionless combined tidal deformability parameter is defined by,

(2)

where, Λ1 and Λ2 are tidal deformabilities of two neutron stars having the masses m1 and m2, respectively. Tidal deformabilities of neutron stars are sensitive to the EoS of dense matter. The LIGO and VIRGO observations of GW170817 introduced an upper limit on the dimensionless tidal deformability parameter at a 90% confidence interval [3, 4]. A lower limit on was obtained by the EM counterpart of GW170817 [22, 23].

Now we discuss how the EoS could be constrained using the upper limit on the maximum mass of a nonrotating neutron star and the tidal deformabilities of merger components in the following sections.

 

Fig. 2: Tidal deformabilities Λ1 and Λ2 are plotted here. Dash-dotted lines denote 50% (bottom curve) and 90% (upper curve) confidence levels as extracted from the gravitational wave signal. Solid lines represent different EoSs.

CONSTRAINING THE EQUATION OF STATE OF DENSE MATTER

Relativistic mean field (RMF) models with and without density dependent couplings are exploited here to study the EoS of -equilibrated and charge neutral matter. In RMF models, baryon-baryon interaction is mediated by exchange of scalar (σ), vector (ω) and isovector (ρ) mesons to describe neutron star matter from the crust to the core in a unified manner. An extended version of the nuclear statistical equilibrium model is adopted to model the in-homogeneous matter at the sub-saturation density [24] with nucleon-nucleon interaction taken care of by RMF models. In this case, the composition of matter is dictated by the Saha Equation [24, 25]. Furthermore, the high density uniform matter is described by RMF models. Different parametizations of RMF models used in this calculation are SFHo, SFHx, TMA and BHBΛ𝜙 [26]. All these RMF models, except BHBΛ𝜙, deal with matter made of neutrons and protons. The SFHo and SFHx models are further constrained by inputs from radius measurements [27]. In the case of BHBΛ𝜙, the RMF model is extended to include Λ-hyperons; hyperon-hyperon interaction is mediated by 𝜙 mesons and couplings of the model are density dependent [25, 28]. We have also exploited a hadron-quark(HQ1) EoS involving a first order phase transition where the hadron phase, including neutrons, proton, hyperons and Δ resonance, is described by the RMF model with density dependent (DD) couplings and a non-local extension of a Nambu-Jona-Lasino model takes care of the quark phase made of u,d,s quarks [29, 30].

Mass-radius relationships are computed using the above mentioned EoSs and shown in Figure 1. Grey lines represent the lower and upper limits of of recently reported millisecond pulsar PSR0740+6620 at 68% confidence level. The upper bound on the maximum mass of a non-rotating star as obtained from the observations of the EM counterpart of GW170817 falls within the mass limits of PSR0740+6620. Although all EoSs presented here are compatible with 2 M neutron stars, only BHBΛ𝜙 and SFHx EoSs are allowed due to the lower mass limit of PSR0740+6620.

Tidal deformabilities (Λ1 and Λ2) of merger components with masses m1 and m2 are plotted against each other. The upper and lower dash-dotted lines are 90% and 50% confidence levels that were extracted from the gravitational wave signal of GW170817. We have also shown the results of tidal deformabilities calculated using SFHo, SFHx, TMA, BHBΛ𝜙 and HQ1 EoSs. The compactness of neutron stars increases from the right top corner to the left bottom corner. It is noted that SFHo and SFHx EoSs are more compact than other EoSs employed here. Furthermore, we found that SFHo and SFHx EoSs are lying within the region of 50% and 90% confidence levels. BHBΛ𝜙 EoS is residing on or close to 90% confidence level. These three EoSs are compatible with the estimated tidal deformabilities from GW170817. However, stiff EoSs such as TMA and HQ1 are ruled out by the observation.

RADIUS OF A NEUTRON STAR

It is noted that the radius (R) of a neutron star is closely connected to the tidal deformability as defined by

(3)

where k2 is the quadrupolar Love number. The gravitational wave signal from the BNS merger event GW170817 provided a golden opportunity to estimate the radii of merger components, which would be otherwise difficult to determine. Several authors used combined tidal deformability to compute the radii of neutron stars [11, 12, 31- 33]. The LIGO-VIRGO Collaboration obtained neutron star radii employing EoS-insensitive relations as well as the same parametrized EoS for both compact stars [11]. A detailed study of an infinitely large number of EoSs concluded that the radius of a 1.4 M neutron star could be 12.00 ≤ R /km ≤ 13.45 [12]. The radius of a 1.4 M neutron star was shown to be < 13.76 km [31, 32]. De et al. demonstrated that the correlation in deformabilities led to the following radii of neutron stars: 8.7 < R /km < 14.1 [33]. Zhao and Lattimer formulated a relation between the radius of a 1.4 M neutron star and the upper bound of tidal deformability [34].

OUTLOOK

The first detection of a binary neutron star merger event in gravitational waves and light has heralded in a new era of multi-messenger astrophysics. In many respects, we have been very lucky to detect GW170817. If this kind of event happened further away, the EM counterpart would have been so faint that it might not have been detectable. Furthermore, the sky localization was such that the EM counterpart was observed quickly using ground- and space-based telescopes. The third observing (O3) run of LIGO and VIRGO has been ongoing since 1 April, 2019. This run has already generated huge excitement about two possible merger events [35]; one of them could be a binary neutron star merger and the other one might be a NS-BH merger. However, there are no reports of EM counterparts because the sky localization was poor in both cases.

More BNS merger events would tightly constrain the upper bound on the maximum mass of non-rotating neutron stars. Consequently, it would allow certain EoSs and rule out others. It is noted that the galactic binary neutron star systems have chirp masses of 1-1.3 M and low spin at ~ 0.12 [34]. However, we could encounter much higher chirp masses for BNS systems in other galaxies. This could open up interesting possibilities if one of the neutron stars would be very heavy, ~ 2 M, and if the other neutron star would be a lighter one. The massive neutron star might harbor exotic forms of matter such as hyperons and quarks. This would allow us to use observations to evaluate the predictions of EoSs involving exotic matter.

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Debades Bandyopadhyay is a senior professor at the Astroparticle Physics and Cosmology Division, Saha Institute of Nuclear Physics, Kolkata, India. He obtained his PhD from the University of Calcutta. He was the recipient of an Alexander von Humboldt Fellowship and worked at the Institute for Theoretical Physics, Frankfurt University, Germany. His areas of research include topics ranging from nuclei to neutron stars and he is particularly involved in the study of dense matter in neutron star interiors.

 
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