> home > APCTP Section
 
Physics of Dense Matter -From Rare Isotopes to Neutron Stars
Chang-Hwan Lee
File 1 : Vol29_No6_APCTP Section-3.pdf (0 byte)

DOI: 10.22661/AAPPSBL.2019.29.6.46

Physics of Dense Matter -From Rare Isotopes to Neutron Stars

CHANG-HWAN LEE1
1DEPARTMENT OF PHYSICS, PUSAN NATIONAL UNIVERSITY, BUSAN 46241, KOREA

After the first detection of gravitational waves from the merger of a neutron star binary GW170817 which allowed the first measurement of tidal deformability of neutron stars, investigations of the neutron star equations of state that determine the inner structure of neutron stars have increased dramatically. In addition, electromagnetic wave observations at various wave lengths from the same system (GRB170817A and AT 2017gfo) proved the possibility that nuclear and hadronic physics can be studied extensively from neutron star observations. On the other hand, heavy ion collision experiment facilities, including RAON (Rare isotope Accelerator complex for ON-line experiments) which is being built in Korea, are expected to provide excellent environments for the study of dense matter physics. In this review, I summarize recent research activities in Korea in the field of astro-hadron physics focusing on the structure of finite nuclei, rare isotope collisions, and dense stellar matter in neutron stars. Structures of finite nuclei can give constraints to the nuclear matter equations of state near nuclear saturation density (ρ0), rare isotope collisions can give constrains up to 2ρ0, and neutron star can give constraints up to several times nuclear saturation density.

INTRODUCTION

Neutron stars have been a major research subject in the field of astrophysics because they can provide important information on the properties of the extreme dense QCD matter. Even though the inner structure of a neutron star is not completely understood, yet. it is believed that the central density of neutron stars can reach several times the normal nuclear matter saturation density ρ0. At such high densities, exotic states with kaons, hyperons, deconfined quarks can appear. Before the detection of gravitational waves from the merger of a neutron star binary, masses, radii, glitches, and cooling of neutron stars were the main observable quantities [1-3]. Based on these observations, various neutron star equations of state have been suggested.

Three high-mass (> 2.0M) neutron stars have been observed in neutron star-white dwarf binaries [4-6], while well-measured neutron star masses in double neutron star binaries are still consistent with the limit of 1.5M [7]. These observations indicate that the masses of neutron stars may strongly depend on the evolution of progenitors of neutron star binaries. Before the observation of high-mass neutron stars, based on the masses in double neutron star binaries, many soft equation of states with strangeness (kaons, hyperons, and strange quarks) which give lower maximum neutron star mass (< 2.0M) have been suggested [1, 3]. However, observations of high-mass neutron stars ruled out soft equations of state, which cannot explain the existence of neutron stars with mass 2.14M [6]. In order to have high-mass neutron stars, a stiff equation of state at high densities, which delays the appearance of hyperons (and kaons), is required. This problem is pharased as 'hyperon puzzle'. The origin of stiff equations of state at high density is still unknown and the 'hyperon puzzle' remains as an open problem. Radii of neutron stars have been estimated in low-mass X-ray binaries (LMXB). However, the uncertainties in the radii estimates are lager than those in the mass estimates. LMXB is composed of a neutron star and its companion and the material from the companion is accreted to the neutron star through an accretion disk. NICER (Neutron Star Interior Composition Explorer) will be able to provide radii within 5 % in near future.

Gravitational waves opened a new window for the neutron star research. Gravitational waves from the merger of a neutron star binary GW170817 have been detected by LIGO [8, 9] followed by a series of electromagnetic wave observations including gamma-ray burst GRB 170817A [10] and afterglows AT2017gfo [11]. These observations confirmed the existence of kilonova [12], and opened a new era of multi-messenger astronomy and astrophysics [12]. The existence of kilonova has been expected from gamma-ray burst models. When a gamma-ray burst was generated along the rotation axis, the beaming angle widens as time goes on and photon energy decreases. So, if the line of sight is off the rotation axis, one may be able to observe the kilonova with afterglows from X-ray to radio. Electromagnetic observations of 170817AT cover a wide range of wavelengths from X-ray to radio. From these observation, the amount of produced heavy nuclei has been estimated because the merging nuclei can be a good site for the r-process [12].

By analyzing the accumulated phase shift of gravitational waves in GW170817, in addition to the masses of the two neutron stars, the tidal deformabilities of neutron stars has been obtained for the first time. Estimated masses of neutron stars in the source of GW170817 are still consistent with the 1.5M limit for double neutron star binaries. Tidal deformability combined with two neutron star masses favors softer equations of states excluding very stiff equations of state. In Fig. 1, two constraints to the neutron star equations of states in the M-R diagram are indicated. High-mass neutron stars in neutron star-white dwarf binaries exclude too soft (lowerleft) equations of state and the tidal deformability of neu-tron stars and the existence of particles with strangeness exclude too stiff (upper-right) neutron star equations of state [13]. With future observations of the properties of neutron stars, the two constraints may narrow down the allowed regions.

Constraints on the neutron star equations of state can also be provided by ground-based heavy-ion experimental facilities. Rare isotope collision experiments with beam energies of a few hundred MeV per nucleon will be able produce high density nuclear matter up to 2ρ0. Since the tidal deformability is sensitive to the equation of state near 2ρ0, the results from rare isotope experiments will be able to provide constraints on the neutron star equation of state [14, 15]. New rare isotope experiment facilities such as RAON (Rare isotope Accelerator complex for ON-line experiments) which is under construction in Korea will be able to provide new results in a few years. For the simulation of rare isotope collisions, a new transport code DJBUU (DaeJeon Boltzmann-Uehling-Uhlenbeck) has been developed [16]. Since DJBUU is newly developed, it can be used to test various nuclear models and to simulate collision experiments which are expected at rare isotope facilities such as RAON. DJBUU will be able to provide valuable results by the time RAON is perform-ing rare isotope collision experiments. In addition, the PREX II experiment measured the neutron skin depth of 208Pb within 1% accuracy and CREX will measure the neutron skin depth of 48Ca within 0.6% accuracy. These measurements will be able to give better constraints on the neutron star equation of state near saturation density ρ0 [15]. When the new results from PREX II and CREX are released, the new energy density functionals KIDS (Korea-IBS-Daegu-Sungkyunkwan) model, which has been developed in Korea [13, 17-19], will be able to provide better constraints on the low density equation of state. Deformation of nuclei is another quantity which can be used to constrain the nuclear matter equation of state around ρ0. The DRHBc (Deformed Relativistic Hartree-Bogoliubov theory in continuum) project will be able to provide independent constraints.

In this article, firstly I review recent research activities on deformed nuclei and rare isotope collisions that can be used to constrain low and medium density (< 2M) effective nuclear matter theory. Next, I review the research on the neutron stars and relevant problelms. Finally, I discuss future prospects.

FROM RARE ISOTOPES TO NEUTRON STARS

A. Effective Models for Dense Nuclear Matter

In order to describe finite nuclei and dense matter, various effective theories have been introduced. For the hadronic sector, relativistic mean field approaches, chiral perturbation theory, Skyrme interactions, energy density functionals, etc., have been studied to describe the low and medium density nuclear matter. For high density QCD matter, quarks and gluons are introduced as explicit degrees of freedom with effective interaction terms. The main uncertainty in describing dense matter comes from the nature of strong interactions that govern the interactions for hadrons and quarks.

 

Fig. 1: Constraints to the neutron star equations of state in M-R diagram. Background figure with selected equations of state is taken from Lim et al. [2]. Horizonal lines indicate three high-mass neutron stars observed in neutron star-white dwarf binaries; PSR J0740+6620 with 2.14M [6], PSR J0348+0432 with 2.01짹0.04M [5], and PSR J1614-2230 with 1.97 짹 0.04M [4]. Observations of high-mass (> 2M) neutron stars exclude very soft equations of state, and the observation of tidal deformability and the possibility of strangeness in the core exclude very stiff equations of state. These constraints narrowed down the allowed region of neutron star equations of state.

Independently of equations of states, properties of dense nuclear matter near saturation density can be parameterized as [13, 20]

(1)

where E0 is the binding energy per particle, K0 is the imcompressibility (compression modulus), Q0 is skewness, y ≡ (ρ - ρ0)/3ρ0 is the dimensionless density parameter, and xρp /(ρp + ρn) is the proton fraction.

 

Table I: Properties of nuclear matter near ρ0. Exp/Emp values are quoted from Ref. [21]. KτKsym-6L-(Q0/K0)L.

 

The symmetry energy S(ρ) is conventionally expanded as

(2)

Experimental or empirical values of these parameters are summarized in Table I [21]. As one can see from the table, the uncertainties are still quite large. Experiments on the neutron skin depth, such as PREX II and CREX, and rare isotope experiments, such as RAON, and neutron star observations will be able to provide better constraints on some of these parameters.

B. Finite Nuclei and Rare Isotope Collisions

Among many effective models, recently developed energy density functional KIDS has an advantage that the physical parameters in Eq.(1) and Eq.(2) can be easily tested. Since KIDS is based on the systematic expansion in terms of the ratio of Fermi momentum to the rho meson mass, kF/mρ, many parameters that cannot be derived microscopically have been introduced. However, these parameters can be fitted by the experimental results for a large number of isotopes of various nuclei. Since the number of isotopes is much bigger than the number of parameters introduced in the effective model, one can find best-fit parameters, and then the model can be extended to describe neutron star equations of state.

Another approach we are currently working on to establish the low-density effective theory is DRHBc, which is a joint project between China and Korea. In Korea, researchers from IBS, Sungkyunkwan University, Soongsil University, and Pusan National University are participating in this project. There exist many calculations of the properties of nuclei with spherical shape [22], but rare isotopes far from double magic nuclei are expected to have deformed shape in the ground state. Since RAON is planning to perform collision experiments using rare isotopes, understanding the shape of rare isotopes is very important to understand the experimental results and establish valid effective models for nuclear matter at low and medium nuclear matter density (< 2ρ0).

In order to understand the results of rare isotope collision experiments, a new transport code DJBUU has been developed in collaboration with researchers from IBS, Pusan National University and McGill University [16]. There exist many Boltzmann-type transport codes. However, those codes have been developed over a long period and it is not easy to implement new features of modern computer languages and test various effective models including KIDS. Because the new rare isotope experimental facility RAON is under construction in Korea, it is necessary and timely to develop a new transport code which can be used for RAON and other experiments. When the DJBUU project was initiated, the TCCP (Transport Code Comparison Project) had been already developed to compare various transport codes. TCCP provided valuable results which can be used to test the validity of DJBUU. In the near future, new results from the DJBUU project will be available.

Since the maximum density in rare isotope collisions can reach ~ 2ρ0, results from the DJBUU project in combination with the results for finite nuclei can be used to establish effective nuclear models which are valid up to 2ρ0. One of the main research topics for RAON is symmetry energy. Symmetry energies in the available effective nuclear models vary significantly even near 2ρ0. Therefore, if symmetry energy can be tested by future experiments, it will provide valuable constraints to the effective models.

C. Neutron Star Structure

As discussed above, the validity of nuclear effective models up to 2ρ0 can tested by finite nuclei and rare isotope collision experiments. However, the major uncertainties in understanding the neutron star equation of state lie in the high-density (> 2ρ0) behavior of nuclear effective models and the possibility of phase transitions to quark matter. Because the central densities of neutron stars can reach several times the nuclear saturation density ρ0, many exotic particles including strange quarks can exist at such high densities.

The dimensionless tidal deformability Λ parametrizes the correlation between the induced quadrupole moment of a neutron star and the external quadrupolar tidal field Ɛij which induces the deformation of a neutron star in response. The dimensionless tidal deformability is defined as

(3)

In the mass range of neutron stars that are observed, the dimensionless tidal deformability is approximately given as

(4)

where CM /R is the compactness of a neutron star. From Fig. 1, in general, one can see that the radii of neutron stars decrease as the mass increases. Therefore the tidal deformability is smaller for higher mass neutron stars. This behavior of tidal deformability can be easily understood because the extended object can have a bigger tidal effect in response to the external gravitational field while the dense core has smaller effet. Because the extended outer part of a neutron star is composed of low density nuclear matter, the tidal deformability can be a probe of nuclear matter around 2ρ0 [14]. Thus properties of finite nuclei, rare isotope collisions and tidal deformabilities of neutron stars will provide constraints on nuclear matter effective models up to 2ρ0. In Kim et al. [13], we investigated the tidal deformability of neutron stars with realistic nuclear energy functions for selected Skyrme type models and the KIDS model. In this work, all the selected models satisfy the constraints of 2M neutron stars [4, 5] and the tidal deformability of neutron stars [8, 9]

High-density (> 2ρ0) nuclear matter can be tested mainly by neutron stars. In order to explain the 2.14M neutron star that is observed in a neutron star-white dwarf binary [6], a stiff high-density equation of state (with large sound speed at high densities) is required [14, 15]. Since observable quantities of neutron stars are limited, in addition to the mass measurements, accurate measurements of radii of neutron stars are essential to test the high-density nuclear effective models. New radii measurements from NICER may help to understand the high-density equation of state.

From the multi-messenger observations of GW190817, the amount of material ejected during the collapse has been estimated and gave constraint on the lower limit of the tidal deformability [23]. The existence of the electromagnetic afterglows indicate that the merging neutron stars might not have gone through the prompt collapse into a black hole. In addition, from the reanalysis of the gravitational wave signals of GW170817, the existence of a hypermassive magnetar which is more massive than the usual neutron star has been suggested [24]. Possible candidates are a rapidly rotating neutron star with high temperature and strong magnetic field or a hybrid neutron star with a phase transition to quark states at the core.

In summary, neutron stars will be able to provide constraints to the nuclear matter equations of state up to several times the nuclear saturation density. Observable quantities include masses and radii of neutron stars, tidal deformability of neutron stars, and the electromagnetic afterglows. Since we have only one observation of a binary neutron star merger, GW170817, we cannot make any firm conclusion about the high-density nuclear matter equation of state. Future multi-messenger observations of neutron stars will improve understanding of the high-density nuclear matter equation of state.

 

Fig. 2: Binary evolution with supercritical accretion [27, 28]. (a) Production of double neutron star binaries with similar masses. (b) Production of neutron star-white dwarf binaries as a consequence of common envelope evolution and the supercritical accretion [26].

 



Fig. 3: Possibility of three classes of neutron star binaries [27, 28].

D. Formation of Neutron Star Binaries

All the high-mass neutron stars have been observed in neutron star-white dwarf binaries [4-6] while well-measured neutron star masses in double neutron star binaries are less than 1.5M. This indicates that the observed neutron star masses strongly depend on the evolution processes. In Fig. 2.(a), a possible formation scenario for double neutron star binaries is summarized. If the masses of progenitors (A and B) are nearly equal, the evolution of the two stars is closely similar and the neutron stars will form nearly at the same time. Therefore, there is no time for accretion after neutron star formation. If the neutron star masses in close binaries are less than 1.5M [25], this evolution process will produce double neutron star binaries with nearly equal masses (< 1.5M). In Fig. 2.(b), a possible formation scenario for high mass neutron stars in neutron star-white dwarf binaries is summarized. If the mass difference of the progenitors is big enough, when the more massive star evolves to leave a neutron star at the center, the companion is still on the main sequence. Therefore, during the evolution of the companion, the first-born neutron star can accrete a significant amount of matter during the common envelope evolution. Finally it becomes a high-mass neutron star if supercritical accretion is allowed [26]. The key to supercritical accretion is the temperature of the accreting material near the neutron star surface. If the temperature can increase beyond 1 MeV, thermal neutrino production dominates over thermal photon production. Because the neutrino barely interacts with accreting material, thermal neutrino production removes the energy and pressure out of the accreting gas and the amount of material accreted to the neutron star can be much larger than the Eddington limit [26-28]. In Fig. 3, high mass neutron stars (PSR J0740+6620, PSR J1614-2230, PSR J0348+0432) are marked in red. Double neutron star binaries with smaller masses (< 1.5M) have been observed (lower-right circle), high-mass neutron stars in neutron star-white dwarf binaries have been observed (middle-left). If this scenario with supercritical accretion holds, another class of neutron star binaries can exist. For a binary in this class, one neutron star is a typical neutron star with mass around or less than 1.5M, while the companion is a high-mass neutron star or black hole with mass larger than 2M (upper-right). This new class of neutron binaries will be a source of gravitational waves with larger chirp masses.

Note that in this scenario the neutron star binaries, which are good sources of gravitational waves, have at least one neutron star with mass around 1.5M or a bit smaller. Because lower mass neutron stars can have bigger tidal deformabilities (with higher detectability) as in Eq. (4), any double neutron star binary will be a good source for tidal deformability if the source distance is close enough. Even though the probability is very low, the possibility of double high-mass neutron star binary formation still exists. If the progenitor of a neutron star evolves as a single star or in a wide binary, the mass of the neutron star can be bigger than 1.5M when it is born [25] (even without supercritical accretion after formation). Such high mass neutron stars can form close binaries by stellar interactions in globular clusters.

PROSPECT

Two candidates for the mergers of neutron star binaries (detected on April 25th and 26th, 2019) have been reported by the LSC-Virgo collaboration [29]. The first one (April 25th) is estimated to be a neutron star-neutron star merger event and the second one (April 26th) to be neutron star-black hole merger event. However, the distances to their sources are about 153 Mpc and 368 Mpc, respectively, much larger than 40 Mpc (distance to the source of GW170817). Hence, no afterglows have been observed. We need more close events to have afterglow observations and to have tidal deformability estimation. In addition, since the tidal deformabilities of high mass neutron stars are much small than those for lighter ones, we need observations of lower mass neutron stars for good estimates of tidal deformability.

For the study of dense matter physics in astro-hadron physics, the BUD2 (Busan-Ulsan-Daegu-Daejeon) Collaboration has been established in Korea. The collaboration name is derived from the city names. Main projects in the BUD2 Collaboration include KIDS, DRHBc and DJBUU. KIDS is a new energy density functional approach developed in Korea [13, 17-19]. DRHBc is an international collaboration project between China and Korea. The main goal of DRHBc is to understand and predict the structure of deformed nuclei. DJBUU is a new Boltzmann-type transport code which has been developed in collaboration with the nuclear physics theory group in McGill University [16]. All these theoretical activities combined with new experimental results from RAON will enhance our understanding of the dense matter equation of state that can be applied to neutron stars.

Acknowledgments: This work was supported by National Research Foundation of Korea (NRF) grants funded by the Korea government (Ministry of Sciencd and ICT and Ministry of Education) (No. 2016R1A5A1013277 and No. 2018R1D1A1B07048599).

References

[1] Y. Lim, K. Kwak, C. H. Hyun, and C.-H. Lee, Phys. Rev. C 89, 055804 (2014).
[2] Y. Lim, C. H. Hyun, C.-H. Lee, Int. J. Mod. Phys. E 26, 1750015 (2017).
[3] Y. Lim, C.-H. Lee, Y. Oh, Phys. Rev. D 97, 023010 (2018).
[4] P. Demorest, T. Pennucci, R. Ransom, M. Roberts, and J. W. T. Hessels, Nature 467, 1081 (2010).
[5] J. Antoniadis et al., Science 340, 448 (2013).
[6] H. T. Cromartie, et al., Nature Astronomy (2019).
[7] M. Prakash, Proceedings of 8th International Workshop on Critical Point and Onset of Deconfinement (CPOD 2013), Proceedings of Science, Vol. 185, p.24 (2013); arXiv:1307.0397.
[8] B. P. Abbott et al., Phys. Rev. Lett. 119, 161101 (2017).
[9] B. P. Abbott et al., Phys. Rev. Lett. 121, 161101 (2018).
[10] A. Goldstein et al., Astrophys. J. Lett. 848, L14 (2017).
[11] B. P. Abbott et al., Astrophys. J. Lett. 848, L12 (2017).
[12] LIGO Scientific Collaboration and Virgo Collaboration, et al., Astrophys. J. Lett. 848, L12 (2017).
[13] Y.-M. Kim, Y. Lim, K. Kwak, C. H. Hyun, and C.-H. Lee, Phys. Rev. C 98, 065805 (2018).
[14] B. Reed and C. J. Horowitz, arXiv:1910.05463.
[15] C. J. Horowitz, Mergers and the PREX neutron density experiments, The first compact star merger event -Implications for nuclear and particle physics, 14-18 Oct., 2019, ECT*, Italy; http://indico.ectstar.eu/event/57
[16] M. Kim, C.-H. Lee, Y. Kim, and S. Jeon, New Physics: Sae Mulli 66, 1563 (2016).
[17] P. Papakonstantinou, T.-S. Park, Y. Lim, and C. H. Hyun, Phys. Rev. C 97, 014312 (2018).
[18] H. Gil, P. Papakonstantinou, C. H. Hyun, Y. Oh, Phys. Rev. C 99, 064319 (2019).
[19] H. Gil, Y.-M. Kim, C. H. Hyun, P. Papakonstantinou, and Y. Oh, Phys. Rev. C 100, 014312 (2019).
[20] J. M. Lattimer and Y. Lim, Astrophys. J 771, 51 (2013).
[21] M. Dutra, O. Lourenco, J. S. S쨈a Martins, and A. Delfino, Phys. Rev. C 85, 035201 (2012).
[22] X. W. Xia, et al., Atomic Data and Nuclear Data Tables 121-122, 1 (2018).
[23] E. R. Most, L. R. Weih, L. Rezzolla, J. Schaffner-Bielich, Phys. Rev. Lett. 120, 261103 (2018).
[24] M. H. P. M. van Putten and M. Della Valle, Monthly Notice of the Royal Astronomical Society: Letters 482, L46 (2018).
[25] G. E. Brown, A. Heger, N. Langer, C.-H. Lee, S. Well-stein, and H. A. Bethe, New Astronomy 6, 457 (2001).
[26] G. E. Brown, C.-H. Lee, H. A. Bethe, Astrophysical J. 541, 918 (2000).
[27] C.-H. Lee, H. J. Park, G. W. Brown, Astrophysical J. 670, 741 (2007).
[28] C.-H. Lee and H.-S. Cho, Nuclear Physics A 928, 296 (2014).
[29] LIGO Scientific Collaboration, https://www.ligo.org.

 

 
AAPPS Bulletin        ISSN: 0218-2203
Copyright 짤 2018 Association of Asia Pacific Physical Societies. All Rights Reserved.
Hogil Kim Memorial Building #501 POSTECH, 67 Cheongam-ro, Nam-gu, Pohang-si, Gyeongsangbuk-do, 37673, Korea
Tel: +82-54-279-8663Fax: +82-54-279-8679e-mail: aapps@apctp.org