-
Here we present a phenomenological approach for the QCD equation of state, the Chiral
$ SU(3) $ -flavor parity-doublet Polyakov-loop Mean Field (CMF) model[21-24]. The CMF model can be used to calculate an EOS which describes nuclear matter properties at low temperatures and agrees with LQCD data at high temperatures and vanishing baryon density[23]. The CMF model is based on the main aspects of QCD phenomenology and includes the following concepts:● Interactions among baryons of the groundstate octet (nucleons,
$ \Lambda $ ,$ \Sigma $ , and$ \Xi $ baryons) are carried via mesonic mean fields according to the SU(3)$_{\rm f}$ chiral lagrangian$ {{\cal{L}}_{\cal{B}}} $ [25]:$$\begin{split} {{\cal{L}}_{\cal{B}}} =& \sum\limits_i (\bar{B_i} {\rm i} {\partial\!\!\!/} B_i) + \sum\limits_i \left(\bar{B_i} m^*_i B_i \right)+\\& \sum\limits_i \left(\bar{B_i} \gamma_\mu (g_{\omega i} \omega^\mu + g_{\rho i} \rho^\mu + g_{\phi i} \phi^\mu) B_i \right), \end{split}$$ (1) where the various coupling constants
$ g^{(j)}_i $ are determined by nuclear matter properties, here baryon effective masses read as:$$\begin{split} m^*_{i\pm} =& \sqrt{ \left[ (g^{(1)}_{\sigma i} \sigma + g^{(1)}_{\zeta i} \zeta )^2 + (m_0+n_s m_s)^2 \right]} \pm\\& g^{(2)}_{\sigma i} \sigma \pm g^{(2)}_{\zeta i} \zeta . \end{split}$$ (2) The repulsion among the baryons is mediated by the vector meson fields:
$ \omega $ meson field provides repulsion at finite baryon densities, the$ \rho $ meson field provides repulsion at finite isospin densities, and the$ \phi $ vector meson field generates repulsion when a finite strangeness density is generated.● Parity doubling among groundstate octet baryons which assumes that baryons with same quantum numbers but opposite parity are degenerate in mass at chirally restored phase, while at chirally broken phase (which is at lower energy densities) the mass gap between them is generated by non-strange and strange chiral mean fields
$ \sigma $ and$ \zeta $ , respectively[26-29]. The baryon parity determines 'plus' or 'minus' sign in Eq. (2);● The CMF model explicitly includes quark degrees of freedom similar to the Polyakov-loop-extended Nambu Jona-Lasinio (PNJL) model[30], where the quark thermal contribution is controlled by the Polyakov Loop order parameter
$ \Phi $ and the quark masses are dynamically generated by$ \sigma $ and$ \zeta $ fields[23]:$$\begin{split} P_{\rm q} =& T \sum\limits_{i\in Q}\frac{d_i}{(2 \pi)^3}\int{{\rm d}^3k} \frac{1}{N_c}\ln\left(1+3\Phi {\rm e}^{-\left(E_i^*-\mu_i\right)/T}+\right.\\&\left.3\bar{\Phi}{\rm e}^{-2\left(E_i^*-\mu^*_i\right)/T} +{\rm e}^{-3\left(E_i^*-\mu_i\right)/T}\right).\\[-15pt] \end{split}$$ (3) The sums run over all light quark flavors (u, d, and s),
$ d_i = 2\times3 $ being the quark degeneracy factor,$ E^*_i = \sqrt{m^{*2}_i+p^2} $ is the quark energy. The effective masses$ m^{*}_i $ of the light quarks are generated by the$ \sigma $ field, the mass of the strange quark is generated by the$ \zeta $ field. The small explicit mass terms are$ \delta m_{\rm q} = 5 $ MeV, and$ \delta m_{\rm s} = 150 $ MeV for the strange quark, and$ m_{0{\rm q}} = 253 $ MeV which corresponds to an explicit mass term which does not originate from chiral symmetry breaking:$$ \begin{split}& m_{\rm q}^* = -g_{{\rm q}\sigma}\sigma+\delta m_{\rm q} + m_{0{\rm q}},\\& m_{\rm s}^* = -g_{{\rm s}\zeta}\zeta+\delta m_{\rm s} + m_{0{\rm q}}. \end{split} $$ (4) The Polyakov-loop order parameter
$ \Phi $ effectively describes the gluon contribution to the thermodynamic potential and is controlled by the temperature dependent potential[23]:$$ \begin{split} U_{\rm{Pol}}(\Phi,\overline{\Phi},T) =& -\frac12 a(T)\Phi\overline{\Phi} + b(T)\log \Big[1-\\&6\Phi\overline{\Phi} + 4(\Phi^3+\overline{\Phi}^{3})-3(\Phi\overline{\Phi})^2\Big], \\ a(T) =& a_0 T^4+a_1 T_0 T^3+a_2 T_0^2 T^2, \\ b(T) =& b_3 T_0^4. \end{split} $$ (5) ● The CMF model includes full PDG list of hadrons[31] to provide a description of the QCD thermodynamics at intermediate temperatures
$ T \lesssim 160 $ MeV where meson and hadron resonances contribute significantly to the thermodynamics in the form of hadron resonance gas (HRG)[32-33]. The hadrons in the CMF model are attributed a finite size within excluded-volume (EV) model which mimics hard-core repulsion among hadrons[34-35]. This interaction mechanism allows to suppress the hadronic degrees of freedom at higher energy densities where quarks are expected to be dominant. Within the EV approach all particle densities, including quarks, read as:$$ \rho_i = \frac{\rho^{\rm{id}}_i (T, \mu^*_i - v_i\,p)}{1+\sum\limits_{j{ \epsilon {\rm{HRG}}}} v_j \rho^{\rm{id}}_j (T, \mu^*_j - v_j\,p)}, $$ (6) the
$ v_j $ are the eigenvolume parameters for the hadron species.$ p $ is total system pressure,$ \mu^* $ is the chemical potential of the hadron. In the standard CMF parameterization the$ v $ is assumed to be$ v_{\rm B} \!=\! 1 $ fm3 for (anti-) baryons,$ v_{\rm M} \!=\! 1/8 $ fm3 for mesons, and is set to zero$ v_{\rm q} \!=\! 0 $ for quarks.In the CMF model quarks appear smoothly so there is no deconfinement phase transition, the transition to quark matter is of crossover type. Note, there are also earlier implementations of the CMF model where quarks appear abruptly due to a phase transition[36-37] in the following we dub this model as
$ {\rm{CMF}}_{\rm{Q}} $ . In the$ {\rm{CMF}}_{\rm{Q}} $ model hadrons are treated as point-like particles and parity-doubling is not considered, the high density QCD transition is caused by coupling of Polyakov loop order parameter$ \Phi $ to the baryon and quark effective masses.The CMF model has two critical points. The first one is due to the established nuclear liquid-vapor phase transition[38], the critical endpoint of this transition is located at low temperature
$ T\approx 17 $ MeV and chemical potential close to the mass of the nucleon$ \mu_{\rm B}\approx 900 $ MeV. The second transition is attributed to the sudden vanishing of the chiral field. The endpoint of this transition is also located at low temperature$ T\approx 17 $ MeV but at higher values of the chemical potential$ \mu_ {\rm B}\approx 1\,400 $ MeV. The second critical point comes from the baryon parity pairing, this was also found in a similar model with only hadronic degrees of freedom[39]. None of these critical points are attributed to the quark deconfinement.The phase structure of QCD matter can be studied experimentally in HIC by measuring hadronic fluctuations[11] which are assumed to be sensitive to the proximity of the QCD critical point[40]. Usually fluctuations of
$ i $ -th conserved charge are measured by means of$ n $ -th order charge susceptibilities$ \chi^i_n $ which are theoretically calculated as derivatives of pressure with respect to the corresponding chemical potential:$ \chi^i_n = \frac{\partial^n P/T^4}{\left(\partial \mu_i/T \right)^n} $ . Significant interest is attributed to the third and fourth order baryon number fluctuations measures, namely skewness$ S \sigma = \chi^3_{\rm B}/\chi^2_{\rm B} $ and kurtosis$ \kappa \sigma^2 = \chi^4_{\rm B}/\chi^2_{\rm B} $ . The recent measurements by the STAR collaboration[41] at RHIC collider and by the HADES collaboration[42] at SIS18 accelerator present findings of rather large proton numbter fluctuations at low energy heavy ion collisions. These findings may be attributed to a critical behavior due to QCD interactions, however dynamical effects, e.g. centrality selection, finite particle acceptance, etc., are not yet ruled out.In the vicinity of the freeze out region the CMF model suggests that fluctuations are dominated by the remnants of the nuclear liquid-vapor phase transition. The chiral transition takes place at much higher chemical potentials and is located in the region which is reachable by BNS mergers.
The kurtosis values at Fig. 2 (a) suggests that the CMF model has 3 critical regions, with two of them having a critical endpoint at
$ T\approx17 $ MeV, so at$ T\gtrsim 17 $ MeV all transitions are smooth crossovers. Fig. 1 (b) indicates that quarks appear in the CMF model smoothly without a phase transition attributed to the deconfinement.Figure 2. (color online) (a): Ratios of the CMF baryon number susceptibilities
$\chi_4^{\rm{B}}/\chi_2^{\rm{B}}$ kurtosis in the baryon chemical potential -$\mu_{\rm{B}}$ and temperature -$T$ plane. Note the 3 distinct critical regions, with their remnants reaching from$T\!=\!0$ up to$T>200$ MeV. (b): The quark fraction$\frac13{n_ {\rm q}}/{n_{\rm B}}$ of the CMF model in baryon chemical potential$\mu_{\rm{B}}$ and temperature$T$ plane. Note that the deconfinement smoothly appears only at higher energy densities/chemical potentials.We illustrate which regions of the phase diagram are probed in heavy ion collisions at low and moderate energies by using the one dimensional Taub adiabat model[43-45]. This model describes the expansion by lines of constant entropy per baryon
$ S/A = \, $ const (isentropes). These lines describe the isentropic matter evolution of ideal fluid dynamics at different collision energies. The input to the hydro simulations is the initial stage produced in a rapid and violent nuclear collision. In the initial state the entropy is produced by a violent shock compression[46]. While the system cools down during the expansion, the entropy increases only moderately due to a rather small viscosity[47-48], thus an isentropic expansion scenario is a reasonable approximation[49].The isentropic expansion of the equilibrated matter continues until the system becomes so dilute that the chemical freezeout occurs and the chemical composition is fixed.
We calculate initial entropy per baryon (
$ S/A $ ) assuming a 1-dimensional stationary scenario of central HIC – two colliding slabs of cold nuclear matter[44, 46, 50-54]. The relativistic Rankine-Hugoniot equation which results in Taub adiabat (RRHT)[43, 45], provides conservation of the baryon number, energy and momentum across the shock front. The initial state thermodynamics (density, temperature and entropy) of the hot, dense participant matter is obtained from RRHT as a function of the collision energy. The known initial entropy yields the lines of constant entropy which leads to the trajectories of the heavy ion collisions in the phase diagram.The predicted isentropic expansion trajectories are shown in the
$\mu_ {\rm B}-T$ phase diagram in Fig. 3.Figure 3. (color online) Evolution of heavy-ion collisions in the high baryon density region of the
$T-\mu_ {\rm B}$ phase diagram for different collision energies. Black line - Taub adiabat which describes the initial state of heavy ion collisions as an implicit function of$\sqrt{s_{\rm{NN}}}$ . Colored lines - isentropic lines of constant entropy per baryon$S/A$ at different bombarding energies$\sqrt{s_{\rm {NN}}}$ respectively.The RRHT-adiabat scenario predicts a very strong compression and heating already at an intermediate lab (fixed target) bombarding energies. The hot and dense system passes the chiral transition predicted by the present CMF model already at
$ E_{\rm{lab}}\approx 2 $ AGeV, i.e. at energies available at GSI's SIS18 accelerator facility. Here the total entropy is predicted to reach$ S/A\approx 3 $ , in accord with previous RMF-calculations[54] which also used the 1-D RRHT-scenario. The$\mu_ {\rm B}-T$ values,$ T\approx 70 $ MeV,$\mu_{\rm B}\approx 1.2$ GeV, with net baryon densities$ n_{\rm B}/n_0\approx 3 $ , reached here in HIC, coincide with the$\mu_{\rm B}-T$ values reached in binary NS collisions, as recent general relativistic fully 3+1-dimensional megneto-hydrodynamical calculations have confirmed[12, 55] for the gravitational wave event GW170817. At these temperatures and densities,$ T\approx 70 $ MeV and$n_{\rm B}/n_0\approx 3$ , the RRHT model predicts that there are about 20% of the dense matter is already transformed to quarks.Heavy ion fixed target experiments of SIS at FAiR and SPS at CERN as well as STAR BES program at RHIC probe temperatures from
$ 50<T<280 $ MeV and chemical potentials from$ 500<\mu_{\rm B}<1\,700 $ MeV for the collision energy range$ \sqrt{s_{\rm{NN}}}<10 $ GeV considered here. In this region the CMF model shows not an additional phase transition, but the remnants of the nuclear liquid-vapor transition at$ T \approx 20 $ MeV. The chiral transition at larger chemical potentials may influence the dynamical evolution as well. The present results suggest that heavy-ion collisions mostly probe regions where the nuclear matter liquid-vapor critical point dominates, there the observed baryon fluctuations are mostly due to remnants of the nuclear liquid-vapor phase transition. This had been suggested also in previous works[22, 56-60]. The CP associated with the chiral symmetry restoration in the CMF model lies at$\mu_{\rm B} \approx 1.4$ GeV and$ T \approx 17 $ MeV and is strongly affected by baryon parity doubling. This high density region is, to the best of our knowledge, reachable in the interiors of NS and in binary general relativistic NS mergers[ 12, 20, 61-64].The resulting CMF EOS at
$ T = 0 $ is used as input for the Tolman-Oppenheimer-Volkoff (TOV) equation, so a relation between the mass and the radius can be obtained for any static, spherical, gravitationally bound object[65-66], here a static NS. The outer NS layers presumably consist of mostly neutron rich nuclei and clusters in chemical and$ \beta $ -equilibrium. Those nuclei are not yet a part of the CMF model. Therefore, we use a classical crust-EOS[67] matched additionally to the CMF-EOS at$n_{\rm B}\approx 0.05\; {{\rm{fm}}^{-3}}$ . The NS mass-radius relation obtained using the TOV equation with the CMF EOS is presented in Fig. 4. The discussion of the quark and hadron content of the stars is presented in Refs. [23, 68]. Note that an unstable branch in the mass radius diagram is created by stars with the quark contribution to the baryon density$ 30\% $ and more. The central densities of the stable stars can not exceed$n_{\rm{B}} = 6\,n_0$ , where the maximum mass indicates the "last stable star". The continuous monotonous transition from NS matter to a deconfined quark phase provides a smooth appearance of quarks in the star structure and prevents a "second family" of stable solutions. Therefore there is no strict separation between a quark core and the hadronic interior of the star. This is a CMF result due to the Polyakov loop implementation of the deconfinement mechanism and no vector repulsion among quarks[70]. Though LQCD data disfavors repulsive forces for quarks, there are currently active discussions concerning vector repulsion in dense baryonic matter in NS interiors[71-72]. We present the resulting dimensionless tidal deformability coefficient$ \varLambda $ in Fig. 4, see Ref. [23] for discussion.Figure 4. (color online) Neutron star mass-radius diagram (a) and tidal deformability
$\Lambda$ as function of NS radii (b) as calculated in the CMF model. In figure (b) blue bands correspond to$\Lambda$ constraints of NS with$M\!=\!1.4\sim M_{\rm{sun}}$ , and red bands- constraints on radius of NS with$M\!=\!1.4\sim M_{\rm{sun}}$ [69].
-
摘要: 通过相对论性磁流体力学的计算知道,由双中子星合并产生的引力波对中子星内部是否存在夸克物质以及QCD物质状态方程的硬度度非常敏感。这些天文学上创造的热力学极限在20%以内跟某些快度、碰撞参数等条件下的相对论重离子碰撞产生的温度和密度相当。本文结合相对论模拟双中子星系统及实验室中重离子碰撞的结果,从而确定高密物质的状态方程和相结构。讨论了中子星合并后残留物的引力波发射,这将有助于了解夸克强子过渡的性质。Abstract: The gravitational waves emitted from a binary neutron star merger, as predicted from general relativistic magneto-hydrodynamics calculations, are sensitive to the appearance of quark matter and the stiffness of the equation of state of QCD matter present in the inner cores of the stars. These astrophysically created extremes of thermodynamics do match, to within 20%, the values of densities and temperatures which are found in relativistic heavy ion collisions, if though at quite different rapidity windows, impact parameters and bombarding energies of the heavy nuclear systems. In this article we combine the results obtained in general relativistic simulations of binary neutron star systems with ones from heavy ion collisions in the lab to pin down the EOS and the phase structure of dense matter. We discuss that the postmerger gravitational wave emission of the neutron star merger remnant might give, in the near future, insides about the properties of the hadron quark transition.
-
Key words:
- QCD matter /
- heavy ion collision /
- neutron star /
- binary neutron star mergers
-
Figure 1. (color online) The maximum value of the temperature (triangles) and rest-mass density (diamonds) during the evolution of the hypermassive hybrid star using the simulation results of the LS220-M135 run (for details, see Refs. [18-19]). The color coding of triangles/diamonds indicate the time of the simulation after the merger in milliseconds (see the colorbar at the right border of the figure). The gray and black curves show the trajectories of hydrodynamic simulation of heavy-ion collision at energies
$E_{\rm{lab}}\! =\! 1.23$ AGeV and$E_{\rm{lab}} \!= \!0.65$ AGeV within the CMF model. The colorbar right next to the picture displays the quark fraction$Y_{\rm q}$ of the corresponding hot and dense matter within the CMF model. Contour lines indicate constant values of quark fraction at$Y_{\rm q}\!=\![0.0001, 0.001, 0.01]$ (green dotted lines) and$Y_{\rm q} \!= \![0.1, 0.2, 0.3]$ (green solid lines). Adapted from Ref. [20].Figure 2. (color online) (a): Ratios of the CMF baryon number susceptibilities
$\chi_4^{\rm{B}}/\chi_2^{\rm{B}}$ kurtosis in the baryon chemical potential -$\mu_{\rm{B}}$ and temperature -$T$ plane. Note the 3 distinct critical regions, with their remnants reaching from$T\!=\!0$ up to$T>200$ MeV. (b): The quark fraction$\frac13{n_ {\rm q}}/{n_{\rm B}}$ of the CMF model in baryon chemical potential$\mu_{\rm{B}}$ and temperature$T$ plane. Note that the deconfinement smoothly appears only at higher energy densities/chemical potentials.Figure 3. (color online) Evolution of heavy-ion collisions in the high baryon density region of the
$T-\mu_ {\rm B}$ phase diagram for different collision energies. Black line - Taub adiabat which describes the initial state of heavy ion collisions as an implicit function of$\sqrt{s_{\rm{NN}}}$ . Colored lines - isentropic lines of constant entropy per baryon$S/A$ at different bombarding energies$\sqrt{s_{\rm {NN}}}$ respectively.Figure 4. (color online) Neutron star mass-radius diagram (a) and tidal deformability
$\Lambda$ as function of NS radii (b) as calculated in the CMF model. In figure (b) blue bands correspond to$\Lambda$ constraints of NS with$M\!=\!1.4\sim M_{\rm{sun}}$ , and red bands- constraints on radius of NS with$M\!=\!1.4\sim M_{\rm{sun}}$ [69].Figure 5. (color online) Upper panel: Spatial distribution of the rest-mass density
$\rho$ (left) and temperature$T$ (right) of the HMHS using the${\rm{CMF}}_{\rm{Q}}$ EOS with an initial masses of$M\!=\!1.40\,M_{\odot}$ at$t\!=\!15.26$ ms after merger. The white circles/diamonds mark the maximum values of temperature/density. Lower panel: Density-temperature profiles inside the inner region of the HMHS in the style of a$T$ -$\rho$ QCD phase diagram. The color-coding displayed on the right side indicates the radial position$r$ of the corresponding fluid element inside the HMHS, while the colorbar on the top displays the logarithm of the quark fraction$Y_{\rm q}$ which is displayed in the background of the figure. -
[1] ABBOTT B P, ABBOTT R, ABBOTT T D, et al. Phys Rev Lett, 2017, 119(16): 161101. doi: 10.1103/PhysRevLett.119.161101 [2] RAJAGOPAL K. Nucl Phys, 1999, A661: 150. doi: 10.1016/S0375-9474(99)85017-9 [3] ALFORD M G. Nucl Phys Proc Suppl, 2003, 117: 65. doi: 10.1016/S0920-5632(03)01411-7 [4] BUBALLA M. Phys Rept, 2005, 407: 205. doi: 10.1016/j.physrep.2004.11.004 [5] SCHÄFER T. arXiv:hep-ph/0304281. [6] FUKUSHIMA K, HATSUDA T. Rept Prog Phys, 2011, 74: 014001. doi: 10.1088/0034-4885/74/1/014001 [7] HOFMANN J, STOECKER H, HEINZ U W, et al. Phys Rev Lett, 1976, 36: 88. doi: 10.1103/PhysRevLett.36.88 [8] STOECKER H, MARUHN J A, GREINER W. Phys Rev Lett, 1980, 44: 725. doi: 10.1103/PhysRevLett.44.725 [9] NARA Y, STEINHEIMER J, STOECKER H. Eur Phys J, 2018, A54(11): 188. doi: 10.1140/epja/i2018-12626-y [10] NARA Y, STOECKER H. Phys Rev, 2019, C100(5): 054902. doi: 10.1103/PhysRevC.100.054902 [11] KOCH V. Hadronic Fluctuations and Correlations[M/OL]//STOCK R. Relativistic Heavy Ion Physics. 2010. http://materials.springer.com/lb/docs/sm_lbs_978-3-642-01539-7_20. [12] MOST E R, PAPENFORT L J, DEXHEIMER V, et al. Phys Rev Lett, 2019, 122(6): 061101. doi: 10.1103/PhysRevLett.122.061101 [13] RISCHKE D H, BERNARD S, MARUHN J A. Nucl Phys, 1995, A595: 346. doi: 10.1016/0375-9474(95)00355-1 [14] PANG L G, ZHOU K, SU N, et al. Nature Commun, 2018, 9(1): 210. doi: 10.1038/s41467-017-02726-3 [15] DU Y L, ZHOU K, STEINHEIMER J, et al. arXiv: 1910. 11530, 2019. [16] STEINHEIMER J, RANDRUP J. Phys Rev Lett, 2012, 109: 212301. doi: 10.1103/PhysRevLett.109.212301 [17] STEINHEIMER J, PANG L, ZHOU K, et al. JHEP, 2019, 12: 122. doi: 10.1007/JHEP12(2019)122 [18] HANAUSKE M, TAKAMI K, BOVARD L, et al. Phys Rev D, 2017, 96(4): 043004. doi: 10.1103/PhysRevD.96.043004 [19] BOVARD L, MARTIN D, GUERCILENA F, et al. Phys Rev, 2017, D96(12): 124005. doi: 10.1103/PhysRevD.96.124005 [20] HANAUSKE M, STEINHEIMER J, MOTORNENKO A, et al. Particles, 2019, 2(1): 44. doi: 10.3390/particles2010004 [21] STEINHEIMER J, SCHRAMM S, STOECKER H. J Phys G, 2011, 38: 035001. doi: 10.1088/0954-3899/38/3/035001 [22] MUKHERJEE A, STEINHEIMER J, SCHRAMM S. Phys Rev C, 2017, 96(2): 025205. doi: 10.1103/PhysRevC.96.025205 [23] MOTORNENKO A, STEINHEIMER J, VOVCHENKO V, et al. Phys Rev C, 2020, 101(3): 034904. doi: 10.1103/PhysRevC.101.034904 [24] MOTORNENKO A, STEINHEIMER J, VOVCHENKO V, et al. arXiv:2002.01217. [25] PAPAZOGLOU P, SCHRAMM S, SCHAFFNER-BIELICH J, et al. Phys Rev C, 1998, 57: 2576. doi: 10.1103/PhysRevC.57.2576 [26] DETAR C E, KUNIHIRO T. Phys Rev D, 1989, 39: 2805. doi: 10.1103/PhysRevD.39.2805 [27] ZSCHIESCHE D, TOLOS L, SCHAFFNER-BIELICH J, et al. Phys Rev C, 2007, 75: 055202. doi: 10.1103/PhysRevC.75.055202 [28] AARTS G, ALLTON C, DE BONI D, et al. JHEP, 2017, 06: 034. doi: 10.1007/JHEP06(2017)034 [29] SASAKI C. Nucl Phys A, 2018, 970: 388. doi: 10.1016/j.nuclphysa.2018.01.004 [30] FUKUSHIMA K. Phys Lett B, 2004, 591: 277. doi: 10.1016/j.physletb.2004.04.027 [31] TANABASHI M, HAGIWARA K, HIKASA K, et al. Phys Rev D, 2018, 98(3): 030001. doi: 10.1103/PhysRevD.98.030001 [32] BORSANYI S, FODOR Z, HOELBLING C, et al. Phys Lett B, 2014, 730: 99. doi: 10.1016/j.physletb.2014.01.007 [33] BAZAVOV A, BHATTACHARYA T, DETAR C, et al. Phys Rev D, 2014, 90: 094503. doi: 10.1103/PhysRevD.90.094503 [34] RISCHKE D H, GORENSTEIN M I, STOECKER H, et al. Z Phys C, 1991, 51: 485. doi: 10.1007/BF01548574 [35] STEINHEIMER J, SCHRAMM S, STOECKER H. Phys Rev C, 2011, 84: 045208. doi: 10.1103/PhysRevC.84.045208 [36] DEXHEIMER V, SCHRAMM S. Astrophys J, 2008, 683: 943. doi: 10.1086/589735 [37] DEXHEIMER V A, SCHRAMM S. Phys Rev C, 2010, 81: 045201. doi: 10.1103/PhysRevC.81.045201 [38] POCHODZALLA J, MOHLENKAMP T, RUBEHN T, et al. Phys Rev Lett, 1995, 75: 1040. doi: 10.1103/PhysRevLett.75.1040 [39] MOTOHIRO Y, KIM Y, HARADA M. Phys Rev C, 2015, 92(2): 025201. doi: 10.1103/PhysRevC.92.025201 [40] STEPHANOV M A. Phys Rev Lett, 2009, 102: 032301. doi: 10.1103/PhysRevLett.102.032301 [41] ADAM J, ADAMCZYK L, ADAMS J R, et al. arXiv: 2001.02852. [42] ADAMCZEWSKI-MUSCH J, ARNOLD O, BEHNKE C, et al. arXiv: 2002.08701. [43] TAUB A H. Phys Rev, 1948, 74: 328. doi: 10.1103/PhysRev.74.328 [44] STOECKER H, GREINER W, SCHEID W. Z Phys A, 1978, 286: 121. doi: 10.1007/BF01434620 [45] THORNE K S. Astrophys J, 1973, 179: 897. doi: 10.1086/151927 [46] STOECKER H, GREINER W. Phys Rept, 1986, 137: 277. doi: 10.1016/0370-1573(86)90131-6 [47] CSERNAI L P, KAPUSTA J, MCLERRAN L D. Phys Rev Lett, 2006, 97: 152303. doi: 10.1103/PhysRevLett.97.152303 [48] ROMATSCHKE P, ROMATSCHKE U. Phys Rev Lett, 2007, 99: 172301. doi: 10.1103/PhysRevLett.99.172301 [49] STEINHEIMER J, BLEICHER M, PETERSEN H, et al. Phys Rev C, 2008, 77: 034901. doi: 10.1103/PhysRevC.77.034901 [50] BAUMGARDT H G, SCHOTT J U, SAKAMOTO Y, et al. Z Phys A, 1975, 273: 359. doi: 10.1007/BF01435578 [51] STOECKER H, GRAEBNER G, MARUHN J A, et al. Phys Lett B, 1980, 95: 192. doi: 10.1016/0370-2693(80)90467-0 [52] STOECKER H, OGLOBLIN A A, GREINER W. Z Phys A, 1981, 303: 259. doi: 10.1007/BF01421522 [53] STOECKER H, GYULASSY M, BOGUTA J. Phys Lett B, 1981, 103: 269. doi: 10.1016/0370-2693(81)90222-7 [54] HAHN D, STOECKER H. Nucl Phys A, 1988, 476: 718. doi: 10.1016/0375-9474(88)90332-6 [55] HANAUSKE M, STEINHEIMER J, BOVARD L, et al. J Phys Conf Ser, 2017, 878(1): 012031. doi: 10.1088/1742-6596/878/1/012031 [56] FUKUSHIMA K. Phys Rev C, 2015, 91(4): 044910. doi: 10.1103/PhysRevC.91.044910 [57] VOVCHENKO V, GORENSTEIN M I, STOECKER H. Phys Rev Lett, 2017, 118(18): 182301. doi: 10.1103/PhysRevLett.118.182301 [58] VOVCHENKO V, JIANG L, GORENSTEIN M I, et al. Phys Rev C, 2018, 98(2): 024910. doi: 10.1103/PhysRevC.98.024910 [59] STEINHEIMER J, WANG Y, MUKHERJEE A, et al. Phys Lett B, 2018, 785: 40. doi: 10.1016/j.physletb.2018.07.068 [60] YE Y, WANG Y, STEINHEIMER J, et al. Phys Rev C, 2018, 98(5): 054620. doi: 10.1103/PhysRevC.98.054620 [61] DIETRICH T, BERNUZZI S, UJEVIC M, et al. Phys Rev D, 2015, 91(12): 124041. doi: 10.1103/PhysRevD.91.124041 [62] RADICE D, BERNUZZI S, DEL POZZO W, et al. Astrophys J, 2017, 842(2): L10. doi: 10.3847/2041-8213/aa775f [63] BAUSWEIN A, BASTIAN N U F, BLASCHKE D B, et al. Phys Rev Lett, 2019, 122(6): 061102. doi: 10.1103/PhysRevLett.122.061102 [64] HANAUSKE M, BOVARD L, MOST E, et al. Universe, 2019, 5(6): 156. doi: 10.3390/universe5060156 [65] TOLMAN R C. Phys Rev, 1939, 55: 364. doi: 10.1103/PhysRev.55.364 [66] OPPENHEIMER J R, VOLKOFF G M. Phys Rev, 1939, 55: 374. doi: 10.1103/PhysRev.55.374 [67] BAYM G, PETHICK C, SUTHERLAND P. Astrophys J, 1971, 170: 299. doi: 10.1086/151216 [68] MOTORNENKO A, STEINHEIMER J, VOVCHENKO V, et al. PoS, 2019, CORFU2018: 150. doi: 10.22323/1.347.0150 [69] MOST E R, WEIH L R, REZZOLLA L, et al. Phys Rev Lett, 2018, 120(26): 261103. doi: 10.1103/PhysRevLett.120.261103 [70] STEINHEIMER J, SCHRAMM S. Phys Lett B, 2014, 736: 241. doi: 10.1016/j.physletb.2014.07.018 [71] BENIC S, BLASCHKE D, ALVAREZ-CASTILLO D E, et al. Astron Astrophys A, 2015, 577: 40. doi: 10.1051/0004-6361/201425318 [72] SONG Y, BAYM G, HATSUDA T, et al. arXiv: 1905.01005. [73] LATTIMER J M, SWESTY F D. Nucl Phys A, 1991, 535: 331. doi: 10.1016/0375-9474(91)90452-C [74] HANAUSKE M, STEINHEIMER J, BOVARD L, et al. Journal of Physics: Conference Series, 2017, 878: 012031. [75] HANAUSKE M, BOVARD L, STEINHEIMER J, et al. Journal of Physics: Conference Series. IOP Publishing, 2019, 1271: 012023. [76] BOVARD L, REZZOLLA L. Classical and Quantum Gravity, 2017, 34(21): 215005. [77] MOST E R, PAPENFORT L J, DEXHEIMER V, et al. arXiv: 1910.13893, 2019. [78] WEIH L R, HANAUSKE M, REZZOLLA L. arXiv: 1912. 09340, 2019. [79] FISCHER T, BASTIAN N U F, WU M R, et al. Nature Astronomy, 2018, 2: 980. doi: 10.1038/s41550-018-0583-0 [80] TOLOS L, CENTELLES M, RAMOS A. Astrophys J, 2017, 834: 3. doi: 10.3847/1538-4357/834/1/3 [81] TOLOS L, CENTELLES M, RAMOS A. Publ Astron Soc Austral, 2017, 34: e065. doi: 10.1017/pasa.2017.60 [82] WEIH L R. et al. to be published.