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The cores of massive neutron stars offer a unique environment for the nuclear matter at intermediate density in the universe. The global characteristics of a neutron star, as well as the gravitational waves emitted from the mergers of two neutron stars, offer valuable insights into dense nuclear matter. In this paper, we investigate the effect of the potential hadron-quark transition on the properties of neutron stars and the signals of the gravitational waves stemming from the merger of binary neutron stars, including waveforms, frequency evolutions as well as the spectrum curves, utilizing the equations of state constructed from the Maxwell ansatz, Gibbs ansatz and, the crossover scenario. We explicitly construct the equations of state in such a way that they converge at low and high densities therefore the differences are only from the scenarios of the transitions and the locations -- or the parameters in the equation of state. Using such constructed equations of state, we simulate the signals of the GW and analyze their differences due to locations of the transition, the scenarios of the transition, and the masses of the component stars. By combining our findings with the expected detection of gravitational waves around $(2-4)$ kHz from binary neutron star mergers and their associated electromagnetic signals, we expect to uncover some key characteristics of dense nuclear matter., Comment: A major revision including more figures, further discussions, and more references was made

It has been found that the topology effect and the possible emergent scale and hidden local flavor symmetries at high density reveal a novel structure of the compact star matter. The $N_f\geq2$ baryons can be described by the skyrmion in the large $N_c$ limit and there is a robust topology change in the skyrmion matter approach to dense nuclear matter. The hidden scale and local flavor symmetries which are sources introducing the lightest scalar meson -- dilaton -- and lowest lying vector mesons into to nonlinear chiral effective theory are seen to play important roles in understanding the nuclear force. We review in this paper the generalized nuclear effective theory (G$n$EFT), which applicable to nuclear matter from low density to the compact star density, constructed with the robust conclusion from the topology approach to dense matter and emergent scale and hidden local flavor symmetries. The topology change at density larger than two times saturation density $n_0$ encoded in the parameters of the effective field theory is interpreted as the hadron-quark continuity in the sense of Cheshire Cat Principle. A novel feature predicted in this theory that has not been found before is the precocious appearance of the conformal sound velocity in the cores of massive stars, although the trace of the energy-momentum tensor of the system is not zero. That is, in contrast to the usual picture, the cores of massive stars are composed of quasiparticles of fractional baryon charges, neither baryons nor deconfined quarks. Hidden scale and local flavor symmetries emerge and give rise a resolution of the longstanding $g_A$ quench problem in nuclei transition. To illustrate the rationality of the GnEFT, we finally confront the generalized effective field theory to the global properties of neutron star and the data from gravitational wave detections., Comment: Invited contribution to Special Issue of MDPI "Symmetries and Ultra Dense Matter of Compact Stars"

Topological structure has been extensively studied and confirmed in highly correlated condensed matter physics. We explore the gravitational waves emitted from binary neutron star mergers using the pseudoconformal model for dense nuclear matter for compact stars. This model considers the topology change and the possible emergent scale symmetry and satisfies all the constraints from astrophysics. We find that the location of the topology change affects gravitational waves dramatically owing to its effect on the equation of state. In addition, the effect of this location on the waveforms of the gravitational waves is within the ability of the on-going and up-coming facilities for detecting gravitational waves, thus suggesting a possible way to measure the topology structure in nuclear physics., Comment: Version published in Sci. China-Phys. Mech. Astron