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This paper investigates the optical images of neutron stars within the framework of the radiatively inefficient accretion flow model, taking into account a polytropic equation of state. After obtaining the numerical solutions of the neutron star, we solved numerically the geodesic equations together with the radiative transfer equation. We mainly examine the effects of the polytropic index N and the observer inclination angle θ<SUB>o</SUB> on the image morphology. The obtained images are also compared with the shadow of a Schwarzschild black hole. It is shown that, under the assumption that photon trajectories are terminated at the neutron star surface, the image exhibits a bright higher order structure surrounding an inner dark region. As N increases, the size of the higher order image gradually expands. As θ<SUB>o</SUB> increases, the obscuration of the neutron star silhouette by radiation originating outside the equatorial plane becomes more pronounced. Compared with the black hole shadow obtained under the same parameter configuration, the neutron star exhibits a larger higher order image and a more extended obscured inner dark region, whereas the higher order image of the black hole is more readily distinguishable. These results indicate significant differences in the optical appearance of neutron stars and black holes, and thus provide a theoretical basis for distinguishing between them through high resolution imaging.

We revisit QCD-induced little inflation in which the Universe starts with a large baryon chemical potential and undergoes a strong first-order QCD phase transition, generating an observable stochastic gravitational-wave background in the nano-Hz range relevant for pulsar timing array (PTA) observations. We point out that the conventional homogeneous transition from the quark-gluon plasma phase to the hadronic gas phase faces an unavoidable difficulty in achieving the required strength of supercooling for the observed baryon density. This motivates us to explore whether a qualitatively different phase structure at a large baryon chemical potential can alter the relation between the baryon density and the chemical potential, and thereby modify the supercooling history of the transition. Using the nucleon-meson model with isoscalar vector mesons, we determine the critical and spinodal structure of the chiral density wave (CDW) phase in the <inline-formula><mml:math><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mrow><mml:mi>μ</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> plane. We find that the CDW phase exhibits a nontrivial structure and can remain metastable down to a low baryon density in a certain region of the parameter space. Taking into account the subsequent liquid-gas transition and phase separation, however, the released latent heat is too small to realize a viable QCD-induced little inflation scenario and its associated PTA-scale gravitational-wave signal. Our analysis sharpens the conditions under which QCD phase transitions may act as cosmological sources of nano-Hz gravitational waves, while clarifying the possible cosmological relevance of inhomogeneous QCD phases.

A particular solution to the three-body problem is the circular Lagrange three-body system, where the masses move in circular orbits such that they always constitute an equilateral triangle. Such a system has been found to emit gravitational waves with a waveform similar to that of a binary system. In this work, we study the gravitational waveform degeneracy between quasicircular binary systems and Lagrange three-body systems up to 0.5PN order. Assuming we know the parameters of a given binary system, we determine the parameters of the Lagrange triple that produces the same waveform as that of the binary. We show that there exists a mass quadrupole degeneracy in both the plus and cross modes, characterized by two parameters. We also find that there are binary systems and linearly stable Lagrange three-body systems that can have the same mass quadrupole waveform up to the coalescence time. In such cases, the normalized overlap of the waveforms with respect to the power spectral density of the advanced LIGO design remains above 0.97 as long as the binary has nearly symmetric masses. Beyond the mass quadrupole, there is a unique degeneracy at the 0.5PN. However, the Lagrange triple that satisfies this degeneracy is unstable.