We revisit the constraint on the maximum mass of cold spherical neutron stars coming from the observational results of GW170817. We develop a new framework for the analysis by employing both energy and angular momentum conservation laws as well as solid results of latest numerical-relativity simulations and of neutron stars in equilibrium. The new analysis shows that the maximum mass of cold spherical neutron stars can be only weakly constrained as $M_{\max }\lesssim 2.3M_{\odot }$. Our present result illustrates that the merger remnant neutron star at the onset of collapse to a black hole is not necessarily rapidly rotating and shows that we have to take into account the angular momentum conservation law to impose the constraint on the maximum mass of neutron stars.

Glitch (sudden spin-up) is a common phenomenon in pulsar observations. However, the physical mechanism of glitch is still a matter of debate because it depends on the puzzle of pulsar's inner structure, i.e. the equation of state of dense matter. Some pulsars (e.g. Vela like) show large glitches (Δν/ν ∼ 10⁻⁶) but release negligible energy, whereas the large glitches of AXPs/SGRs (anomalous X-ray pulsars/soft gamma repeaters) are usually (but not always) accompanied with detectable energy releases manifesting as X-ray bursts or outbursts. We try to understand this aspect of glitches in a starquake model of solid quark stars. There are two kinds of glitches in this scenario: bulk-invariable (type I) and bulk-variable (type II) ones. The total stellar volume changes (and then energy releases) significantly for the latter but not for the former. Therefore, glitches accompanied with X-ray bursts (e.g. that of AXP/SGRs) could originate from type II starquakes induced probably by accretion, while the others without evident energy release (e.g. that of Vela pulsar) would be the result of type I starquakes due to, simply, a change of stellar ellipticity.

Gravitational waves emitted from the binary neutron star (BNS) systems can carry information about the dense matter phase in these compact stars. The crust-core interfacial mode is an oscillation mode in a neutron star, and it depends mostly on the equation of state of the matter in the crust-core transition region. This mode can be resonantly excited by the tidal field of an inspiraling-in BNS system, thereby affecting the emitted gravitational waves and hence could be used to probe the equation of state in the crust-core transition region. In this work, we investigate, in detail, how the first-order phase transition inside the neutron star, if it exists, affects the properties of the crust-core interfacial mode using a Newtonian fluid perturbation theory on a general relativistic background solution of the stellar structure. Two possible types of phase transitions are considered: (1) the phase transitions happen in the fluid core but near the crust-core interface, which results in density discontinuities, and (2) the strong interaction phase transitions in the dense core (as in the conventional hybrid star case). We study how these phase transitions affect the properties of the neutron star oscillation mode excited at the interface, where there exists a shear modulus discontinuity (interfacial mode). In particular, the former phase transition has a minor effect on the mass-radius relation, and the adiabatic tidal deformability, but has the potential to significantly affect the interfacial mode frequency and thereby could be probed using gravitational waves. For the BNS systems, we discuss the possible observational signatures of these phase transitions in the gravitational waveforms and their detectability. Our work enriches the exploration of the physical properties of the crust-core interfacial mode and provides a promising method for probing the phase transition using the seismology of a compact star.

The investigation of the phase state of dense matter is hindered by complications of first-principle nonperturbative quantum chromodynamics. By performing the first consistent general-relativistic calculations of tidal-excited g-mode of neutron stars with a first-order strong interaction phase transition in the high-density core, we demonstrate that the gravitational-wave signal during binary neutron star inspiral probes their innermost hadron-quark transition and provides potent constraints from present and future gravitational-wave detectors.

Glitch is supposed to be a useful probe into pulsar’s interior, but the underlying physics remains puzzling. The glitch activity may reflect a lower limit of the crustal moment of inertia in conventional neutron star models. Nevertheless, its statistical feature could also be reproduced in the strangeon star model, which is focused here. We formulate the glitch activity of normal radio pulsars under the framework of starquake of solid strangeon star model, the shear modulus of strangeon matter is constrained to be |$\mu \simeq 3\times 10^{34}~\rm erg\,cm^{-3}$|⁠, consistent with previous work. Nevertheless, about ten times the shift in oblateness accumulated during glitch interval is needed to fulfill the statistical observations. The fact that typical glitch sizes of two rapidly evolving pulsars (the Crab pulsar and PSR B0540-69) are about two orders of magnitude lower than that of the Vela pulsar, significantly lower than the oblateness change they can supply, indicates probably that only a part of oblateness change is relieved when a pulsar is young. The unreleased oblateness and stress may relax as compensation in the following evolution. The small glitch sizes and low glitch activity of the Crab pulsar can be explained simultaneously in this phenomenological model. Finally, we obtain energy release to be |$\Delta E\sim 2.4\times 10^{40}~\rm erg$| and |$\Delta E\sim 4.2\times 10^{41}~\rm erg$| for typical glitch size of Δν/ν ∼ 10⁻⁶ (Vela-like) and ∼10⁻⁸ (Crab-like). The upcoming SKA may test this model through the energy release and the power-law relation between the reduced recovery coefficient |$Q/|\dot{\nu }|^{1/2}$| and Δν/ν.