The origin of the shallow decay segment in γ-ray bursts' (GRB) early light curves remains a mystery, especially those cases with a long-lived plateau followed by an abrupt falloff. In this paper, we propose to understand the origins of the long-lived plateau by considering the solidification of newborn quark stars with latent heat released as energy injection to the GRB afterglow, and we suggest that an abrupt falloff would naturally appear after the plateau due to the energy injection cutoff. We estimated the total latent heat released during the phase transition of quark stars from liquid to solid states to be on the order of ～ 1051 ergs, which is comparable to the emission energy in the shallow decay segment. We also estimated the time scale of radiating the latent heat through thermal photon emission, and found that the time scale agrees with the observations. Based on our estimation, we analyzed the process of energy injection to GRB afterglow. We will show that the steady latent heat of quark star phase transition will continuously inject into the GRB afterglow in a form similar to that of a Poynting-flux-dominated outflow and naturally produce the shallow decay phase and the abrupt falloff after the plateau. We conclude that the latent heat of quark star phase transition is an important contribution to the shallow decay radiation in some GRB afterglows, and explains the long-lived plateau followed by an abrupt falloff, if pulsar-like stars are really (solid) quark stars.
We investigate a unique accreting millisecond pulsar with X-ray eclipses, SWIFT J1749.4-2807 （hereafter J1749）, and try to set limits on the binary system by various methods including use of the Roche lobe, the mass-radius relations of both main sequence （MS） and white dwarf （WD） companion stars, as well as the measured mass function of the pulsar. The calculations are based on the assumption that the radius of the companion star has reached its Roche radius （or is at 90%）, but the pulsar＇s mass has not been assumed to be a certain value. Our results are as follows. The companion star should be an MS one. For the case that the radius equals its Roche one, we have a companion star with mass M ≈ 0.51 Me and radius Rc ≈ 0.52 R⊙, and the inclination angle is i ≈ 76.5°; for the case that the radius reaches 90% of its Roche one, we have M ≈ 0.43M⊙, Rc ≈ 0.44R⊙ and i ≈ 75.7°. We also obtain the mass of J1749, Mp ≈ 1 M⊙, and conclude that the pulsar could be a quark star if the ratio of the critical frequency of rotation-mode instability to the Keplerian one is higher than - 0.3. The relatively low pulsar mass （about - M⊙） may also challenge the conventional recycling scenario for the origin and evolution of millisecond pulsars. The results presented in this paper are expected to be tested by future observations.
It is still a matter of debate to understand the equation of state of cold matter with supra-nuclear density in compact stars because of unknown non-perturbative strong interaction between quarks. Nevertheless, it is speculated from an astrophysical view point that quark clusters could form in cold quark matter due to strong coupling at realistic baryon densities. Although it is hard to calculate this conjectured matter from first principles, one can expect that the inter-cluster interaction will share some general features with the nucleon- nucleon interaction successfully depicted by various models. We adopt a two-Gaussian component soft-core potential with these general features and show that quark clusters can form stable simple cubic crystal structure if we assume that the wave function of quark clusters have a Gaussian form. With this parametrization, the Tolman-Oppenheimer-Volkoff equation is solved with reasonably constrained parameter space to give massradius relations of crystalline solid quark stars. With baryon number densities truncated at 2n0 at surface and the range of the interaction fixed at 2 fm we can reproduce similar mass-radius relations to that obtained with bag model equations of state. The maximum mass ranges from - 0.5M⊙ to 〉 ～ 3M⊙. The recently measured high pulsar mass （〉～ 2M⊙） is then used to constrain the parameters of this simple interaction potential.
X-ray dim isolated neutron stars are peculiar pulsar-like objects, characterized by their Planck-like spectrum. In studying their spectral energy distributions, optical/ultraviolet （UV） excess is a long standing problem. Recently Kaplan et al. measured the optical/UV excess for all seven sources, which is understandable in the resonant cyclotron scattering （RCS） model previously addressed. The RCS model calculations show that the RCS process can account for the observed optical/UV excess for most sources. The flat spectrum of RX J2143.0＋0654 may be due to contributions from the bremsstrahlung emission of the electron system in addition to the RCS process.
It is conventionally thought that the state equation of dense matter softens and thus cannot result in high maximum mass if pulsars are quark stars and that a recently discovered 2M⊙ pulsar （PSR J1614–2230） may make pulsars unlikely to be quark stars. However, this standard point of view would be revisited and updated if quark clustering could occur in cold quark matter because of the strong coupling be- tween quarks at realistic baryon densities in compact stars. It can be argued that the state equation of clustered quark matter stiffens to support compact stars with maxi- mum mass Mmax 2M⊙. In this brief note, it is demonstrated that large parameter space ranges are allowed for Mmax 2M⊙ in a Lennard-Jones model of clustered quark matter and the newly measured highest mass of PSR J1614–2230 would be meaningful for constraining the number of quarks inside a single quark-cluster to be Nq ≤ 103.
Quarks are proposed to be grouped together to make quark-clusters due to the strong interaction in cold quark matter at a few nuclear densities,because a weakly coupling treatment of the interaction between quarks there would be inadequate.Cold quark matter is then conjectured to be in solid state （i.e.,forming a crystal structure） if the inter-cluster potential is deep enough to localize clusters in lattice.Such a solid state of cold quark matter would be very necessary for us to understand different manifestations of pulsar-like compact stars,and could not be ruled by first principles.
We compute the characteristic parameters of the magneto-dipole radiation of a neutron star undergoing torsional seismic vibrations under the action of Lorentz restoring force about an axis of a dipolar magnetic field experiencing decay. After a brief outline of the general theoretical background of the model of a vibration-powered neutron star, we present numerical estimates of basic vibration and radiation characteristics, such as frequency, lifetime and luminosity, and investigate their time dependence on magnetic field decay. The presented analysis suggests that a gradual decrease in frequencies of pulsating high-energy emission detected from a handful of currently monitored AXP/SGR-like X-ray sources can be explained as being produced by the vibration-powered magneto-dipole radiation of quaking magnetars.
