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Pulsar-like compact stars usually have strong magnetic fields, with the strength from $\sim 10^8$ to $\sim 10^{12}$ Gauss on surface. How such strong magnetic fields can be generated and maintained is still an unsolved problem, which is, in principle, related to the interior structure of compact stars, i.e., the equation of state of cold matter at supra-nuclear density. In this paper we are trying to solve the problem in the regime of solid quark-cluster stars. Inside quark-cluster stars, the extremely low ratio of number density of electrons to that of baryons $n_e/n_b$ and the screening effect from quark-clusters could reduce the long-range Coulomb interaction between electrons to short-range interaction. In this case, the Stoner's model could apply, and we find that the condition for ferromagnetism is consistent with that for validity of Stoner's model. Under the screened Coulomb repulsion, the electrons inside the stars could spontaneously magnetized and become ferromagnetic, and hence would contribute non-zero net magnetic momentum to the whole star. We conclude that, for most cases in solid quark-cluster stars, the amount of net magnetic momentum, which is proportional to the amount of unbalanced spins $\xi=(n_+-n_-)/n_e$ and depends on the number density of electrons $n_e=n_++n_-$, could be significant with non-zero $\xi$. The net magnetic moments of electron system in solid quark-cluster stars could be large enough to induce the observed magnetic fields for pulsars with $B\sim 10^{11}$ to $\sim 10^{13}$ Gauss., Comment: 7 pages, 1 figure. Accepted by Chinese Physics C

Magnetars are proposed to be peculiar neutron stars powered by their super strong magnetic field. Observationally, anomalous X-ray pulsars and soft gamma-ray repeaters are believed to be magnetar candidates. While more and more multiwave observations of magnetars are available, unfortunately, we see accumulating failed predictions of the traditional magnetar model. These challenges urge rethinking of magnetar. Wind braking of magnetars is one of the alternative modelings. The release of magnetic energy may generate a particle outflow (i.e., particle wind), that results in both an anomalous X-ray luminosity and significantly high spindown rate. In this wind braking scenario, only strong multipole field is necessary for a magnetar (a strong dipole field is no longer needed). Wind braking of magnetars may help us to understand their multiwave radiation properties, including (1) Non-detection of magnetars in Fermi-LAT observations, (2) The timing behaviors of low magnetic field magnetars, (3) The nature of anti-glitches, (4) The criterion for magnetar's radio emission, etc. In the wind braking model of magentars, timing events of magnetars should always be accompanied by radiative events. It is worth noting that the wind engine should be the central point in the research since other efforts with any reasonable energy mechanism may also reproduce the results., Comment: 6 pages, 1 figure, submitted to conference proceeding of SMFNS2013 (Strong electromagnetic field and neutron stars 2013)

Intermittent pulsars are part-time radio pulsars. They have higher slow down rate in the on state (radio-loud) than in the off state (radio-quiet). This gives the evidence that particle wind may play an important role in pulsar spindown. The effect of particle acceleration is included in modeling the rotational energy loss rate of the neutron star. Applying the pulsar wind model to the three intermittent pulsars (PSR B1931+24, PSR J1841-0500, and PSR J1832+0029), their magnetic field and inclination angle are calculated simultaneously. The theoretical braking indices of intermittent pulsars are also given. In the pulsar wind model, the density of the particle wind can always be the Goldreich-Julian density. This may ensure that different on states of intermittent pulsars are stable. The duty cycle of particle wind can be determined from timing observations. It is consistent with the duty cycle of the on state. Inclination angle and braking index observations of intermittent pulsars may help to test different models of particle acceleration. At present, the inverse Compton scattering induced space charge limited flow with field saturation model can be ruled out., Comment: 15 pages, 2 figures, ApJ accepted. There is a typo in equation (14) in the published version. It is corrected here

The different timing results of the magnetar Swift J1822.3-1606 is analyzed and understood theoretically. It is pointed that different timing solutions are caused not only by timing noise, but also that the period derivative is decreasing after outburst. Both the decreasing period derivative and the large timing noise may be originated from wind braking of the magnetar. Future timing of Swift J1822.3-1606 will help us make clear whether its period derivative is decreasing with time or not., Comment: 5 pages, 1 figure. Accepted by Research in Astronomy and Astrophysics

The very small braking index of PSR J1734-3333, $n=0.9\pm0.2$, challenges the current theories of braking mechanisms in pulsars. We present a possible interpretation that this pulsar is surrounded by a fall-back disk and braked by it. A modified braking torque is proposed based on the competition between the magnetic energy density of a pulsar and the kinetic energy density of a fall-back disk. With this torque, a self-similar disk can fit all the observed parameters of PSR J1734-3333 with natural initial parameters. In this regime, the star will evolve to the region having anomalous X-ray pulsars and soft gamma repeaters in the $P-\dot{P}$ diagram in about 20000 years and stay there for a very long time. The mass of the disk around PSR J1734-3333 in our model is about $10M_{\oplus}$, similar to the observed mass of the disk around AXP 4U 0142+61., Comment: 8 pages, 3 figures, 1 table

Timing observations from the Parkes 64-m radio telescope for 165 pulsars between 1990 and 2011 have been searched for period glitches. A total of 107 glitches were identified in 36 pulsars, where 61 have previously been reported and 46 are new discoveries. Glitch parameters were measured by fitting the timing residual data. Observed relative glitch sizes \Delta\nu_g/\nu range between 10^-10 and 10^-5, where \nu = 1/P is the pulse frequency. We confirm that the distribution of \Delta\nu_g/\nu is bimodal with peaks at approximately 10^-9 and 10^-6. Glitches are mostly observed in pulsars with characteristic ages between 10^3 and 10^5 years, with large glitches mostly occurring in the younger pulsars. Exponential post-glitch recoveries were observed for 27 large glitches in 18 pulsars. The fraction Q of the glitch that recovers exponentially also has a bimodal distribution. Large glitches generally have low Q, typically a few per cent, but large Q values are observed in both large and small glitches. Observed time constants for exponential recoveries ranged between 10 and 300 days with some tendency for longer timescales in older pulsars. Shorter timescale recoveries may exist but were not revealed by our data which typically have observation intervals of 2 - 4 weeks. For most of the 36 pulsars with observed glitches, there is a persistent linear increase in \dot\nu in the inter-glitch interval. Where an exponential recovery is also observed, the effects of this are superimposed on the linear increase in \dot\nu. In some cases, the slope of the linear recovery changes at the time of a glitch. The \ddot\nu values characterising the linear changes in \dot\nu are almost always positive and, after subtracting the magnetospheric component of the braking, are approximately proportional to the ratio of |\dot\nu| and the inter-glitch interval, as predicted by vortex-creep models., Comment: Accepted for publication in MNRAS

The key point of studying AXPs/SGRs (anomalous X-ray pulsars/soft gamma-ray repeaters) is relevant to the energy budget. Historically, rotation was thought to be the only free energy of pulsar until the discovery of accretion power in X-ray binaries. AXPs/SGRs could be magnetars if they are magnetism-powered, but would alternatively be quark-star/fallback-disk systems if more and more observations would hardly be understood in the magnetar scenario., Comment: Proceedings of IAUS 291 "Neutron Stars and Pulsars: Challenges and Opportunities after 80 years", J. van Leeuwen (ed.); 3 pages, 1 figure

We have analyzed the physical implications of Fermi observations of magnetars. Observationally, no significant detection is reported in Fermi observations of all magnetars. Then there are conflicts between outer gap model in the case of magnetars and Fermi observations. One possible explanation is that magnetars are wind braking instead of magnetic dipole braking. In the wind braking scenario, magnetars are neutron stars with strong multipole field. A strong dipole field is no longer required. A magnetism-powered pulsar wind nebula and a braking index smaller than three are the two predictions of wind braking of magnetars. Future deeper Fermi observations will help us make clear whether they are wind braking or magnetic dipole braking. It will also help us to distinguish between the magnetar model and the accretion model for AXPs and SGRs., Comment: 3 pages, 1 figure. Submitted to proceeding of IAUS291, "Neutron Stars and Pulsars: Challenges and Opportunities after 80 years", 2012

The state of super-dense matter is essential for us to understand the nature of pulsars, but the non- perturbative quantum chromodynamics (QCD) makes it very difficult for direct calculations of the state of cold matter at realistic baryon number densities inside compact stars. Nevertheless, from an observational point of view, it is conjectured that pulsars could be made up of quark clusters since the strong coupling between quarks might render quarks grouped in clusters. We are trying an effort to find an equation of state of condensed quark-cluster matter in a phenomenological way. Supposing that the quark-clusters could be analogized to inert gases, we apply here the corresponding-state approach to derive the equation of state of quark-cluster matter, as was similarly demonstrated for nuclear and neutron-star matter in 1970s. According to the calculations presented, the quark-cluster stars, which are composed of quark-cluster matter, could then have high maximum mass that is consistent with observations and, in turn, further observations of pulsar mass would also put constraints to the properties of quark-cluster matter. Moreover, the melting heat during solid-liquid phase conversion and the related astrophysical consequences are also briefly discussed., Comment: 10 pages, 8 figures, 1 table

The origin of the 6.67 hr period X-ray source, 1E161348-5055, in the young supernova remnant RCW 103 is puzzling. We propose that it may be the descendant of a Thorne-Zytkow Object (TZO). A TZO may at its formation have a rapidly spinning neutron star as a core, and a slowly rotating envelope. We found that the core could be braked quickly to an extremely long spin period by the coupling between its magnetic field and the envelope, and that the envelope could be disrupted by some powerful bursts or exhausted via stellar wind. If the envelope is disrupted after the core has spun down, the core will become an extremely long-period compact object, with a slow proper motion speed, surrounded by a supernova-remnant-like shell. These features all agree with the observations of 1E161348-5055. TZOs are expected to have produced extraordinary high abundances of lithium and rapid proton process elements that would remain in the remnants and could be used to test this scenario., Comment: 6 pages

The spin down behaviors of SGR 0418+5729 are investigated. The pulsar spin down model of Contopoulos & Spitkovsky (2006) is applied to SGR 0418+5729. It is shown that SGR 0418+5729 lies below the pulsar death line and its rotation-powered magnetospheric activities may therefore have stopped. The compact star is now spun down by the magnetic dipole moment perpendicular to its rotation axis. Our calculations show that under these assumption there is the possibility of SGR 0418+5729 having a strong dipole magnetic field, if there is a small magnetic inclination angle. Its dipole magnetic field may be much higher than the characteristic magnetic field. Therefore, SGR 0418+5729 may be a normal magnetar instead of a low magnetic field magnetar., Comment: 9 pages, 1 figure, accepted for publication in ApJ Letters

(adapted)Considering recent observations challenging the traditional magnetar model, we explore the wind braking of magnetars. There is evidence for strong multipole magnetic fields in active magnetars, but the dipole field inferred from spin down measurements may be strongly biased by a particle wind. Recent challenging observations of magnetars may be explained naturally in the wind braking scenario: (1) The supernova energies of magnetars are of normal value; (2) The non-detection in Fermi observations of magnetars; (3) The problem posed by the low-magnetic field soft gamma-ray repeaters; (4) The relation between magnetars and high magnetic field pulsars; (5) A decreasing period derivative during magnetar outbursts. Transient magnetars may still be magnetic dipole braking. This may explain why low luminosity magnetars are more likely to have radio emissions. In the wind braking scenario, magnetars are neutron stars with strong multipole field. For some sources, a strong dipole field may be no longer needed. A magnetism-powered pulsar wind nebula and a braking index smaller than three are the two predictions of the wind braking model., Comment: 34 pages, 1 table, 6 figures, accepted by ApJ

To investigate the missing compact star of Supernova 1987A, we analyzed both the cooling and the heating processes of a possible compact star based on the upper limit of observational X-ray luminosity. From the cooling process we found that a solid quark-cluster star, which has a stiffer equation of state than that of conventional liquid quark star, has a heat capacity much smaller than a neutron star. It can cool down quickly, which can naturally explain the non-detection of a point source (neutron star or quark star) in X-ray band. On the other hand, we consider the heating process from magnetospheric activity and possible accretion, and obtain some constraints to the parameters of a possible pulsar. We conclude that a solid quark-cluster star can be fine with the observational limit in a large and acceptable parameter space. A pulsar with a short period and a strong magnetic field (or with a long period and a weak field) would has luminosity higher than the luminosity limit if the optical depth is not large enough to hide the compact star. The constraints of the pulsar parameters can be tested if the central compact object in 1987A is discovered by advanced facilities in the future., Comment: 5 pages, 2 figures (submitted to MNRAS)

Anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs) are enigmatic pulsar-like objects. The energy budget is the fundamental problem in their studies. In the magnetar model, they are supposed to be powered by the extremely strong magnetic fields (>~ 10^14 G) of neutron stars. Observations for and against the magnetar model are both summarized. Considering the difficulties encountered by the magnetar model to comfortably understand more and more observations, one may doubt that AXPs and SGRs are really magnetars. If they are not magnetar candidates (including magnetar-based models), then they must be "quark star/fallback disk" systems., Comment: 10 pages, 1 figure; talk at SMFN2011

If quark stars exist, they may be enveloped in thin electron layers (electron seas), which uniformly surround the entire star. These layers will be affected by the magnetic fields of quark stars in such a way that the electron seas would transmit hydromagnetic cyclotron waves, as studied in this paper. Particular attention is devoted to vortex hydrodynamical oscillations of the electron sea. The frequency spectrum of these oscillations is derived in analytic form. If the thermal X-ray spectra of quark stars are modulated by vortex hydrodynamical vibrations, the thermal spectra of compact stars, foremost central compact objects (CCOs) and X-ray dim isolated neutron stars (XDINSs), could be used to verify the existence of these vibrational modes observationally. The central compact object 1E 1207.4-5209 appears particularly interesting in this context, since its absorption features at 0.7 keV and 1.4 keV can be comfortably explained in the framework of the hydro-cyclotron oscillation model., Comment: 5 pages; Phys. Rev. D (accepted)

The relationship between pulsar-like compact stars and gravitational waves is briefly reviewed. Due to regular spins, pulsars could be useful tools for us to detect ~nano-Hz low-frequency gravitational waves by pulsar-timing array technique; besides, they would also be ~kilo-Hz high-frequency gravitational wave radiators because of their compactness. The wave strain of an isolate pulsar depends on the equation state of cold matter at supra-nuclear densities. Therefore, a real detection of gravitational wave should be very meaningful in gravity physics, micro-theory of elementary strong interaction, and astronomy., Comment: 11 pages, 3 figures; in: Gravitation and Astrophysics (Proceedings of the IX Asia-Pacific International Conference, 29 June - 2 July, 2009, Wuhan), eds. J. Luo, Z. B. Zhou, H. C. Yeh, and J. P. Hsu, World Scientific, p.162-172

The inverse Compton scattering (ICS) model can explain various pulse profile shapes and diversity of pulse profile evolution based on the mechanism that the radio emission is generated through inverse Compton scattering between secondary relativistic particles and radio waves from polar gap avalanches. In this paper, we study the parameter space of ICS model for 15 pulsars, which share the common pulse profile evolution phenomena that the pulse profiles are narrower at higher observing frequencies. Two key parameters, the initial Lorentz factor and the energy loss factor of secondary particles are constrained using the least square fitting method, where we fit the theoretical curve of the "beam-frequency mapping" of the ICS model to the observed pulse widths at multiple frequencies. The uncertainty of the inclination and viewing angles are taken into account in the fitting process. It is found that the initial Lorentz factor is larger than 4000, and the energy loss factor is between 20 and 560. The Lorentz factor is consistent with the prediction of the inner vacuum gap model. Such high energy loss factors suggest significant energy loss for secondary particles at altitudes of a few tens to hundreds of kilometers., Comment: 32 pages,18 figures, Accepted by the ApJ

The X-ray dim isolated neutron stars (XDINSs) are peculiar pulsar-like objects, characterized by their very well Planck-like spectrum. In studying their spectral energy distributions, the optical/UV excess is a long standing problem. Recently, Kaplan et al. (2011) have 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 due to contribution from bremsstrahlung emission of the electron system in addition to the RCS process., Comment: 6 pages, 2 figures, 1 table, accepted for publication in Research in Astronomy and Astrophysics

The study of dense matter at ultra-high density has a very long history, which is meaningful for us to understand not only cosmic events in extreme circumstances but also fundamental laws of physics. It is well known that the state of cold matter at supra-nuclear density depends on the non-perturbative nature of quantum chromo-dynamics (QCD) and is essential for modeling pulsars. A so-called H-cluster matter is proposed in this paper as the nature of dense matter in reality. In compact stars at only a few nuclear densities but low temperature, quarks could be interacting strongly with each other there. That might render quarks grouped in clusters, although the hypothetical quark-clusters in cold dense matter has not been confirmed due to the lack of both theoretical and experimental evidence. Motivated by recent lattice QCD simulations of the H-dibaryons (with structure uuddss), we are therefore considering here a possible kind of quark-clusters, H-clusters, that could emerge inside compact stars during their initial cooling, as the dominant components inside (the degree of freedom could then be H-clusters there).Taking into account the in-medium stiffening effect, we find that at baryon densities of compact stars $H$-cluster matter could be more stable than nuclear matter. We also find that for the H-cluster matter with lattice structure, the equation of state could be so stiff that it would seem to be "superluminal" in most dense region. However, the real sound speed for H-cluster matter is in fact hard to calculate, so at this stage we do not put constraints on our model from the usual requirment of causality., Comment: 9 pages and 7 figures. MNRAS, in press

We compute the characteristic parameters of magnetic dipole radiation of a neutron star undergoing torsional seismic vibrations under the action of Lorentz restoring force about axis of a dipolar magnetic field experiencing decay. After brief outline of general theoretical background of the model of vibration powered neutron star, we present numerical estimates of basic vibration and radiation characteristics, such as the oscillation frequency, lifetime, luminosity of radiation, and investigate their time dependence upon magnetic field decay. The presented analysis suggests that 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 vibration powered magneto-dipole radiation of quaking magnetars. \keywords{neutron stars, torsion Alfv\'en vibrations, vibration powered radiation, magnetic field decay, magnetars}, Comment: Preprint of article accepted for publication in "Research in Astronomy and Astrophysics" [RAA-Vol.11-No9-(2011)-p.1074]

The atomic nucleus capability of responding by hydromagnetic vibrations, that has been considered long ago by Hannes Alfven, is re-examined in the context of current development of nuclear physics and pulsar astrophysics., Comment: Physica Scripta, accepted

We analyze individual pulses detected from RRAT J1819$-$1458. From April 2007 to April 2010, we carried out observations using the Nanshan 25-m radio telescope of Urumqi Observatory at a central frequency of 1541.25 MHz. We obtain a dispersion measure $DM=195.7\pm0.3$ pc cm^{-3} by analyzing all the 423 detected bursts. The tri-band pattern of arrival time residuals is confirmed by a single pulse timing analysis. Twenty-seven bimodal bursts located in the middle residual band are detected, and, profiles of two typical bimodal bursts and two individual single-peak pulses are presented. We determine the statistical properties of SNR and W$_{50}$ of bursts in different residual bands. The W$_{50}$ variation with SNR shows that the shapes of bursts are quite different from each other. The cumulative probability distribution of intensity for a possible power law with index $\alpha=1.6\pm0.2$ is inferred from the number of those bursts with $SNR\ge6$ and high intensities., Comment: 6 pages, 8 figures, 1 table, accepted for publication in A&A

We revisit the well-known Hoyle-Narlikar-Wheeler proposition that neutron star emerging in the magnetic-flux-conserving process of core-collapse supernova can convert the stored energy of Alfven vibrations into power of magneto-dipole radiation. We show that the necessary requirement for the energy conversion is the decay of internal magnetic field. In this case the loss of vibration energy of the star causes its vibration period, equal to period of pulsating emission, to lengthen at a rate proportional to the rate of magnetic field decay. These prediction of the model of vibration powered neutron star are discussed in juxtaposition with data on pulsating emission of magnetars whose radiative activity is generally associated with the decay of ultra strong magnetic field., Comment: Accepted for publication in Astrophysics & Space Science

In juxtaposition with the standard model of rotation powered pulsar, the model of vibration powered magnetar undergoing quake-induced torsional Alfven vibrations in its own ultra strong magnetic field experiencing decay is considered. The presented line of argument suggests that gradual decrease of frequencies (lengthening of periods) of long-periodic pulsed radiation detected from a set of X-ray sources can be attributed to magnetic-field-decay induced energy conversion from seismic vibrations to magneto-dipole radiation of quaking magnetar., Comment: Text of talk presented at "Mini-Workshop on Pulsars", Nov. 12th, 2010; KIAA-PKU, Beijing

We analyze the emission plateaus in the X-ray afterglow lightcurves of gamma-ray bursts (GRBs) and in the optical lightcurves of Type II superpernovae (SNe IIP) in order to study whether they have similar late energy injection behaviors. We show that correlations of bolometric energies (or luminosities) between the prompt explosions and the plateaus for the two phenomena are similar. The Type II SNe are in the low energy end of the GRBs. The bolometric energies (or luminosities) in prompt phase E_{\rm expl} (or L_{\rm expl}) and in plateau phase E_{\rm plateau} (or L_{\rm plateau}) share relations of E_{\rm expl} \propto E_{\rm plateau}^{0.73\pm 0.14} and L_{\rm expl} \propto L_{\rm plateau}^{\sim 0.70}. These results may indicate a similar late energy injection behavior to reproduce the observed plateaus of the plateaus in the two phenomena., Comment: 10 pages, 3 tables, 1 figure, RAA accepted

Anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs) are magnetar candidates, i.e., neutron stars powered by strong magnetic field. If they are indeed magnetars, they will emit high-energy gamma-rays which are detectable by Fermi-LAT according to the outer gap model. However, no significant detection is reported in recent Fermi-LAT observations of all known AXPs and SGRs. Considering the discrepancy between theory and observations, we calculate the theoretical spectra for all AXPs and SGRs with sufficient observational parameters. Our results show that most AXPs and SGRs are high-energy gamma-ray emitters if they are really magnetars. The four AXPs 1E 1547.0-5408, XTE J1810-197, 1E 1048.1-5937, and 4U 0142+61 should have been detected by Fermi-LAT. Then there is conflict between out gap model in the case of magnetars and Fermi observations. Possible explanations in the magnetar model are discussed. On the other hand, if AXPs and SGRs are fallback disk systems, i.e., accretion-powered for the persistent emissions, most of them are not high-energy gamma-ray emitters. Future deep Fermi-LAT observations of AXPs and SGRs will help us make clear whether they are magnetars or fallback disk systems., Comment: 15 pages, 3 figures, 1 table, accepted for publication in The Astrophysical Journal

Magneto-solid-mechanical model of two-component, core-crust, paramagnetic neutron star responding to quake-induced perturbation by differentially rotational, torsional, oscillations of crustal electron-nuclear solid-state plasma about axis of magnetic field frozen in the immobile paramagnetic core is developed. Particular attention is given to the node-free torsional crust-against-core vibrations under combined action of Lorentz magnetic and Hooke's elastic forces; the damping is attributed to Newtonian force of shear viscose stresses in crustal solid-state plasma. The spectral formulae for the frequency and lifetime of this toroidal mode are derived in analytic form and discussed in the context of quasi-periodic oscillations of the X-ray outburst flux from quaking magnetars. The application of obtained theoretical spectra to modal analysis of available data on frequencies of oscillating outburst emission suggests that detected variability is the manifestation of crustal Alfven's seismic vibrations restored by Lorentz force of magnetic field stresses., Comment: 10 pages, 10 figures

We study radiative activity of magnetic white dwarf undergoing torsional vibrations about axis of its own dipole magnetic moment under the action of Lorentz restoring force. It is shown that pulsating white dwarf can convert its vibration energy into the energy of magneto-dipole emission, oscillating with the frequency equal to the frequency of Alfv\'en torsional vibrations, provided that internal magnetic field is decayed. The most conspicuous feature of the vibration energy powered radiation in question is the lengthening of periods of oscillating emission; the rate of period elongation is determined by the rate magnetic field decay., Comment: Mod. Phys. Lett. A 26 (2011) 359-366

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 $2M_\odot$ pulsar (PSR J1614-2230) may make quark stars to be unlikely. 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 between quarks at realistic baryon densities of compact stars, and it is addressed that the state equation of clustering quark matter stiffs to support compact stars with maximum mass $M_{\rm max}>2M_\odot$. In this brief note, it is demonstrated that large parameter spaces are allowed for $M_{\rm max}>2M_\odot$ in a Lennard-Jones model of clustered quark matter, and the newly measured highest mass of PSR J1614-2230 would be meaningful to constrain the number of quarks inside single quark-cluster, to be $N_q<\sim 10^3$., Comment: Minor chances have been made, submitted

It is still a matter of debate to understand the equation of state of cold supra-nuclear matter in compact stars because of unknown on-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 the inter-cluster interaction to share some general features to nucleon-nucleon interaction. 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 Gaussian form wave function. With this parameterizing, Tolman-Oppenheimer-Volkoff equation is solved with reasonable constrained parameter space to give mass-radius relation of crystalline solid quark star. With baryon densities truncated at 2 times nuclear density at surface and range of interaction fixed at 2fm we can reproduce similar mass-radius relation to that obtained with bag model equations of state. The maximum mass ranges from about 0.5 to 3 solar mass. Observed maximum pulsar mass (about 2 solar mass) is then used to constrain parameters of this simple interaction potential., Comment: 5 pages, 2 figures

Significant research in compact stars is currently focused on two kinds of enigmatic sources: anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs). Although AXPs and SGRs are popularly thought to be magnetars, other models (e.g. the accretion model) to understand the observations can still not be ruled out. It is worth noting that a non-detection in a Fermi/LAT observation of AXP 4U 0142+61 has been reported recently by Sasmaz Mus & Gogus. We propose here that Fermi/LAT observations may distinguish between the magnetar model and the accretion model for AXPs and SGRs. We explain how this null observation of AXP 4U 0142+61 favors the accretion model. Future Fermi/LAT observations of AXP 1E 1547.0-5408 and AXP 1E 1048.1-5937 are highly recommended., Comment: 10 pages, 3 figures, Accepted for publication in ApJ(Letters)

Anomalous X-ray Pulsars and Soft Gamma-Ray Repeaters have been generally recognized as neutron stars with super strong magnetic fields, namely "magnetars". The "magnetars" manifest that the luminosity in X-ray band are larger than the rotational energy loss rate, i.e. $L_{X}>\dot {E}_{\rm rot}$, and then the radiation energy is coming from the energy of magnetic field. Here it is argued that magnetars may not really exist. Some X-ray and radio observational results are contradicted with the magnetar model. (1) The X-ray luminosity of PSR J1852+0040 is much larger than the rotational energy loss rate ($L_{X}/\dot {E}_{\rm rot}\simeq 18)$, but the magnetic field is just $3.1\times 10^{11}$ G. Does this X-ray radiation energy come from the magnetic field? (2) In contrast to the above, the magnetic fields of radio pulsars J1847-0130 and PSR J1718-3718 are higher than that of AXP 1E 2259+586, why is the radiation energy of those two radio pulsars still coming from rotational energy? Furthermore, the magnetic field of the newly discovered SGR 0418+5729 with the lowest magnetic field is 3.0 e13 G, lower than the critical magnetic field $B_{\rm C}=4.414$ e13 G) (Esposito et al. 2010). (3) Some "magnetars" also emit normal transient radio pulses, what is the essential difference between radio pulsars and the "magnetars"? The observational fact arguments will be presented at first, then we discuss in what situation the conventional method to obtain magnetic field could not be correct.

It is shown that depletion of the magnetic field pressure in a quaking neutron star undergoing Lorentz-force-driven torsional seismic vibrations about axis of its dipole magnetic moment is accompanied by the loss of vibration energy of the star that causes its vibration period to lengthen at a rate proportional to the rate of magnetic field decay. Highlighted is the magnetic-field-decay induced conversion of the energy of differentially rotational Alfv\'en vibrations into the energy of oscillating magneto-dipole radiation. A set of representative examples of magnetic field decay illustrating the vibration energy powered emission with elongating periods produced by quaking neutron star are considered and discussed in the context of theory of magnetars., Comment: extended version

Pulsed high energy radiation from pulsars is not yet completely understood. In this paper, we use the 3D self-consistent annular gap model to study light curves for both young and millisecond pulsars observed by the Fermi Gamma-ray Space Telescope. The annular gap can generate high energy emission for short-period pulsars. The annular gap regions are so large that they have enough electric potential drop to accelerate charged particles to produce gamma-ray photons. For young pulsars, the emission region is from the neutron star surface to about half of the light cylinder radius, and the peak emissivity is in the vicinity of the null charge surface. The emission region for the millisecond pulsars is located much lower than that of the young pulsars. The higher energy gamma-ray emission comes from higher altitudes in the magnetosphere. We present the simulated light curves for three young pulsars (the Crab, the Vela, the Geminga) and three millisecond pulsars (PSR J0030+0451, PSR J0218+4232, PSR J0437-3715) using the annular gap model. Our simulations can reproduce the main properties of observed light curves., Comment: 9 pages, 3 figures and 1 table; accepted for publication in MNRAS

We investigate the possibilities that pulsars act as the lens in gravitational microlensing events towards the galactic bulge or a spiral arm. Our estimation is based on expectant survey and observations of FAST (Five hundred meter Aperture Spherical Telescope) and SKA (Square Kilometer Array), and two different models of pulsar distribution are used. We find that the lensing rate is > 1 event/decade, being high enough to search the real events. Therefore, the microlensing observations focusing on pulsars identified by FAST or SKA in the future are meaningful. As an independent determination of pulsar mass, a future detection of microlensing pulsars should be significant in the history of studying pulsars, especially in constraining the state of matter (either hadronic or quark matter) at supra-nuclear densities. The observations of such events by using advanced optical facilities (e.g., the James Webb Space Telescope and the Thirty Meter Telescope) in future are highly suggested., Comment: 5pages, 2figures

Determining radiation location observationally plays a very important role in testing the pulsar radiation models. One-photon pair production in the strong magnetic field, $\gamma-e^{+}e^{1}$, is one of the important physical processes in pulsar radiation mechanisms. Photons near pulsar surface with sufficient energy will be absorbed in the magnetosphere and the absorption optical depth for these GeV $\gamma$-ray photons is usually large. In this paper, we include the aberrational, rotational and general relativistic effects and calculate the $\gamma$-B optical depth for $\gamma$-ray photons. Then we use the derived optical depth to determine the radiation altitude lower bounds for photons with given energies. As a case study, we calculate the lower bounds of radiation altitudes of Crab pulsar for photons with energy from 5 GeV to 1 TeV., Comment: 11 pages, 5 figures,Accepted by MNRAS

We present an analysis of timing residual (noise) of 54 pulsars obtained from 25-m radio telescope at Urumqi Observatory with a time span of 5~8 years, dealing with statistics of the Hurst parameter. The majority of these pulsars were selected to have timing noise that look like white noise rather than smooth curves. The results are compared with artificial series of different constant pairwise covariances. Despite the noise like appearance, many timing residual series showed Hurst parameters significantly deviated from that of independent series. We concluded that Hurst parameter may be capable of detecting dependence in timing residual and of distinguishing chaotic behavior from random processes., Comment: 7 pages, 3 figures, 2 tables, Submitted to MNRAS

Pulsars have been recognized as normal neutron stars, but sometimes argued as quark stars. {\it Sub-millisecond pulsars, if detected, would play an essential and important role in distinguishing quark stars from neutron stars.} We focus on the formation of such sub-millisecond pulsars in this paper. A new approach to form a sub-millisecond pulsar (quark star) via accretion induced collapse (AIC) of a white dwarf is investigated here. Under this AIC process, we found that: (1) almost all the newborn quark stars could have an initial spin period of $\sim 0.1$ ms; (2) the nascent quark stars (even with a low mass) have sufficiently high spin-down luminosity and satisfy the conditions for pair production and sparking process to be as sub-millisecond radio pulsars; (3) in most cases, the timescales of newborn quark stars in the phase of spin period $< 1$ (or $<0.5$) ms can be long enough to be detected. As a comparison, an accretion spin-up process (for both neutron and quark stars) is also investigated. It is found that, quark stars formed through AIC process can have shorter periods ($\leq$ 0.5 ms); while the periods of neutron stars formed in accretion spin-up process must be longer than 0.5ms. Thus if a pulsar with a period less than 0.5 ms can be identified in the future, it should be a quark star., Comment: 10 pages, 4 figures, 4 tables, accepted by MNRAS

We present a theoretical model for the thermal X-ray emission and cooling of isolated pulsars, assuming that pulsars are solid quark stars. We calculate the heat capacity for such a quark star, and the results show that the residual thermal energy cannot sustain the observed thermal X-ray luminosities seen in typical isolated X-ray pulsars. We conclude that other heating mechanisms must be in operation if the pulsars are in fact solid quark stars. Two possible heating mechanisms are explored. Firstly, for pulsars with little magnetospheric activities, accretion from the interstellar medium or from the material in the associated supernova remnants may power the observed thermal emission. In the propeller regime, a disk-accretion rate ${\dot M}\sim$1% of the Eddington rate with an accretion onto the stellar surface at a rate of $\sim 0.1% {\dot M}$ could explain the observed emission luminosities of the dim isolated neutron stars and the central compact objects. Secondly, for pulsars with significant magnetospheric activities, the pulsar spindown luminosities may have been as the sources of the thermal energy via reversing plasma current flows. A phenomenological study between pulsar bolometric X-ray luminosities and the spin energy loss rates presents the probable existence of a 1/2-law or a linear law, i.e. $L_{\rm bol}^{\infty}\propto\dot{E}^{1/2}$ or $L_{\rm bol}^{\infty}\propto\dot{E}$. This result together with the thermal properties of solid quark stars allow us to calculate the thermal evolution of such stars. Thermal evolution curves, or cooling curves, are calculated and compared with the `temperature-age' data obtained from 17 active X-ray pulsars. It is shown that the bolometric X-ray observations of these sources are consistent with the solid quark star pulsar model., Comment: Astroparticle Physics Accepted

Quark clustering could occur in cold quark matter because of the strong coupling between quarks at realistic baryon densities of compact stars. Although one may still not be able to calculate this conjectured matter from first principles, the inter-cluster interaction might be analogized to the interaction between inert molecules. Cold quark matter would then crystallize in a solid state if the inter-cluster potential is deep enough to trap the clusters in the wells. We apply the Lennard-Jones potential to describe the inter-cluster potential, and derive the equations of state, which are stiffer than that derived in conventional models (e.g., MIT bag model). If quark stars are composed of Lennard-Jones matter, they could have high maximum masses ($>2M_{\odot}$) as well as very low masses ($<10^{-3}M_{\odot}$). These features could be tested by observations., Comment: 5 pages, 2 figures. Accepted by MNRAS (Letters)

A polytropic quark star model is suggested in order to establish a general framework in which theoretical quark star models could be tested by observations. The key difference between polytropic quark stars and the polytropic model studied previously for normal (i.e., non-quarkian) stars is related to two issues: (i) a constant term representing the contribution of vacuum energy may be added in the energy density and the pressure for a quark star, but not for a normal star; (ii) the quark star models with non-vanishing density at the stellar surface are not avoidable due to the strong interaction between quarks. The first one implies that the vacuum inside a quark star is different from that outside, while the second one is relevant to the effect of color confinement. The polytropic equations of state are stiffer than that derived in conventional realistic models (e.g., the bag model) for quark matter, and pulsar-like stars calculated with a polytropic equation of state could then have high maximum masses (> 2 M_sun). Quark stars can also be very low massive, and be still gravitationally stable even if the polytropic index, n, is greater than 3. All these would result in different mass-radius relations, which could be tested by observations. In addition, substantial strain energy would develop in a solid quark star during its accretion/spindown phase, and could be high enough to take a star-quake. The energy released during star-quakes could be as high as ~ 10^{47} ergs if the tangential pressure is ~ 10^{-6} higher than the radial one., Comment: 17 pages, 4 figures, last version accepted for publication in Astroparticle Physics

Pulsars have been recognized as normal neutron stars or quark stars. Sub-millisecond pulsars, if detected, would play an essential and important role in distinguishing quark stars from neutron stars. A key question is how sub-millisecond pulsars could form. Both sub-Keplerian (for neutron and quark stars) and super-Keplerian cases (only for quark stars, which are bound additionally by strong interaction) have been discussed in this paper in order to investigate possible ways of forming sub-millisecond pulsars. In the sub-Keplerian case, the equilibrium periods of both neutron and quark stars could be as low as ~0.4 ms when they are spun up through accretion in binary systems. In the super-Keplerian case, pulsars could very likely have an initial period of ~0.1 ms if quark stars with different mass could be formed from accretion-induced collapse (AIC) of white dwarfs. The timescale for a sub-millisecond pulsar to keep its period <1 ms is restricted due to gravitational wave radiation. We found that the timescales of neutron stars within sub-millisecond periods are approximately ~10 yr, but the timescales estimated (>10 Myr) for low-mass quark stars could be long enough for us to detect., Comment: 12pages, 1 figure, 3 table, this paper has been withdrawn

Many models for the pulsar radio and $\gamma$-ray emissions have been developed. The tests for these models using observational data are very important. Tests for the pulsar radio emission models using frequency-altitude relation are presented in this paper. In the radio band, the mean pulse profiles evolve with observing frequencies. There are various styles of pulsar profile - frequency evolutions (which we call as "beam evolution" figure), e.g. some pulsars show that mean pulse profiles are wider and core emission is higher at higher frequencies than that at lower frequencies, but some other pulsars show completely the contrary results. We show that all these "beam evolution" figures can be understood by the Inverse Compton Scattering(ICS) model (see Qiao at al.2001 also). An important observing test is that, for a certain observing frequency different emission components are radiated from the different heights. For the $\gamma$-ray pulsars, the geometrical method (Wang et al. 2006) can be used to diagnose the radiation location for the $\gamma$-ray radiation. As an example, Wang et al. (2006) constrain the $\gamma$-ray radiation location of PSR B1055-52 to be the place near the null charge surface. Here we show that Wang's result matches the proposed radiation locations by the annular gap model as well as the outer gap models., Comment: 6 pages, 5 figures, Proceedings of "Astrophysics of Compact Objects", 1th-7th, July, 2007

A series of five unusual slow glitches of the radio pulsar B1822-09 (PSR J1825-0935) were observed over the 1995-2005 interval. This phenomenon is understood in a solid quark star model, where the reasonable parameters for slow glitches are presented in the paper. It is proposed that, because of increasing shear stress as a pulsar spins down, a slow glitch may occur, beginning with a collapse of a superficial layer of the quark star. This layer of material turns equivalently to viscous fluid at first, the viscosity of which helps deplete the energy released from both the accumulated elastic energy and the gravitation potential. This performs then a process of slow glitch. Numerical calculations show that the observed slow glitches could be reproduced if the effective coefficient of viscosity is ~10^2 cm^{2}/s and the initial velocity of the superficial layer is order of 10^{-10} cm/s in the coordinate rotating frame of the star., Comment: 5 pages, 5 figures, accepted for publication in MNRAS (Main Journal)