Search

Timing observations are crucial for determining the basic parameters of newly discovered pulsars. Using the Five-hundred-meter Aperture Spherical radio Telescope (FAST) with the L-band 19-beam receiver covering the frequency range of 1.0–1.5 GHz, the FAST Galactic Plane Pulsar Snapshot (GPPS) Survey has discovered more than 600 faint pulsars with flux densities of only a few or a few tens of μJy at 1.25 GHz. To obtain accurate position, spin parameters and dispersion measure of a pulsar, and to calculate derived parameters such as the characteristic age and surface magnetic field, we collect available FAST pulsar data obtained either through targeted follow-up observations or through coincidental survey observations with one of the 19 beams of the receiver. From these data we obtain time of arrival (TOA) measurements for 30 newly discovered pulsars as well as for 13 known pulsars. We demonstrate that the TOA measurements acquired by the FAST from any beams of the receiver in any observation mode (e.g. the tracking mode or the snapshot mode) can be combined to get timing solutions. We update the ephemerides of 13 previously known pulsars and obtain the first phase-coherent timing results for 30 isolated pulsars discovered in the FAST GPPS Survey. Notably, PSR J1904+0853 is an isolated millisecond pulsar, PSR J1906+0757 is a disrupted recycled pulsar, and PSR J1856+0211 has a long period of 9.89 s that can constrain pulsar death lines. Based on these timing solutions, all available FAST data have been added together to obtain the best pulse profiles for these pulsars. [ABSTRACT FROM AUTHOR]

Strangeon star model has passed various observational tests, such as the massive pulsars and the tidal deformability during binary mergers. Pulsar glitch, as a useful probe for studying the interior structure of pulsars, has also been studied in strangeon star model in our previous papers, including the recovery coefficient, the waiting time of glitches, and glitch activity. In this paper, the recovery process of a glitch is described in the strangeon star model, based on the starquake picture established before (in Paper I). After the starquake, the inner motion of the stellar matter would reduce the tangential pressure in the cracked places at the equatorial plane. The recovery (increase) of the tangential pressure would be achieved by a viscous flow towards the cracked places at equatorial plane, which leads to the exponential recovery of the spin frequency. A uniform viscous flow can reproduce the single exponential decay observed in some glitches, and the viscous time-scale τ and the depth h of the cracking place below the surface can be fitted by the recovery data. It is found that h increases with glitch size Δν/ν, which is expected in the glitch scenario of strangeon stars. The magnitude of the recovery predicted in this recovery model is also consistent with that derived from observations. The single exponential decay reproduced by a uniform viscous flow can be generalized to two or more exponentials by the multicomponent of viscous flows. [ABSTRACT FROM AUTHOR]

More than 100 rotating radio transients (RRATs) have been discovered since 2006. However, it is unclear whether RRATs radiate in nulling states. PSR J0628+0909 has been classified as an RRAT. In this paper, we study the single pulses and integrated pulse profile of PSR J0628+0909 to check whether we can detect pulsed radio emission in the nulling states. We also aim to study the polarization of the RRAT and its relationship to the general pulsar population. We used the Five-hundred-meter Aperture Spherical radio Telescope (FAST) to observe PSR J0628+0909 in the frequency range from 1.0 to 1.5 GHz. We searched for strong single pulses and looked for pulsed emission in the RRAT nulling states. Polarization profiles, the single-pulse energy distribution, and waiting-time statistics were measured. The Faraday rotation measure and dispersion measure values are updated with the current observation. The single-pulse polarization behaviours show great diversity, similar to the case of pulsars. Based on the integrated pulse profile and single-pulse energy statistics, we argue that continuous pulsar-like emission exists in addition to the transient-like burst emission for PSR J0628+0909. We find that the pulse waiting time is not correlated with the pulse energy and conclude that the strong transient emission of RRAT is not generated by the energy store–release mechanism. [ABSTRACT FROM AUTHOR]

Pulsar-like compact stars provide us a unique laboratory to explore properties of dense matter at supra-nuclear densities. One of the models for pulsar-like stars is that they are totally composed of "strangeons", and in this paper, we studied the pulsar glitches in a strangeon star model. Strangeon stars would be solidified during cooling, and the solid stars would be natural to have glitches as the result of starquakes. Based on the starquake model established before, we proposed that when the starquake occurs, the inner motion of the star which changes the moment of inertia and has impact on the glitch sizes, is divided into plastic flow and elastic motion. The plastic flow which is induced in the fractured part of the outer layer, would move tangentially to redistribute the matter of the star and would be hard to recover. The elastic motion, on the other hand, changes its shape and would recover significantly. Under this scenario, we could understand the behaviors of glitches without significant energy releasing, including the Crab and the Vela pulsars, in an uniform model. We derive the recovery coefficient as a function of glitch size, as well as the time interval between two successive glitches as the function of the released stress. Our results show consistency with observational data under reasonable ranges of parameters. The implications on the oblateness of the Crab and the Vela pulsars are discussed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

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, we see unfortunately an accumulation of failed predictions of the traditional magnetar model. These challenges urge a reconsidering of the magnetar phenomenon. Wind braking of magnetars is one of the alternative modelings. The release of magnetic energy may generate a particle outflow (i.e., particle wind) which results in both an anomalous X-ray luminosity (LX) and a significantly high spindown rate (Ṗ). In this wind braking scenario, only a 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 the Fermi -LAT observations, (2) timing behaviors of low magnetic field magnetars, (3) nature of anti-glitches, (4) criterion for magnetar radio emission, etc. In the wind braking model of magnetars, timing events of magnetars should always be accompanied by radiative events. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

The study of dense matter at ultrahigh 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 supranuclear density depends on the non-perturbative nature of quantum chromodynamics (QCD) and is essential for modelling 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 have 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 therefore consider 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 the most dense region. However, the real sound speed for H-cluster matter is in fact difficult to calculate, so at this stage we do not put constraints on our model from the usual requirement of causality.We study the stars composed of H-clusters, i.e. H-cluster stars, and derive the dependence of their maximum mass on the in-medium stiffening effect, showing that the maximum mass could be well above 2 M⊙ as observed and that the resultant mass–radius relation fits the measurement of the rapid burster under reasonable parameters. Besides a general understanding of different manifestations of compact stars, we expect further observational and experimental tests for the H-cluster stars in the future. [ABSTRACT FROM AUTHOR]

We explore the wind braking of magnetars considering recent observations challenging the traditional magnetar model. 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 particle wind. Recent observations challenging the traditional model of magnetars may be explained naturally by 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 low magnetic field soft gamma-ray repeaters; (4) the relation between magnetars and high magnetic field pulsars; and (5) a decreasing period derivative during magnetar outbursts. Transient magnetars with Lx< - Erot may still be magnetic dipole braking. This may explain why low luminosity magnetars are more likely to have radio emissions. A strong reduction of the dipole magnetic field is possible only when the particle wind is very collimated at the star surface. A small reduction of the dipole magnetic field may result from detailed considerations of magnetar wind luminosity. In the wind braking scenario, magnetars are neutron stars with a strong multipole field. For some sources, a strong dipole field may no longer be needed. A magnetism-powered pulsar wind nebula will be one of the consequences of wind braking. For a magnetism-powered pulsar wind nebula, we should see a correlation between the nebula luminosity and the magnetar luminosity. Under the wind braking scenario, a braking index smaller than three is expected. Future braking index measurement of a magnetar may tell us whether magnetars are wind braking or magnetic dipole braking. [ABSTRACT FROM AUTHOR]

Timing observations from the Parkes 64-m radio telescope for 165 pulsars between 1990 and 2011 have been searched for period glitches. Data spans for each pulsar ranged between 5.3 and 20.8 yr. From the total of 1911 yr of pulsar rotational history, 107 glitches were identified in 36 pulsars. Out of these glitches, 61 have previously been reported whereas 46 are new discoveries. Glitch parameters, both for the previously known and the new glitch detections, were measured by fitting the timing residual data. Observed relative glitch sizes Δνg/ν range between 10−10 and 10−5, where ν = 1/P is the pulse frequency. We confirm that the distribution of Δνg/ν is bimodal with peaks at approximately 10−9 and 10−6. Glitches are mostly observed in pulsars with characteristic ages between 103 and 105 yr, 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 just 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 d with some tendency for longer time-scales in older pulsars. Shorter time-scale 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 $\dot{\nu }$ (i.e. decrease in the slow-down rate $|\dot{\nu }|$) in the interglitch interval. Where an exponential recovery is also observed, the effects of this are superimposed on the linear increase in $\dot{\nu }$. In some but not all cases, the slope of the linear recovery changes at the time of a glitch. The $\ddot{\nu }$ values characterizing 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 interglitch interval, as predicted by vortex-creep models. [ABSTRACT FROM AUTHOR]

ABSTRACT To investigate the missing compact star of Supernova 1987A (SN1987A), we analysed the cooling and 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 (SQS), having a stiffer equation of state than that of a conventional liquid quark star, has a heat capacity much smaller than a neutron star. The SQS can cool down quickly, naturally explaining the non-detection of a point source in X-ray wavelengths. On the other hand, we considered the heating processes due to magnetospheric activity and possible accretion, and obtained some constraints on the parameters of a possible pulsar. Therefore, we concluded that an SQS can explain the observational limit in a confident parameter space. With a short period and a strong magnetic field (or with a long period and weak field), a pulsar would have a luminosity higher than the observational limit if the optical depth is not large enough to hide the compact star. As possible central compact objects, the parameters constrained for a pulsar can be tested for SN1987A with advanced facilities in the future. [ABSTRACT FROM AUTHOR]

The inverse Compton scattering (ICS) model can explain various pulse profile shapes and the diversity of the pulse profile evolution based on the mechanism where the radio emission is generated through ICS between secondary relativistic particles and radio waves from polar gap avalanches. In this paper, we study the parameter space of the ICS model for 15 pulsars that share the common pulse profile evolution phenomenon, where 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-squares 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. [ABSTRACT FROM AUTHOR]

Anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs) are magnetar candidates, i.e., neutron stars powered by a strong magnetic field. If they are indeed magnetars, they will emit high-energy gamma rays that are detectable by the Fermi Large Area Telescope (LAT), according to the outer gap model. However, no significant detection is reported in recent Fenni-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 IE 1547.0-5408, XTE J1810-197, IE 1048.1-5937, and 4U 0142+61 should have been detected by Fermi-LAT. There is therefore a conflict between the outer 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. [ABSTRACT FROM AUTHOR]

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 (MSPs) 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 γ-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 γ-ray emission comes from higher altitudes in the magnetosphere. We present the simulated light curves for three young pulsars (the Crab, the Vela and the Geminga) and three millisecond pulsars (PSR J0030+0451, PSR J0218+4232 and PSR J 3715) using the annular gap model. Our simulations can reproduce the main properties of the observed light curves. [ABSTRACT FROM AUTHOR]

We investigate the possibility that pulsars act as the lens in gravitational microlensing events towards the Galactic bulge or a spiral arm. Our estimation is based on the anticipated survey and observations of the Five hundred metre Aperture Spherical Telescope (FAST) and the Square Kilometer Array (SKA). Two different models of pulsar distribution are used. We find that the lensing rate is ≥1 event per decade, which is high enough to search for the real events. Therefore, microlensing observations that will focus on pulsars identified by FAST or SKA in the future are important. As an independent determination of pulsar mass, the 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. Observations of such events in the future using advanced optical facilities (e.g. the James Webb Space Telescope and the Thirty Meter Telescope) are highly recommended. [ABSTRACT FROM AUTHOR]

The observational determination of radiation locations can constrain pulsar radiation models. The process in a strong magnetic field is one of the fundamental physical processes contributing to pulsar radiation mechanisms. Photons generated near a pulsar surface with sufficient energy will be absorbed in the magnetosphere. Considering aberrational, rotational and general relativistic effects, we calculate the optical depth for γ-ray photons, and we use the derived optical depth to determine the lower bounds of the radiation altitude for photons with given energies. As a case study, we obtain the low bounds of radiation altitude for the Crab pulsar for photons with energies of 5 GeV–1 TeV. [ABSTRACT FROM AUTHOR]

Pulsars have been recognized to be normal neutron stars, but sometimes have been argued to be quark stars. Submillisecond pulsars, if detected, would play an essential and important role in distinguishing quark stars from neutron stars. We focus on the formation of such submillisecond pulsars in this paper. A new approach to the formation of a submillisecond pulsar (quark star) by means of the accretion-induced collapse (AIC) of a white dwarf is investigated. Under this AIC process, we found that: (i) almost all newborn quark stars could have an initial spin period of ∼0.1 ms; (ii) nascent quark stars (even with a low mass) have a sufficiently high spin-down luminosity and satisfy the conditions for pair production and sparking process and appear as submillisecond radio pulsars; (iii) in most cases, the times of newborn quark stars in the phase with spin period <1 (or <0.5) ms are long enough for the stars 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 the AIC process can have shorter periods (≤0.5 ms), whereas the periods of neutron stars formed in accretion spin-up processes must be longer than 0.5 ms. Thus, if a pulsar with a period shorter than 0.5 ms is identified in the future, it could be a quark star. [ABSTRACT FROM AUTHOR]

A series of five unusual slow glitches of the radio pulsar B1822–09 (PSR J1825–0935) was observed between 1995 and 2005. This is a phenomenon that is understood in a solid quark star model, and reasonable parameters for slow glitches are given in this paper. We propose that, because of increasing shear stress as the pulsar spins down, a slow glitch may occur, beginning with the collapse of a superficial layer of the quark star. This layer of material turns to viscous fluid at first, the viscosity of which helps to deplete the energy released from both the accumulated elastic energy and the gravitation potential. There is then a slow glitch. Numerical calculations show that the slow glitches that have been observed could be reproduced if the effective coefficient of viscosity is ∼102 cm2 s−1 and the initial velocity of the superficial layer is of the order of 10−10 cm s−1 in the coordinate rotating frame of the star. [ABSTRACT FROM AUTHOR]

We propose to determine the mass and radius of a neutron star (NS) using three measurable mass–radius relationships, namely the ‘apparent’ radius inferred from the NS thermal emission, the gravitational redshift inferred from the absorption lines, as well as the averaged stellar mass density inferred from the orbital Keplerian frequency derived from the kilohertz quasi-periodic oscillation data. We apply the method to constrain the NS mass and radius of the X-ray sources, 1E 1207.4−5209, Aql X-1 and EXO 0748−676. [ABSTRACT FROM AUTHOR]

Three supergiant flares from soft γ-ray repeaters are observed, with typical released energy of ∼1044—47 erg. A conventional model (i.e. the magnetar model) for such events is catastrophic magnetism-powered instability through a magnetohydrodynamic process, in which a significant part of the short–hard γ-ray bursts could also be the result of magnetars. Based on various observational features (e.g. precession, glitches, thermal photon emission) and the underlying theory of strong interaction (quantum chromodynamics), it cannot yet be ruled out that pulsar-like stars might be actually solid quark stars. Strain energy develops during the life of a solid star, and starquakes could occur when stellar stresses reach a critical value, with a huge amount of energy released. An alternative model for supergiant flares of soft γ-ray repeaters is presented, in which the energy release during a starquake of a solid quark star is calculated. Numerical results for spherically asymmetric solid stars show that the gravitational energy released during a giant quake could be as high as 1048 erg if the tangential pressure is slightly higher than the radial one. Difficulties in magnetar models may be overcome if anomalous X-ray pulsars/soft γ-ray repeaters are accreting solid quark stars with mass ∼1—2M . [ABSTRACT FROM AUTHOR]

A unique transient bursting radio source, GCRT J1745−3009, has been discovered near the direction of the Galactic Centre. The explanation of this phenomenon is still an open question, although some efforts to understand its nature have been made. This Letter shows that most of the observed features can be reproduced by our proposed precessing pulsar model. It is found that the precession angle of the pulsar should be larger (≳15°) than that of previously known precessing pulsars, which have a precession angle ≲10°, if the beam width of the pulsar is larger than 10°. The pulsar could be a nulling (or even extremely nulling) radio pulsars to account for the transient nature of the source. This model can be confirmed if a pulsar is detected at the position of the source. The pulsar could hardly be a normal neutron star (but could probably be a solid quark star) if the spin period of the pulsar is detected to be ≳10 ms in the future. [ABSTRACT FROM AUTHOR]

Both rotation- and accretion-powered low-mass bare strange stars are studied, with particular regard to their astrophysical appearance. It is suggested that low-mass bare strange stars, with weaker ferromagnetic fields than that of normal pulsars, could result from the accretion-induced collapse of white dwarfs. According to its peculiar timing behaviour, we propose that the radio-quiet object, 1E 1207.4−5209, could be a low-mass bare strange star with a polar surface magnetic field ofand a radius of a few kilometres. The low-mass bare strange star idea is helpful in distinguishing neutron and strange stars, and is testable by imaging pulsar-like stars with the future Constellation-X telescope. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM PUBLISHER]

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. In compact stars at only a few nuclear densities but low temperature, quarks could be interacting strongly with each other. That might produce quarks grouped in clusters, although the hypothetical quark-clusters in cold dense matter have not been confirmed due to the lack of both theoretical and experimental evidence. A so-called H-cluster matter is proposed in this paper as the nature of dense matter in reality.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). We study the stars composed of H-clusters, i.e., H-cluster stars, and derive the dependence of their maximum mass on the in-medium stiffening effect, showing that the maximum mass could be well above 2 M⊙ as observed and that the resultant mass-radius relation fits the measurement of the rapid burster under reasonable parameters. Besides a general understanding of different manifestations of compact stars, we expect further observational and experimental tests for the H-cluster stars in the future. [ABSTRACT FROM PUBLISHER]

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 the first principles, the intercluster interaction might be analogized to the interaction between inert molecules. Cold quark matter would then crystallize in a solid state if the intercluster potential is deep enough to trap the clusters in the wells. We apply the Lennard-Jones potential to describe the intercluster potential and derive the equations of state, which are stiffer than those derived in conventional models (e.g. MIT bag model). If quark stars are composed of the Lennard-Jones matter, they could have high maximum masses ( ) as well as very low masses ( ). These features could be tested by observations. [ABSTRACT FROM AUTHOR]