The state of cold quark matter really challenges both astrophysicists and particle physicists, even many-body physicists. It is conventionally suggested that BCS-like color superconductivity occurs in cold quark matter; however, other scenarios with a ground state rather than of Fermi gas could still be possible. It is addressed that quarks are dressed and clustering in cold quark matter at realistic baryon densities of compact stars, since a weakly coupling treatment of the interaction between constituent quarks would not be reliable. Cold quark matter is conjectured to be in a solid state if thermal kinematic energy is much lower than the interaction energy of quark clusters, and such a state could be relevant to different manifestations of pulsar-like compact stars.
First of all, I would like to note that the word "solid " in the title does not relate to solid evidence for quark matter, but represents a new solid state of quark matter. To identify a quark star should certainly be a milestone and could be possible in the future, but now there isn't any solid and model-independent evidence yet.
The state of cold quark matter is debated since 1970s, being interested by either particle physicists or astrophysicists. Because of asymptotic freedom, extremely dense and cold matter is supposed to be of a Fermi gas of free quarks, and a condensate of quark pairs near the Fermi surface (i.e., color superconductivity; CSC) may occur according to perturbative quantum chromodynamics (pQCD) or QCD-based effective models. Astrophysically, however, realistic cold quark matter could only exist in pulsar-like compact stars, and those QCD-based speculations should be tested by different manifestations of such compact stars. I will explain why a solid state of realistic cold quark matter would be necessary from a view point of astrophysics in §1 and §2. More issues related are addressed in later sections.
What’s the nature of pulsars (PSRs)? The final answer to the question surely depends on the understanding of non-pertubative QCD, and relates to one of the 7 Millennium Prize Problems named by the Clay Mathematical Institute. Nevertheless, the models for pulsars can be classified into 4 kinds: hadronic stars (no quark matter), hybrid stars (quark matter in the cores), crusted and bare quark stars (quark matter dominates). The former two are usually called as neutron stars (NSs), while the latter two quark stars (QSs). It is worth noting that hard and model-independent evidence to identify a QS may only be relevant to bare QSs because their quark surfaces have sharp difference distinguishable from others 1 .
Although it is still a matter of debate whether pulsars are neutron or quark stars, some individual PSR-like stars with mass of ∼ 1M ⊙ and ∼ 10 km in radius are certainly detected. Historically, pulsars were supposed to be associated with oscillations of white dwarfs or NSs 2 , but soon recognized as spinning compact NSs 3 , the Kepler frequency of which in Newtonian gravity is
ρ ≃ 841 ρ 10 14 g/cm 3 Hz.
The average densities of NSs or QSs, ρ, are order of M ⊙ /(4π(10 km) 3 /3) ≃ 5 × 10 14 g/cm 3 , a few nuclear densities, which could be high enough to satisfy observational frequency ν < ν Kepler . More than 40 years later, can the NS model works all the way when more and more new phenomena of PSR-like stars are discovered?
1.1, Isolated PSR-like stars: why non-atomic thermal spectra? Many theoretical calculations, first developed by Romani 4 , predicted the existence of atomic features in the thermal X-ray emission of NS (or crusted QS) atmospheres, and advanced facilities of Chandra and XMM-Newton were then proposed to build for detecting those lines in order to constrain stellar mass and radius by spectral red shift and pressure broadening. However, unfortunately, none of the expected spectral features has been detected with certainty up to now, and this negative test may hint a fundamental weakness of the NS models. Though conventional NS models cannot be ruled out by only non-atomic thermal spectra since modified NS atmospheric models with very strong surface magnetic fields 5-6 might reproduce a featureless spectrum too, a natural suggestion to understand the general observation is that pulsars are actually bare QSs 1 because of no atom there on the surfaces.
More observations, however, did show absorption lines of PSR-like stars, particularly from an interesting one, 1E 1207, at ∼ 0.7 keV and ∼ 1.4 keV. When discovered, these lines were suggested to be associated with the atomic transitions of once-ionized helium in an atmosphere with a strong magnetic field, but thought to require artificial assumptions as cyclotron lines 7 . This view was soon criticized by Xu, Wang and Qiao 8 , who addressed that all the 4 criticisms 7 about the cyclotron mechanism can be circumvented and emphasized that 1E 1207 could be a bare QS with surface field of ∼ 10 11 G. Further observations of both spectra feature 9 and precise timing 10 favor the electron-cyclotron model of 1E 1207. The bare QS idea may survive finally if other absorption features (e.g., of the spectra of soft Gamma-ray repeaters and anomalous X-ray pulsars) are also be cyclotron-originated.
1.2, Isolated PSR-like stars: real small X-ray radiation radii? One of the key differences between NSs and (bare) QSs lies in the fact that NSs are gravitationally bound while QSs not only by gravity but also by additional strong interaction due to the strong confinement between quarks. This fact results in an important astrophysical consequence that bare QSs can be very low mass with small radii (and thus spinning very fast, even at sub-millisecond periods 11,12 ), while NSs cannot. We see in Fig. 1 that the radii of gravitationally b
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