Quark matter

After a 20 year break V. H. Ambartsumyan and G. S. Sahakian initiated an intensive research on compact objects during the 1960s in Armenia. In their pioneering work on compact stars they showed, that with increasing density, hyperons appear in nuclear matter and thus a neutron star at high densities consists predominantly of hyperons. Thus, as the density increases more and more heavy particles become stable. After the discovery of quarks as basic constituents of hadrons (including hyperons) the ideas of compact stars with quark cores or stars entirely composed of quark matter were presented. 

Figure 9. Mass-radius relation for pure strange quark matter stars (left) and hybrid stars (right). GO - G4 models of hybrid stars corresponding to different parameters of the model. H pure hadron star, QC star has a quark core, MC star has a mixed core, from Thoma et al. (2003).

Alford, M. J. (2003). Dense quark matter in compact stars. J.Phys.G30 S441-S450. 

Berezhiani, Z., Bombaci, I., Drago, A., Frontera, F., Lavagno, A. (2003). Gamma Ray Bursts from delayed collapse of neutron stars to quark matter stars. Astrophys.J., 586 1250-1253. 

Sedrakian, D. M., Blaschke, D. (2002). Magnetic field of a neutron star with color superconducting quark matter core. Astrofiz., 45 203-212. 

Thoma, M.H., Triimper, J., Burwitz, V. (2003). Strange Quark Matter in Neutron Stars - New Results from Chandra and XMM. J.Phys.G30 S471-S478. 

Neutron stars are important laboratories for the physics of high-density matter. Unlike particles in relativistic heavy-ion colliders, the matter in the cores of neutron stars has a thermal energy that is much less than its rest-mass energy. Various researchers have speculated whether neutron star cores contain primarily nucleons, or whether degrees of freedom such as hyperons, quark matter, or strange matter are prevalent (see Lattimer Prakash 2001 for a recent review of high-density equations of state). 

Equations of state involving only nucleonic matter are consistent with all available data. Some hints of evidence for very compact stars have been proposed (Li et al. 1999), which could indicate strange matter, but these are very model-dependent at the present. Even so, exotic states such as quark matter or strange matter are not excluded. 

The commonly accepted pulsar model is a neutron star of about one solar mass and a radius of the order of ten kilometers. A neutron star consists of a crust, which is about 1 km thick, and a high-density core. In the crust free neutrons and electrons coexist with a lattice of nuclei. The star s core consists mainly of neutrons and a few percents of protons and electrons. The central part of the core may contain some exotic states of matter, such as quark matter or a pion condensate. Inner parts of a neutron star cool up to temperatures 108iT in a few days after the star is formed. These temperatures are less than the critical temperatures Tc for the superfluid phase transitions of neutrons and protons. Thus, the neutrons in the star s crust and the core from a superfluid, while the protons in the core form a superconductor. The rotation of a neutron superfluid is achieved by means of an array of quantized vortices, each carrying a quantum of vorticity... 

Neutron stars (NSs) are perhaps the most interesting astronomical objects from the physical point of view. They are associated with a variety of extreme phenomena and matter states for example, magnetic fields beyond the QED vacuum pair-creation limit, supranuclear densities, superfluidity, superconductivity, exotic condensates and deconfined quark matter, etc. 

Abstract We discuss the high-density nuclear equation of state within the Brueckner-Hartree-Fock approach. Particular attention is paid to the effects of nucleonic three-body forces, the presence of hyperons, and the joining with an eventual quark matter phase. The resulting properties of neutron stars, in particular the mass-radius relation, are determined. It turns out that stars heavier than 1.3 solar masses contain necessarily quark matter. 

However, these results should be considered as only provisory, since it is well known that the inclusion of hyperons [15, 16] or quark matter [28] may... 

The results obtained with a purely baryonic EOS call for an estimate of the effects due to the hypothetical presence of quark matter in the interior of the neutron star. Unfortunately, the current theoretical description of quark matter is burdened with large uncertainties, seriously limiting the predictive power of any theoretical approach at high baryonic density. For the time being we can therefore only resort to phenomenological models for the quark matter EOS and try to constrain them as well as possible by the few experimental information on high density baryonic matter. 

We first review briefly the description of the bulk properties of uniform quark matter, deconfined from the /3-stable hadronic matter mentioned in the previous section, by using the MIT bag model [31]. The thermodynamic potential of f = u,d,s quarks can be expressed as a sum of the kinetic term and the one-gluon-exchange term [32, 33] proportional to the QCD fine structure... 

The EOS resulting from this procedure is shown in Fig. 10(b), where the pure hadron, mixed, and pure quark matter portions are indicated. The mixed phase begins actually at a quite low density around po- Clearly the outcome of the mixed phase construction might be substantially changed, if surface and Coulomb energies were taken into account [36], For the time being these are, however, unknown and have been neglected. 

The final result for the structure of hybrid neutron stars is shown in Fig. 11, displaying mass-radius and mass-central density relations. It is evident that the most striking effect of the inclusion of quark matter is the increase of the maximum mass, now reaching about 1.5 M . At the same time, the typical neutron star radius is reduced by about 3 km to typically 9 km. Hybrid neutron stars are thus more compact than purely hadronic ones and their central energy density is larger. For completeness, the figure shows besides static neutron star... 

In this contribution we reported the theoretical description of nuclear matter in the BHF approach and its various refinements, with the application to neutron star structure calculation. We pointed out the important role of TBF at high density, which is, however, strongly compensated by the inclusion of hyperons. The resulting hadronic neutron star configurations have maximum masses of only about 1.3 M , and the presence of quark matter inside the star is required in order to reach larger values. 

Concerning the quark matter EOS, we found that a density dependent bag parameter B p) is necessary in order to be compatible with the CERN-SPS findings on the phase transition from hadronic to quark matter. Joining the corresponding EOS with the baryonic one, maximum masses of about 1.6 M are reached, in line with other recent calculations of neutron star properties employing various phenomenological RMF nuclear EOS together with either effective mass bag model [39] or Nambu-Jona-Lasinio model [40] EOS for quark matter. 

The value of the maximum mass of neutron stars obtained according to our analysis appears rather robust with respect to the uncertainties of the nuclear and the quark matter EOS. Therefore, the experimental observation of a very heavy (M > 1.6M ) neutron star, as claimed recently by some groups [41] (M ss 2.2 M ), if confirmed, would suggest that either serious problems are present for the current theoretical modelling of the high-density phase of nuclear matter, or that the assumptions about the phase transition between hadron and quark phase are substantially wrong. In both cases, one can expect a well defined hint on the high density nuclear matter EOS. 

Abstract We review our quasiparticle model for the thermodynamics of strongly interacting matter at high temperature, and its extrapolation to non-zero chemical potential. Some implications of the resulting soft equation of state of quark matter at low temperatures are pointed out. 

Astrophysical observations, such as the mass and the radius of dense stars, may in turn also impose constraints on the equation of state of deconfined quark matter. 

The effects of deviations of a from 3 being small, cf. Figure 8, we pointed out [11] the possibility of the existence of very dense and compact objects, M rb 0.9Msun and R rb 6 km, composed mainly of quark matter. 

F. Barrois, Nonperturbative effects in dense quark matter, Ph.D. thesis, Caltech, UMI 79-04847-mc (microfiche). 

C. Vogt, R. Rapp and R. Ouyed, Photon emission from dense quark matter, Nucl. Phys. A735, 543 (2003). 

See M. Alford, Dense quark matter in nature, Prog. Theor. Phys. Suppl. 153,1 (2003), and references therein. 

How does matter behave as we squeeze it extremely hard This question is directly related to one of the fundamental questions in Nature what are the fundamental building blocks of matter and how they interact. According to QCD, matter at high density is quark matter, since quarks interact weaker and weaker as they are put closer and closer. 

At what temperature and density does the phase transition to quark matter occur To determine the phase diagram of thermodynamic QCD is an outstanding problem. The phases of matter are being mapped out by colliding heavy-ions and by observing compact stars. Since QCD has only one intrinsic scale, Aqcd> the phase transition of QCD matter should occur at that scale as matter is heated up or squeezed down. Indeed, recent lattice QCD calculations... 

At low temperature or energy, most degrees of freedom of quark matter are irrelevant due to Pauli blocking. Only quasi-quarks near the Fermi surface are excited. Therefore, relevant modes for quark matter are quasi-quarks near the Fermi surface and the physical properties of quark matter like the symmetry of the ground state are determined by those modes. High density effective theory (HDET) [7, 8] of QCD is an effective theory for such modes to describe the low-energy dynamics of quark matter. 

Now, let us consider the divergence of axial currents in HDET, which is related to the axial anomaly and also to how the quark matter responds to external axial-current sources like electroweak probes. 

While, in the BCS theory, such attractive force for electron Cooper pair is provided by phonons, for dense quark matter, where phonons are absent, the gluon exchange interaction provides the attraction, as one-gluon exchange interaction is attractive in the color anti-triplet channel1 One therefore expects that color anti-triplet Cooper pairs will form and quark matter is color superconducting, which is indeed shown more than 20 years ago [13, 14],... 

It is quite likely to find dense quark matter inside compact stars like neutron stars. However, when we study the quark matter in compact stars, we need to take into account not only the charge and color neutrality of compact stars and but also the mass of the strange quark, which is not negligible at the intermediate density. By the neutrality condition and the strange quark mass, the quarks with different quantum numbers in general have different chemical potentials and different Fermi momenta. When the difference in the chemical potential becomes too large the Cooper-pairs breaks or other exotic phases like kaon condensation or crystalline phase is more preferred to the BCS phase. 

S. C. Frautschi, Asymptotic freedom and color superconductivity in dense quark matter, in Proceedings of the Workshop on Hadronic Matter at Extreme Energy Density, N. Cabibbo, Editor, Erice, Italy (1978). 

COLOR SUPERCONDUCTING QUARK MATTER AND THE INTERIOR OF NEUTRON STARS... 

Abstract We investigate the phase structure of color superconducting quark matter at intermediate densities for two- and three flavor systems. We thereby focus our attention on the influence of charge neutrality conditions as well as /3-equilibrium on the different phases. These constraints are relevant in the context of quark matter at the interior of compact stars. We analyze the implications of color superconductivity on compact star configurations using different hadronic and quark equations of state. 

Keywords Quark matter, color superconductivity, neutron stars... 

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