Superconductivity quark matter

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

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. 

Color superconducting quark matter and the interior of neutron stars... 

Compact stars with a color superconducting quark matter core... 

This section will be devoted to the study of the composition of a compact star including the possibility of a color superconducting quark matter core. Recently this question has been addressed by several authors using a bag-model description of the quark phase [48] or an NJL-type model [49-52], In the following, we will discuss the results of Refs. [49, 52] where -in contrast to Refs. [50, 51]- strange quarks have been taken into account. 

The high-density phases of QCD at low temperatures can be realized in rotating compact stars - pulsars. Therefore, the observational data from pulsars could provide potentially important information on the state of matter at super-nuclear densities, in particular the superconducting quark matter. 

The authors of Ref. [12] reconsidered the problem of magnetic field in quark matter taking into account the rotated electromagnetism . They came to the conclusion that magnetic field can exist in superconducting quark matter in any case, although it does not form a quantized vortex lattice, because it obeys sourceless Maxwell equations and there is no Meissner effect. In our opinion this latter result is incorrect, since the equations for gauge fields were not taken into account and the boundary conditions were not posed correctly. 

The Fourier component of the density of the thermodynamic potential (thermodynamic potential per unit volume V) in the superconducting quark matter with the diquark pairing can be written in the following form [12, 16], cf. also [1,11],... 

As a first step in this direction we will discuss here the two flavor color superconducting (2SC) quark matter phase which occurs at lower baryon densities than the color-flavor-locking (CFL) one, see [18, 32], Studies of three-flavor quark models have revealed a very rich phase structure (see [32] and references therein). However, for applications to compact stars the omission of the strange quark flavor within the class of nonlocal chiral quark models considered here may be justified by the fact that central chemical potentials in stable star configurations do barely reach the threshold value at which the mass gap for strange quarks breaks down and they appear in the system [20], Therefore we will not discuss here first applications to calculate compact star configurations with color superconducting quark matter phases that have employed non-dynamical quark models... 

The phase transition to color superconducting quark matter from the lower density regions at small temperatures (T < 5 a 10 MeV) is of first order, while the melting of the diquark condensate and the corresponding transition to normal quark matter at high temperatures is of second order. The presence... 

Color Superconducting Quark Matter and Compact Star Observables... 

Figure 12. Cooling of hybrid star configurations of Fig. 9 with color superconducting quark matter core in 2SC+X phase. Different lines correspond to hybrid star masses in units of the solar mass.

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