Deconfinement

Another development in the quantum chaos where finite-temperature effects are important is the Quantum field theory. As it is shown by recent studies on the Quantum Chromodynamics (QCD) Dirac operator level statistics (Bittner et.al., 1999), nearest level spacing distribution of this operator is governed by random matrix theory both in confinement and deconfinement phases. In the presence of in-medium effects... 

From this expression we can obtain the value of Tc corresponding to a given value of L. For L 1 fm, which is a value of the order of confining lengths for hadrons, we obtain Tc 0.438 /m 1 87.6 MeV. This gives us a crude estimate of the Casimir contribution of a single quark flavor for the deconfining transition for hadrons. 

Figure 3 compares P(s) of full QCD with Nf = 3 flavors and quark mass ma = 0.05 to the RMT result. In the confinement as well as in the deconfinement phase we observe agreement with RMT up to very high [3 (not shown). The observation that P(s) is not influenced by the presence of dynamical quarks is expected from the results of Ref. (Fox and Kahn, 1964), which apply to the case of massless quarks. Our... 

Mishustin et al. (2003). The results of calculation of hadronic (H) and quark stellar models (SS, QC and MC) in Hard-Dense-Loop approach are represented in Fig. 9 from Thoma et al. (2003), where one of the model parameters is changing. The free quarks exist in the state of deconfined quarks, and the density when deconfined quarks become energetically preferable is also rather indefinite (Berezhiani et al., 2003). 

Bombaci, I. (2003). A possible signature for quark deconfinement in the compact star in 4U 1728-34. astro-ph/0307522. 

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. 

In connection with quark stars one can speculate, that additional energy due to deconfinement can lead to additional kick, so that among high velocity compact objects the fraction of quark stars can be higher. For example, if the... 

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... 

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. 

A new class of effective Lagrangians have been constructed to show how the information about the center group symmetry is efficiently transferred to the actual physical states of the theory [12-15] and will be reviewed in detail elsewhere. Via these Lagrangians we were also able to have a deeper understanding of the relation between chiral restoration and deconfinement [15] for quarks in the fundamental and in the adjoint representation of the gauge group. 

In reality, we are more interested in the intermediate density region, where the color superconducting phase may exist in the interior of neutron stars or may be created in heavy ion collisions. Unfortunately, we have little knowledge about this region we are not sure how the deconfinement and the chiral restoration phase transitions happen, how the QCD coupling constant evolves and how the strange quark behaves in dense matter, etc. Primarily, our current... 

One expects the diquark condensate to dominate the physics at densities beyond the deconfinement/chiral restoration transition and below the critical temperature. Various phases are possible. E.g., the so called 2-color superconductivity (2SC) phase allows for unpaired quarks of one color. There may also exist a color-flavor locked (CFL) phase [7] for not too large value of the strange quark mass ms, for 2A > m2s/fiq, cf. [8], where the color superconductivity... 

Diquark condensation makes the EoS harder, which leads to an increase in the maximum mass of the quark star configuration when compared to the case without diquark condensation. For finite temperatures the masses are smaller than at T = 0. For asymptotically high temperatures and densities the EoS behaves like a relativistic ideal gas, where the relation pressure versus energy density is temperature independent. In contrast to the bag model where this behavior occurs immediately after the deconfinement transition, our model EoS has a temperature dependent P(e) relation also beyond this point. 

According to Quantum Chromodynamics (QCD) a phase transition from hadronic matter to a deconfined quark phase should occur at a density of a few times nuclear matter saturation density. Consequently, the core of the more massive neutron stars is one of the best candidates in the Universe where such deconfined phase of quark matter (QM) could be found. Since /3-stable hadronic matter posses two conserved charges (i.e., electric charge and baryon... 

Let us now consider the more realistic situation in which one takes into account the energy cost due to finite size effects in creating a drop of deconfined... 

The nucleation time r, i. e.. the time needed to form a critical droplet of deconfined quark matter, can be calculated for different values of the stellar central pressure Pc which enters in the expression of the energy barrier in Eq. (5). The nucleation time can be plotted as a function of the gravitational mass... 

To summarize, in the present scenario pure hadronic stars having a central pressure larger than the static transition pressure for the formation of the Q -phase are metastable to the decay (conversion) to a more compact stellar configuration in which deconfined quark matter is present (i. e., HyS or SS). These metastable HS have a mean-life time which is related to the nucleation time to form the first critical-size drop of deconfined matter in their interior (the actual mean-life time of the HS will depend on the mass accretion or on the spin-down rate which modifies the nucleation time via an explicit time dependence of the stellar central pressure). We define as critical mass Mcr of the metastable HS, the value of the gravitational mass for which the nucleation time is equal to one year Mcr = Miis t = lyr). Pure hadronic stars with Mh > Mcr are very unlikely to be observed. Mcr plays the role of an effective maximum mass for the hadronic branch of compact stars. While the Oppenheimer-Volkov maximum mass Mhs,max (Oppenheimer Volkov 1939) is determined by the overall stiffness of the EOS for hadronic matter, the value of Mcr will depend in addition on the bulk properties of the EOS for quark matter and on the properties at the interface between the confined and deconfined phases of matter (e.g., the surface tension a). 

B > B1. These high values of the bag constant do not allow the quark deconfinement to occur in the maximum mass hadronic star either. Here B1 denotes the value of the bag constant for which the central density of the maximum mass hadronic star is equal to the critical density for the beginning of the mixed quark-hadron phase. For these values of B, all compact stars are pure hadronic stars. 

BIU < B < l>11. In this case, the critical mass for the pure hadronic star sequence is less than the maximum mass for the same stellar sequence, i.e., Mcr < Mus,max- Nevertheless (for the present EOS model), the baryonic mass Mb(Mcr) of the hadronic star with the critical mass is larger than the maximum baryonic mass MqS max of the hybrid star sequence. In this case, the formation of a critical size droplet of deconfined matter in the core of the hadronic star with the critical mass, will trigger off a stellar conversion process which will produce, at the end, a black hole (see cases marked as BH in Tab. 1 and Tab. 2). As in the previous case, it is extremely unlikely to populate the hybrid star branch. The compact star predicted by these EOS models are pure HS. Hadronic stars with a gravitational mass in the range Mhs(MqS rnax) < Mhs < Mcr (where MqS max is the baryonic mass of the maximum mass configuration for the hybrid star sequence) are metastable with respect to a conversion to a black hole. 

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