Quark stars configurations

DIQUARK CONDENSATION EFFECTS ON HOT QUARK STAR CONFIGURATIONS... 

Diquark condensation effects on hot quark star configurations... 

Figure 5. Hot (T = 40 MeV) versus cold (T = 0) quark star configurations for the Gaussian model(Left graphic)and Lorentzian(Right graphic) case A with diquark condensation (dashed versus full lines) and case B without diquark condensation (dash-dash-dotted versus dash-dotted lines). When a quark star with initial mass Mi cools down from T = 40 MeV to T = 0 at fixed baryon number Nb the mass defect AM occurs.

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. 

Figure Jt. The maximum mass MQs,max for the quark star configurations (HS or SS), the critical mass Mcr and the mass Mfi of the stable QS to which it evolves are plotted as a function of the bag constant B. The vertical doted fines labeled B1 — BIV mark the boundary of different ranges of the bag constant which give a different astrophysical output for our scenario, as discussed in the text. The dashed horizontal line gives the value of the maximum mass for the pure hadronic star sequence. All the results are relative to the GM3 model for the EOS for the hadronic phase, the surface tension a is taken equal to 30 MeV/fm2.

The stellar conversion process, described so far, will start to populate the new branch of quark stars (the part of the QS sequence plotted as a continuous curve in Fig. 3). Long term accretion on the QS can next produce stars with masses up to the limiting mass Mqs max for the quark star configurations. 

Figure 13. Quark star configurations for different antineutrino chemical potentials r = 0, 100, 150 MeV. The total mass M in solar masses (MsUn = M in the text) is shown as a function of the radius R (left panel) and of the central number density nq in units of the nuclear saturation density no (right panel). Asterisks denote two different sets of configurations (A,B,f) and (A ,B ,f ) with a fixed total baryon number of the set.

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. 

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. 

Figure 6. Mass-radius relation of different compact star configurations. The left panels correspond to calculations with parameter set RKH for the quark matter phase and the right panels to parameter set HK, respectively. From the upper panel downwards the hadronic phase is described by a BHF calculation without hyperons [55], a relativistic mean field calculation [57] and a chiral SU(3) model [53].

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... 

Here we compare configurations with and without CS, in order to investigate the effect of diquark condensation on the total energy of a quark star and to... 

Figure 4. Stable configurations of quark stars for different temperatures T = 0,40,60 MeV. Mass as a function of central baryon density (left panels) and of the radius (right panels) for the Gaussian model (left graph) and for the Lorentzian model (right graph).

It has been shown for a hybrid star model which uses the quark matter EoS presented in this work that the possibility to obtain a stable star configuration with 2SC quark matter core depends on the form-factor of the quark interaction [34], The Gaussian and Lorentzian form-factor models do allow a quark matter core, whereas the NJL form-factor model does not. 

The resulting phase diagram is shown in Fig. 5. It includes a 2-flavor color superconductivity (2SC) phase for which quarks of one color, say blue, remain unpaired. The color-flavor locking (CFL) phase [25] requires approximate SU(3) flavor symmetry and can be excluded from our discussion since strange quarks remain confined up to the highest densities occuring in a compact star configuration [24],... 

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.

Energy release due to (anti)neutrino untrapping. The configurations for the quark stars are obtained by solving the Tolman-Oppenheimer-Volkoff equations for a set of central quark number densities nq for which the stars are stable. In Fig. 13 the configurations for different antineutrino chemical potentials are shown. The equations of state with trapped antineutrinos are softer and therefore this allows more compact configurations. The presence of antineutrinos tends to increase the mass for a given central density. 

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). 

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