Hybrid star

More recently Frechet and Gitsov [130] used a similar approach as above and synthesized a novel series of dendritic copolymers derived from a central penta-erythritol core unit. These hybrid star molecules behaved as unimolecular micelles with different core-shell conformational-structures as a response to the polarity of the solvent used. 

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).

Here and below we will not distinguish between NSs, quark stars, hybrid stars etc. unless explicitely stated. 

Figure 12. Kepler period versus the rotational mass for purely hadronic stars as well as hybrid stars. The following core compositions are considered i) nucleons and leptons (dotted line) ii) nucleons, hyperons, and leptons (dashed line) in) hadrons, quarks, and leptons (solid line). The shaded area represents the current range of observed data.

Besides the crust and the hadron shell, the hybrid star contains also a quark core. Both the nucleon shell and the quark core can be in superconducting phases, in dependence on the value of the temperature. Fluctuations affect transport coefficients, specific heat, emissivity, masses of low-lying excitations and respectively electromagnetic properties of the star, like electroconductivity and magnetic field structure, e.g., renormalizing critical values of the magnetic field (/ ,, Hc, Hc2). 

Abstract Hybrid stars with extremely high central energy density in their core are natural laboratories to investigate the appearance and the properties of compactihed extra dimensions with small compactification radius - if these extra dimensions exist at all. We introduce the necessary formahsm to describe quantitatively these objects and the properties of the formed hydrostatic equilibrium. Different scenarios of the extra dimensions are discussed and the characteristic features of these hybrid stars are calculated. 

Here we display a few of our ideas about these extra dimensions, their possible connection to particle physics and their appearance in the core of hybrid stars. We summarize our numerical results and discuss the observability of extra dimensions in these objects. 

The value of the compactification radius, Rc In the present approach this radius was a free parameter. For demonstration we chose the radius Rc = 0.33 10 13 cm, when the strange A baryon could behave as the first excitation of a neutron. Such an extradimensional object can mimics a compact star with neutrons in the mantle and A s in the core. With smaller Rc the exotic component appears at larger densities - we may run into the unstable region of the hybrid star and the extra dimension remains undetectable. However, with larger Rc the mass gap becomes smaller and the transition happens at familiar neutron star densities. In this way, reliable observations could lead to an upper bound on Rc. 

G.G. Barnafoldi, P. Levai, and B. Lukacs, Heavy quarks or compactified extra dimensions in the core of hybrid stars , in Proceedings of the 4th Int. Workshop on New Worlds in Astroparticle Physics, Faro, Portugal, Worlds Scientific, Singapore, 2003. (astro-ph/0312330). 

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. 

In our scenario, we consider a purely hadronic star whose central pressure is increasing due to spin-down or due to mass accretion, e.g., from the material left by the supernova explosion (fallback disc), from a companion star or from the interstellar medium. As the central pressure exceeds the threshold value Pq at static transition point, a virtual drop of quark matter in the Q -phase can be formed in the central region of the star. As soon as a real drop of Q -matter is formed, it will grow very rapidly and the original Hadronic Star will be converted to and Hybrid Star or to a Strange Star, depending on the detail of... 

In Fig. 3, we show the MR curve for pure HS within the GM1 model for the EOS of the hadronic phase, and that for hybrid stars or strange stars for different values of the bag constant B. The configuration marked with an asterisk on the hadronic MR curves represents the hadronic star for which the central pressure is equal to Pq. The full circle on the hadronic star sequence represents the critical mass configuration, in the case a = 30 MeV/fm2. The full... 

B11 < B < l>1. Now, in addition to pure HS, there is a new branch of compact stars, the hybrid stars but the nucleation time r(MHs,max) to form a droplet of Q -matter in the maximum mass hadronic star, is of the same order or much larger than the age of the Universe. Therefore, it is extremely unlikely to populate the hybrid star branch. Once again, the compact star we can observe are, in this case, pure HS. 

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. 

BIV < B < B111. In this range for B one has Mcr < Musi Qs.max)-There are now two different branches of compact stars pure hadronic stars with MHs < Mcr, and hybrid stars with MQS(Mbr) < Mqs < MQs,max (here MQs(Mbr) = 3 / / , is the gravitational mass of the hybrid star with the same baryonic mass of the critical mass hadronic star). 

Next we consider the compact star in the low mass X-ray binary 4U 1728-34. In a very recent paper Shaposhnikov et al. (2003) (hereafter STH) have analyzed a set of 26 Type-I X-ray bursts for this source. The data were collected by the Proportional Counter Array on board of the Rossi X-ray Timing Explorer (RXTE) satellite. For the interpretation of these observational data Shaposhnikov et al. 2003 used a model of the X-ray burst spectral formation developed by Titarchuk (1994) and Shaposhnikov Titarchuk (2002). Within this model, STH were able to extract very stringent constrain on the radius and the mass of the compact star in this bursting source. The radius and mass for 4U 1728-34, extracted by STH for different best-fits of the burst data, are depicted in Fig. 6 by the filled squares. Each of the four MR points is relative to a different value of the distance to the source (d = 4.0, 4.25, 4.50, 4.75 kpc, for the fit which produces the smallest values of the mass, up to the one which gives the largest mass). The error bars on each point represent the error contour for 90% confidence level. It has been pointed out (Bombaci 2003) that the semi-empirical MR relation for the compact star in 4U 1728-34 obtained by STH is not compatible with models pure hadronic stars, while it is consistent with strange stars or hybrid stars. 

Figure 9. Mass - radius relations for compact star configurations with different EoS purely hadronic star with HHJ EoS (long-dashed), stable hybrid stars for HHJ - INCQM EoS with 2SC (solid) and without 2SC phase (dash-dotted) for the Gaussian formfactor. We show the influence of a tiny variation of the coupling constant Gi by the filled grey band. The difference between the models 2SC and 2SC corresponds to a shift in the bag function (see Fig. 8) 3 MeV/fm3. For comparison, observational constraints on the compactness are given from the "small compact star RX J1856.5-3754 and from the high surface redshift object EXO 0748-676 which can both be obeyed by our hybrid star EoS.

Figure 10. The Mass - radius relation and mass - central energy density dependencies for rotating (dashed lines) and nonrotating (solid lines) hybrid star configurations...

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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