Strange stars

The formation of quark (strange) stars does not follow unambiguously from the theory, which may be compatible either with the existence or nonexistence of these objects. 

Emission properties of the surface of bare strange stars. 

Keywords Gamma rays Gamma Ray Burst. Stars Neutron Stars, Strange Stars. Dense... 

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... 

Bv < B < BIV. Finally, as B falls below the value BIV, the Bodmer-Witten hypothesis starts to be fulfilled. Now the stable quark stars formed in the stellar conversion process are strange stars. 

In Fig. 6, we report the radius an the mass of the compact star RX J1856.5-3754 inferred by Walter Lattimer (2002) (see also Kaplan et al. 2002) from the fit of the full spectral energy distribution for this isolated radio-quite neutron star , after a revised parallax determination (Kaplan et al. 2002) which implies a distance to the source of 117 12 pc. Comparing the mass-radius box for RX J1856.5-3754 reported in Fig. 6 with the theoretical determination of the MR relation for different equations of state, one concludes that RX J1856.5-3754 could be (see e.g. Fig. 2 in Walter Lattimer, 2002) either an hadronic star or an hybrid or strange star (see also Drake et al. 2002). 

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. 

Assuming RX J1856.5-3754 to be a pure hadronic star and 4U 1728-34 an hybrid or a strange star, we see from our results plotted in Fig. 6, that this possibility can be realized as a natural consequence of our scenario. Thus, we find that the existence of quark stars (with small radii) does not exclude the possible existence of pure hadronic stars (with large radii), and vice versa. 

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).

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. 

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. 

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. 

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... 

In the framework of the bag model [5], or, in general, under the assumption that the strange quark mass is small [6], one can exclude the 2SC phase in the interior of compact stars when charge neutrality is considered. 

Fig. 1. compares two calculations. The solid line is 4 dimensional calculation with neutrons and A hyperons, the lightest neutral strange baryon. (Ambartsumyan and Saakyan calculated such hybrid compact stars as far back as in 1960 [12].) The dashed and dotted lines come from 5-dimensional calculations with only neutrons, but moving in the extra dimension, too. The higher excitations are started from the triangles and they are named as E, 2, , at compactified radius Rc = 0.33 fm. In this case the 5 dimensional neutron star is almost indistinguishable from a neutron star with A core. However, choosing another compactification radius (e.g. Rc = 0.66 fm) one obtains reasonable differences, which can be seen on Fig. 1. The I-2- If,. indicate the appearance of the excited modes in the latter case (/ ) was left outside of the figure).

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. 

Keywords Neutron stars, strange quark core, quark phase transition, new branch of stability,... 

---