Models of Strange Stars with a Crust and Strange Dwarfs

Strange quark stars with a crust and strange dwarfs consisting of a compact strange quark core and an extended crust are investigated in terms of a bag model. The crust, which consists of atomic nuclei and degenerate electrons, has a limiting density of _cr=_drip=4.3·10¹¹ g/cm³. A series of configurations are calculated for two sets of bag model parameters and three different values of _cr (10⁹ g/cm³ _{cr drip}) to find the dependence of a star's mass M and radius R on the central density. Sequences of stars ranging from compact strange stars to extended strange dwarfs are constructed out of strange quark matter with a crust. The effect of the bag model parameters and limiting crust density _cr on the parameters of the strange stars and strange dwarfs is examined. The strange dwarfs are compared with ordinary white dwarfs and observational differences between the two are pointed out.     

Models of strange stars having a crust

Models of strange quark stars with a crust consisting of atomic nuclei and degenerate electrons, maintained by an electrostatic barrier at the surface of the strange quark matter, are investigated for a realistic range of parameters of the MIT bag model. The density at which neutrons escape from nuclei, ρ = ρ_drip, is taken as the maximum possible boundary density of the crust. Series of strange stars are calculated as a function of central density. Configurations with masses of 1.44 and 1.77 M{ie330-1} and a gravitational redshift Z_s = 0.23, corresponding to the best-known observational data, are investigated. The presence of a crust results in the existence of a minimum mass for strange stars, and also helps to explain the glitch phenomenon of pulsars within the framework of the existence of strange quark matter. Translated from Astrofizika, Vol. 42, No. 3, pp. 439–448, July–September, 1999.     

Strange stars and their cooling with positron electrical neutralization of quark matter

Questions of the equilibrium, stability, and observational manifestations of strange stars are considered, in which electrical neutralization of the quark matter is provided by positrons, as occurs for some sets of bag parameters resulting in a stiffer equation of state. Such models consist entirely of self-contained, strange quark matter and their maximum mass reaches 2.4–2.5 M_⊙ with a radius of 13–14 km. The cooling of such strange quark stars both in the absence and in the presence of mass accretion is investigated. It is shown that in the absence of mass accretion onto the strange star, the dependence of temperature (T, K) on age (t, yr) depends very little on the mass of the configuration and has the form T ≈ 2.3·10⁸r^−1/5. If the star’s initial temperature is sufficiently high (T₀≥2·10¹⁰K), then the total number of electron-positron pairs emitted does not depend on it and is determined only by the total mass of the configuration. In the case of accretion, the annihilation of electrons of the infalling fatter with positrons of the strange quark matter results in the emission of γ-rays with an energy of∼0.5 MeV, by observing which one can distinguish candidates for strange stars. The maximum temperature of strange stars with mass accretion is calculated. Translated from Astrofizika, Vol. 42, No. 4, pp. 617–630, October–December, 1999.     

On the Structure of the Free Surface of Self-Binding Quark Matter

The distributions of electrons and of electrical potential at the free surface of strange quark matter are determined within the framework of the MIT bag model. It is shown that, with allowance for the decay of quarks near the surface due to the outward escape of electrons, the electric charge density of quarks at the surface increases by a factor of 17-25, the thickness of the transitional layer decreases from 230 Fm to 15 Fm, and the field strength increases by a factor of 1.7. The difference between the chemical potentials of electrons at the surface and in deep layers decreases from 7 MeV to 0.8 MeV, which increases the limiting possible density of ordinary matter above a strange quark star.     

Stability valley for strange dwarfs

This is a study of the stability of strange dwarfs, superdense stars with a small self-confining core (M _core  < 0.02 M_⊙) containing strange quark matter and an extended crust consisting of atomic nuclei and degenerate electron gas. The mass and radius of these stars are of the same orders as those of ordinary white dwarfs. It is shown that any study of their stability must examine the dependence of the mass on two variables, which can, for convenience, be taken to be the rest mass (total baryon mass) of the quark core and the energy density ρ _tr of the crust at the surface of the quark core. The range of variation of these quantities over which strange dwarfs are stable is determined. This region is referred to as the stability valley for strange dwarfs. The mass and radius from theoretical models of strange dworfs are compared with observational data obtained through the HIPPARCOS program and the most probable candidate strange dwarfs are identified.     

Masses of macroscopic quark configurations in metric and dynamic theories of gravitation

Within the bounds of the general relativity and in gravidynamics, spherically-symmetric configurations are considered with the limit equation of state (P = ( - 4B)/3) and with the density increasing to the center. It is shown that unlike GR, where the existence of strange stars only is permissible (u-, d-, s-quarks), in the consistent dynamic theory of gravitation the existence ofstable configuration withr ^–2 (quark star) is possible with a bag out of quark-gluon plasma which includes all possible quark flavors (u, d, s, c, b, t, .. .). The total mass of such a compact object with the bag of the radius of 10 km (whose surface consists of the strange self-bound matter) must be 6 - 7M .     

The Crust Properties and Cooling of Strange Stars

We investigate the influence of the following parameters on the crust properties of strange stars: the strange quark mass (m _s), the strong coupling constant (α_c) and the vacuum energy density (B). It is found that the mass density at the crust base of strange stars cannot reach the neutron drip density. For a conventional parameter set of m _s=200 MeV, B ^1/4 = 145 MeV and α_c = 0.3, the maximum density at the crust base of a typical strange star is only 5.5 × 10¹⁰ gcm^-3, and correspondingly the maximum crust mass is 1.4 ×10^-6 M_⊙. Subsequently, we present the thermal structure and the cooling behavior of strange stars with crusts of different thickness, and under different diquark pairing gaps. Our work might provide important clues for distinguishing strange stars from neutron stars.     

R-mode instability of strange stars and observations of neutron stars in LMXBs

Using a realistic equation of state(EOS) of strange quark matter, namely,the modified bag model, and considering the constraints on the parameters of EOS by the observational mass limit of neutron stars, we investigate the r-mode instability window of strange stars, and find the same result as in the brief study of Haskell,Degenaar and Ho in 2012 that these instability windows are not consistent with the spin frequency and temperature observations of neutron stars in low mass X-ray binaries.     

Implication of existence of hybrid stars and theoretical expectation of submillisecond pulsars

We derive the bulk viscous damping timescale of hybrid stars, neutron stars with quark matter core. The r-mode instability windows of the stars show that the theoretical results are consistent with the rapid rotation pulsar data, which may give an indication for the existence of quark matter in the interior of neutron stars. Hybrid stars instead of neutron or strange stars may lead to submillisecond pulsars.     

Relativistic mean-field theory equation of state of neutron star matter and a Maxwellian phase transition to strange quark matter

The equation of state of neutron star matter is examined in terms of the relativistic mean-field theory, including a scalar-isovector δ-meson effective field. The constants of the theory are determined numerically so that the empirically known characteristics of symmetric nuclear matter are reproduced at the saturation density. The thermodynamic characteristics of both asymmetric nucleonic matter and β-equilibrium hadron-electron npe-plasmas are studied. Assuming that the transition to strange quark matter is an ordinary first-order phase transition described by Maxwell's rule, a detailed study is made of the variations in the parameters of the phase transition owing to the presence of a δ-meson field. The quark phase is described using an improved version of the bag model, in which interactions between quarks are accounted for in a one-gluon exchange approximation. The characteristics of the phase transition are determined for various values of the bag parameter within the range B ∈ [60,120]MeV/fm³ and it is shown that including a δ-meson field leads to a reduction in the phase transition pressure P ₀ and in the concentrations n _N and n _Q at the phase transition point. Translated from Astrofizika, Vol. 52, No. 1, pp. 147–164 (February 2009).     

Fine structure on the surface of bare strange stars

The surface fine structure of bare strange stars is determined. The distribution of electrons and quarks in the surface layer is determined using a phenomenological Thomas-Fermi model. For the MIT bag model, the quark density at the free surface is found to fall off continuously to zero in a layer of finite thickness. Unlike the results of other authors, here the electric field in the transition layer changes direction. The coefficient of surface tension of the quark matter is determined in terms of this model. Depending on the model parameters, it is 60–150 MeV/Fm².Translated from Astrofizika, Vol. 48, No. 1, pp. 139–150 (February 2005).     

Low-Mass Quark Stars or Quark White Dwarfs

An equation of state is considered that, in superdense nuclear matter, results in a phase transition of the first kind from the nucleon state to the quark state with a transition parameter > 3/2 ( = _Q /( _N + P ₀/c ²)). A calculation of the integrated parameters of superdense stars on the basis of this equation of state shows that on the stable branch of the dependence of stellar mass on central pressure (dM/dP _c > 0), in the low-mass range, following the formation of a tooth-shaped break (M = 0.08 M , R = 200 km) due to quark formation, a new local maximum with M _max = 0.082 M and R = 1251 km is also formed. The mass and radius of the quark core of such a star turn out to be M _core = 0.005 M and R _core = 1.7 km, respectively. Mass accretion in this model can result in two successive transitions to a neutron star with a quark core, with energy release like supernova outbursts.     

Remarks on the relative populations of neutron and strange stars

We consider a simple qualitative model to estimate the time-scale forneutronstrange matter decay in dense stellar environments. It is argued that a large mismatch between the former and the microscopic weak interaction time-scale suggests that a dual population of both types of compact objects is unlikely. Assuming the correctness of the strange matter hypothesis all of them should be strange stars. If one instead postulates accretion as the decisive feature for the conversion, a consideration of neutron stars structure indicates a fairly narrow range for the onset of the critical density before the corresponding Chandrasekhar mass is achieved.     

Rotating black holes in neutron and quark stars: Phenomenon of pulsars

The phenomenon of pulsars is considered as the evidence for existence of black holes in neutron and quark stars. Within the framework of the degenerated star model with black-hole interior the existence of millisecond pulsars withP<0.5 ms and single pulsars with negative derivative of the period were predicted. The anisotropic accretion of neutron (or quark) star matter on to a rotating black hole leads to the formation of directed radiation (projector), which makes heat spots at surface (volcanos), that explains the nature of pulsating radiation and the complicated structure of impulses. This model gives both the mechanism of self-acceleration of degenerated star rotation (mass accretion on to the internal black hole) producing millisecond pulsars and also the mechanism of significant deceleration of rotation (ejection of neutral mass through a volcanic crater), leading to long-periodic X-ray pulsars. The black hole produces high densities and temperatures of the degenerated star mass that transforms gradually the neutron star into quark star (Cygnus X-3).     

The r-mode instability windows of hybrid stars

Taking into account the peculiar properties of hybrid stars, stars containing both a core of strange quark matter and the solid crust of a neutron star, and employing a fully self-consistent second-order correction technique, we study the time scale of bulk viscosity dissipation at the low temperature limit (T < 10⁹ K) and with this time scale we calculate the critical spin frequency of the hybrid star. It is found that its minimal value is 704.42 Hz (corresponding to a pulse period of 1.42 ms). When this is compared with the periods of neutron and strange stars, a better interpretation of the observational data is obtained.     

Strange quark star in dilaton gravity

In this work, we first obtain the hydrostatic equilibrium equation in dilaton gravity. Then, we examine some of the structural characteristics of a strange quark star in dilaton gravity in the context of Einstein gravity. We show that the variations of dilaton parameter do not affect the maximum mass, but variations in the cosmological constant lead to changes in the structural characteristics of the quark star. We investigate the stability of strange quark stars by applying the MIT bag model with dilaton gravity. We also provide limiting values for the dilaton field parameter and cosmological constant. We also study the effects of dilaton gravity on the other properties of a quark star such as the mean density and gravitational redshift.We conclude that the last reported value for the cosmological constant does not affect the maximum mass of a strange quark star.     

The conversion from neutron stars to strange stars and its implications

The conversion from neutron stars with different equation of states (EOSs) for neutron matter into strange stars with different EOSs for strange quark matter has been studied in a general relativistic numerical calculation in this paper. For hot neutron stars, their conversion may lead to great variations in their rotation periods, of which the magnitude would be greatly dependent upon the EOS for neutron matter, and of which the timescale would be greatly determined by the EOS for strange matter. This phenomenon appears as giant glitches, which might provide a probe of EOSs for both neutron matter and strange matter. But for cold neutron stars, their conversion may result in a population of gamma-ray bursts.     

Collapsing supra-massive magnetars: FRBs,the repeating FRB121102 and GRBs

Fast Radio Bursts (FRBs) last for \(\sim \) few milli-seconds and, hence, are likely to arise from the gravitational collapse of supra-massive, spinning neutron stars after they lose the centrifugal support (Falcke & Rezzolla 2014). In this paper, we provide arguments to show that the repeating burst, FRB 121102, can also be modeled in the collapse framework provided the supra-massive object implodes either into a Kerr black hole surrounded by highly magnetized plasma or into a strange quark star. Since the estimated rates of FRBs and SN Ib/c are comparable, we put forward a common progenitor scenario for FRBs and long GRBs in which only those compact remnants entail prompt \(\gamma \)-emission whose kick velocities are almost aligned or anti-aligned with the stellar spin axes. In such a scenario, emission of detectable gravitational radiation and, possibly, of neutrinos are expected to occur during the SN Ib/c explosion as well as, later, at the time of magnetar implosion.     

On Low-Mass, Strange Quark Stars with a Crust

Low-mass strange stars with a crust are investigated within the framework of the bag model. The crust, which consists of degenerate electrons and atomic nuclei, has a limiting boundary density _cr , which is determined by the mass of the crust, and it cannot exceed the value _drip = 4.3·10¹¹ g/cm³, corresponding to the density at which neutrons drip from nuclei. For different values of _cr in the low-mass range (M 0.1 M) we calculate several series of configurations: we find the dependence of the stellar mass M on the central density _c for _cr = const, with 10⁹ g/cm³ _{cr drip} , and for each series we determine the parameters of the configuration for which the condition dM/d _c > 0 is violated. When the boundary density of the crust decreases to 10⁹ g/cm³, the minimum mass of a strange star decreases to M _min 10^-3 M, while the radius reaches 600 km.