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.     

Stability of strange dwarfs. I. Static criterion for stability. Statement of the problem

This is a study of the stability of strange dwarfs, superdense stars with a small quark core (M _0core /M _⨀ < 0.017) and an extended crust consisting of atomic nuclei and a degenerate electron gas where the density may be two orders of magnitude greater than the maximum density for white dwarfs. For a given equation of state, the mass, total number of baryons, and radius of strange dwarfs are uniquely determined by the central energy density ρ _c and the energy density ρ _tr of the crust at the surface of the quark core. Thus, the entire range of variation of ρ _c and ρ _tr must be taken into account in studying the stability of these configurations. This can be done by examining a series of configurations with a fixed rest mass M ₀ (total baryon number) of the quark core and different masses of the crust. In each series, ρ _tr ranges from the value for white dwarfs to ρ _drip = 4.3∙10¹¹ g/cm³, at which free neutrons are created in the crust. According to the static criterion for stability, stability is lost in an individual series when the mass of the strange dwarf reaches a maximum as a function of ρ _tr . Translated from Astrofizika, Vol. 52, No. 2, pp. 325–332 (May 2009).     

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.     

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.     

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.     

Stability of strange dwarfs II. Computational results

The stability of strange dwarfs for quark cores with M _0core /M _⨀ = 10⁻⁴, has been studied by calculating, in each individual case, a series of strange dwarfs with configurations in which 5 ⋅ 10⁻⁴, 10⁻³, 5 ⋅ 10⁻³, 10⁻², 1.31 ⋅ 10⁻², 1.6 ⋅ 10⁻², 1.7 ⋅ 10⁻², 2 ⋅ 10⁻², ranges from the values in white dwarfs to ρ _drip = 4.3 ⋅ 10¹¹ g/cm³, at which free neutrons are produced in the crust. For the series with M _0core /M _⨀ < 0.0131, stability is lost when ρ _tr < ρ _drip . For the series with M _0core /M _⨀ > 0.0131, the equality ρ _tr = ρ _drip is reached before the strange dwarf attains its maximum mass. Although the frequency of the radial pulsations in the fundamental mode obeys ω₀² > 0 for these configurations, they are unstable with respect to transitions into a strange star state with the same total number of baryons and a radius on the order of that of neutron stars. An energy on the order of the energy in a supernova explosion is released during these transitions. It is shown that the gravitational red shift of white and strange dwarfs are substantially different for low and limiting (high) masses.     

Low-Mass Quark Stars

More and more observational hints of quark stars are proposed these years though pulsars are considered conventionally to be normal neutron stars. The existence of low-mass quark stars is a direct consequence of the possibility that pulsar-like stars are actually quark stars, because of the ability that quark matter can confine itself by color interaction. After a brief introduction to the study of quark stars, the various astrophysical implications of low-mass quark stars are investigated. It is addressed that some of the transient unidentified γ -ray sources are probably merging quark stars. The observability of low-mass quark stars is discussed.     

Strange quark matter and models of strange stars

In the framework of the MIT bag model we consider absolutely stable strange quark matter consisting of u, d, and s quarks and electrons. For a realistic range of parameters of the quark bag we compute the threshold density for the appearance of strange quark matter that is realized on the surface of self-sustaining strange stars. On the basis of twelve calculated equations of state we give a detailed study of the series of configurations of strange stars consistent with the best known observational data. We show that the binding energy of the models depends essentially on the quark-gluon interaction constant _c.Translated fromAstrofizika, Vol. 37, No. 3, 1994.The authors are grateful to E. V. Chubaryan and A. M. Atoyan for assistance in overcoming the information blockade. The present paper was written in the framework of area 46/101 93-353, supported by the Ministry of Higher Education and Science of the Republic of Armenia.     

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).     

Cooling of quark stars in the colour superconductive phase: effect of photons from glueball decay

The cooling history of a quark star in the colour superconductive phase is investigated. Here we specifically focus on the two-flavour colour (2SC) phase where the novel process of photon generation via glueball (GLB) decay has already been investigated. The picture we present here can, in principle, be generalized to quark stars entering a superconductive phase where similar photon generation mechanisms are at play. As much as 10⁴⁵–10⁴⁷ erg of energy is provided by the GLB decay in the 2SC phase. The generated photons slowly diffuse out of the quark star, keeping it hot and radiating as a blackbody (with possibly a Wien spectrum in gamma-rays) for millions of years. We discuss hot radio-quiet isolated neutron stars in our picture (such as RX J185635–3754 and RX J0720.4–3125) and argue that their nearly blackbody spectra (with a few broad features) and their remarkably tiny hydrogen atmosphere are indications that these might be quark stars in the colour superconductive phase where some sort of photon generation mechanism (reminiscent of the GLB decay) has taken place. Fits to observed data of cooling compact stars favour models with superconductive gaps of  Δ_2SC∼ 15–35 MeV  and densities  ρ_2SC= (2.5–3.0) ×ρ_N  (ρ_N being the nuclear matter saturation density) for quark matter in the 2SC phase. If correct, our model combined with more observations of isolated compact stars could provide vital information to studies of quark matter and its exotic phases.     

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.     

A red giant with a strange star as its core. Principal similarities to and differences from Thorne-Zytkow objects

A model red giant with a mass of 5 M_⊙ a luminosity of 41,740 L_⊙, and a radius of 960 R_⊙ and with a strange quark star as its core is constructed, and it is compared with a Thorne-Zytkow object having similar integrated parameters. The difference in internal structure is manifested right at the dense core: matter above the core is held off only by γ rays from the strange star, and convection is maintained down to the strange star. The lifetime of a red giant containing a strange star turns out to be almost 500 times shorter than that of a Thorne-Zytkow object — on the order of 10⁵ years. Translated from Astrofizika, Vol. 41. No. 4, pp. 533–544, October–December, 1998.     

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.     

A class of well behaved charged superdense star models of embedding class one

A class of well behaved charged superdense star models of embedding class one is obtained by taking perfect fluid to be interior matter. In the process we come across the models for white dwarf, quark and neutron stars. Maximum mass of the star of this class is found to be 6.716998M _Θ with its radius is 18.92112 Km. In the absence of charge the models reduce to Schwarzchild’s interior model with constant density.     

Seismic signatures of strange stars with crust

We study acoustic oscillations (eigenfrequencies, velocity distributions, damping times) of normal crusts of strange stars. These oscillations are very specific because of huge density jump at the interface between the normal crust and the strange matter core. The oscillation problem is shown to be self-similar. For a low (but non-zero) multipolarity l , the fundamental mode (without radial nodes) has a frequency of ∼300 Hz and mostly horizontal oscillation velocity; other pressure modes have frequencies ≳20 kHz and almost radial oscillation velocities. The latter modes are similar to radial oscillations (having approximately the same frequencies and radial velocity profiles). The oscillation spectrum of strange stars with crust differs from the spectrum of neutron stars. If detected, acoustic oscillations would allow one to discriminate between strange stars with crust and neutron stars and constrain the mass and radius of the star.     

Astrometric CCD observations of visual double stars at the Pulkovo Observatory

We present the results of 3489 astrometric observations for 361 visual double stars performed in 2003–2007 with the 26-inch refractor of the Pulkovo Observatory. The angular separations between the components (ρ) and the position angles (θ) are given. The errors in these quantities are, on average, 0″.009 for ρ and 0°.40/ρ for θ, where ρ is the separation in arcseconds.     

Quasinormal modes of a black hole with quintessence-like matter and a deficit solid angle: scalar and gravitational perturbations

In the previous paper (Li et al. in Phys. Lett. B 666:125–130, 2008), we show the solutions of Einstein equations with static spherically-symmetric quintessence-like matter surrounding a global monopole. Furthermore, this monopole become a black hole with quintessence-like matter and a deficit solid angle when it is swallowed by an ordinary black hole. We study its quasinormal modes by WKB method in this paper. The numerical results show that both the real part of the quasinormal frequencies and the imaginary part decrease as the state parameter w, for scalar and gravitational perturbations. And we also show variations of quasinormal frequencies of scalar and gravitational fields via different ε (deficit solid angel parameter) and different ρ ₀ (density of static spherically-symmetric quintessence-like matter at r=1), respectively.     

Bimodal brightness oscillations in models of young binary systems

We consider a model for the cyclic activity of young binary stars that accrete matter from the remnants of a protostellar cloud. If the orbit of such a binary system is inclined at a small angle to the line of sight, then the streams of matter and the density waves excited in the circumbinary disk can screen the primary component of the binary from the observer. To study these phenomena by the SPH (smoothed particle hydrodynamics) method, we have computed grids of hydrodynamic models for binary systems based on which we have constructed the light curves as a function of the orbital phase. The main emphasis is on investigating the properties of the brightness oscillations. Therefore, the model parameters were varied within the following ranges: the component mass ratio q = M ₂: M ₁ = 0.2–0.5 and the eccentricity = 0–0.7. The parameter that defined the binary viscosity was also varied. We adopted optical grain characteristics typical of circumstellar dust. Our computations have shown that bimodal oscillations are excited in binaries with eccentric orbits, provided that the binary components do not differ too much in mass. In this case, the ratios of the periods and amplitudes of the bimodal oscillations and their shape depend strongly on the inclination of the binary plane and its orientation relative to the observer. Our analysis shows that the computed light curves can be used in interpreting the cyclic activity of UX Ori stars.