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.     

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.     

Angular momentum transport in pre-main-sequence stars of intermediate mass

Pre-Main-Sequence stars with masses between 2 and 5 M (Herbig Ae/Be stars) have radiative subphotospheric envelopes. However, they possess strong stellar winds and show definite signs of activity which could be linked to surface magnetic field. Therefore, they must lose angular momentum at a significant rate.We investigate the effect of such angular momentum losses on the internal structure of these stars, and on the distribution of angular velocity inside them. This paper presents a preliminary analysis guided by an analogy with laboratory and geophysical fluids. We propose that the friction exerted at the stellar surface by the angular momentum losses produces a mixed layer below the surface, separated from the unperturbed interior by an interface. Using scaling laws established by experimental studies of sheared stratified fluids, we discuss a simplified model for the evolution of the mixed layer.Although this model is still too preliminary to allow quantitative predictions, we show that for a reasonable choice of parameters, the mixed layer penetrates into the stellar interior on a time-scale of 10⁶ years, comparable to the Kelvin time-scale for the Herbig Ae/Be stars.     

Search for variability in hydrogen-poor stars

The evolutionary status of hydrogen-poor stars is analyzed.Photoelectric observations of six objects are reported as a first step of a long-term project devoted to search for variability of a large sample of hydrogen-poor stars.The observed stars show phenomena of microvariability with an amplitude of the order of 0^m. 1 or less.Two extreme helium stars have been examined: a period in the range of 0^d.162-0^d.164 has been found for BD+ 10⁰2179, andP=0^d.1079962 for BD+13⁰3324.The mass-losing O subdwarf (sdO) BD+37⁰ 443 presents short-term fluctuations with a time-scale of several minutes and long-term variations on a scale of months. The standard sdO BD+75⁰325 is probably non-variable, although light variations of very small amplitude (m0.03) with a time-scale of about 1 hr might be present. The high gravity sdO BD+25⁰4655, which is very close to the white dwarf stage, also presents variability on a time-scale of about 13 minutes, and might be an analog of the recently discovered pulsating sdO, or hot white dwarf, PG 1159-035.The variability of the intermediate helium star HD 37776 is finally confirmed.     

Rapid variations of Hα emission strength of eight Be stars

Rapid observations of H profiles of eight Be stars have been obtained and it is found that rapid (in a time-scale of 4 to 6 minutes) and irregular variations of total emission strength of H line are present in these stars. It has been suggested that these variations may be due to the material circulation in the envelope of Be stars.     

The formation of superdense gaseous cores in the nuclei of disk galaxies: II

In a previous paper (hereafter referred to as Paper I) we have tried to show that superdense cores in the nuclei of disk galaxies can be formed by accretion of gas ejected by the evolved stars which populate the central bulge of these galaxies. Solving the equations for radial flow of a magnetized gas, we found that the accretion of an explodable mass at the core can be achieved over a time-scale ranging from a few times 10⁷ and a few times 10⁸ yr. It was shown, however, that the accretion process is seriously inhibited if the gas possesses sufficient rotational velocity but lacks any dissipative, mechanism within the system. Since rotational velocity is an observed parameter of the stars which shed the gas to be accreted, one must consider the existence of some dissipative force in it in order that the accretion process may be efficient. In the present paper, therefore, we have solved the problem of the flow of a rotating, viscous (variable), magnetized gas. With plausible assumptions regarding some of the parameters involved, the time-scale for the accretion of an explodable mass (10⁹ M ) at the core again turns out to be ranging between a few times 10⁷ and a few times 10⁸yr. Such time-scale has been proposed by several authors as that for repeated explosions in nuclei of these galaxies. It has also been proposed by many authors that the spiral arms are generated and destroyed in disk galaxies over the same time-scale. Our solution also yields a nearly linear rotational velocity law which is usually observed in the central regions of these galaxies.     

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.     

On the mass defect of strange stars

In the context of the MIT bag model we compute the mass defect and the gravitational packing factor for three models of strange stars and study the contribution of gravitational and internal energy to the total energy of the system. For strange stars it is possible to realize a model with negative internal energy, leading to a greater binding energy of these stars compared to neutron stars. This is the reason for the absence of configurations with negative mass defect for the models in question. We analyze the question of identifying the remnants of supernovae with neutron or strange stars.Translated fromAstrofizika, Vol. 38, No. 2, 1995.     

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 .     

Convection in normal stars and metal-deficient stars

The depths at which convection starts have been calculated for main sequence stars and giant stars of various effective temperature and hydrogen-to-metal ratios. It is found that for late-type stars ofT _e4400 K convenction stars at 0.1. In metal-deficient stars convection starts at shallower optical depths compared to normal stars of the same spectral type. The larger the metal deficiency, the shallower is the depth at which convection starts. The importance of convection in the study of metal-deficient stars and late type stars are also discussed.     

Population I pulsating stars

Luminosities of Population I pulsating stars (Delta Scuti variables and classical cepheids) are investigated. From data for 80 Delta Scuti stars, semi-empirical period-luminosity-colour (P-L-C) relations and period-luminosity (P-L) relations are obtained for the four lowest modes of radial pulsations. The improvement of the accuracy of the stellar luminosity is determined when a P-L-C relation is used instead of the corresponding P-L relation. From data for 155 classical cepheids, empirical P-L relations are derived for short-period stars (logP1.1), long-period stars (logP>1.1), and s-cepheids. The comparison of the P-L relations for the two types of variable stars shows good agreement, but between them there is a gap with a dim nature.     

Recent progress in CP star detection and classification

Chemically peculiar (CP) stars are mainly found among B and A stars. Present theories are not able to account fully for the observed spectrum anomalies, suggesting that in the atmospheres of stars in the range ofT _e , where mass loss is no longer very large and convection is still not very important, the present theoretical approach needs further refinement. Moreover, the lack of laboratory data is responsible, at least partly, for the discrepancies between observed and computed stellar energy distributions.The choice for quick detection of CP stars among faint objects is reviewed; the measure of the flux depression at 5200 appears to be very powerful, and the identification of this complex feature is urgently needed.The need to separate the various subclasses of the He abnormal stars in a standard way is underlined and further analyses of the characteristics of the Boo stars are required.The problem of the determination ofT _e and consequently of realistic atmospheric abundance anomalies of CP stars is discussed.     

Stellar analogs of solar magnetic activity

The techniques and principal results of observational studies of stellar activity are summarized. Both chromospheric and coronal emission clearly track surface magnetic field properties, but it is not well known how the detailed relation between the emission and surface magnetic fields varies with spectral type. For lower Main-Sequence stars of the same spectral type, there is clear evidence of a close relationship between mean activity level and rotation period P _rot. There is also less definitive evidence for a similar dependence on convective overturn time _c , such that activity depends on the single parameter Ro = P _rot/ _c . For single stars, stellar rotation, and magnetic activity both decline smoothly with age. This implies a feedback between angular momentum loss rate and activity level. Temporal variations in mean stellar activity level mimic the solar cycle only for old stars like the Sun, being much more irregular for younger stars. The characteristic timescale of the variations (the cycle period) appears to depend on Ro for old stars, but shows no clear dependence on either rotation rate or spectral type for younger stars. Further data on mean activity and its variation for a large number of lower Main-Sequence stars should contribute significantly to our understanding of the causes of stellar magnetic activity.     

The Os-Pt-Hg abundance peak in Ap stars and the problem of very heavy cosmic rays

Relative abundances in the region 74Z83 (W to Bi) are determined for 73 Dra, HR 4072, and some other Ap stars. Abundance peaks occur at atomic massesA=191±2 on 73 Dra, atA=201±3 on HR 4072, atA=199±5 on other main group Ap stars, and atA=201±2 on Mn stars. Pb has a relatively low abundance on Ap stars and also in cosmic rays which have an abundance peak atA=193±3. The abundance peaks on main group Ap stars are due to the cyclicr-process which occurred in explosions of former companion stars. Fission products of transuranic elements are recycled by further rapid neutron captures. At the end of ther-process, the high neutron flux decreases gradually so that the final -decays take place in a neutron-rich environment; superheavy elements (Z110) formed in ther-process may be partly destroyed by neutron-induced fission. The pulsar remnants of the explosions accelerater-process elements to cosmic-ray energies. The peak atA 201 on Mn stars is discussed briefly.     

Observational manifestations of early mixing in B- and O-type stars

The helium and nitrogen enrichment of the atmospheres of early B-type stars during the main sequence (MS) evolutionary phase is re-analysed. It is confirmed that the effect depends on both the aget and the stellar massM. For example, the helium abundanceHe/H increases by 0.04 (60–70% of initial value) for stars withM=8–13M and by 0.025 (about 30%) for stars withM=6M . The nitrogen abundance rises by three times forM=14M and by, two times forM=10M . According to the latest theoretical computations, the observed appearance of CNO-cycled material in surface layers of the stars can be a result of the rotationally induced mixing, in particular, of the turbulent diffusion. Carbon is in deficiency in B stars, but unexpectedly does not show any correlation with the stellar age. However it is shown that the total C+N abundance derived for early B stars conflicts with the theory.Basing on modern data the helium enrichment is first examined in O-type MS stars, as well as in components of binaries. As compared with early B stars, the He abundance for more massive O stars and for components of binaries show a different relation with the relative aget/t _MS . Namely during short time betweent/t _MS 0.5 and 0.7 a sharp jump is observed up toHe/H=0.2 and more. In particular, such a jump is typical for fast rotating O stars (v sini200 km s^–1),. Therefore the effect of mixing depends on massM, relative aget/t _MS , rotational velocityv and duplicity.The mass problem (the discrepancy betweenM _ev andM _sp ) is also analysed, because some authors consider it as a possible evidence of early mixing, too. It is shown that the accurate data for components of binaries lead to the conclusion that the discrepancy is less than 30%. Such a difference can be removed at the expense of theM _ev lowering, if the displacement of evolutionary tracks, owing to the rotationally induced mixing is taken into consideration.     

Search for relativistic companions in ‘non-X-ray’ binary systems

Consideration is given to a search for relativistic objects in massive close binary systems without strong X-ray emission (L _x <10³⁴ erg s^–1). It is pointed out that, according to the present-day theory on the evolution of massive close binaries, the number of neutron stars and black holes in non-X-ray binary systems must be 100 times the number of the known X-ray binaries comprising OB supergiant stars; that is why, in studying non-X-ray binary systems, the chances are to detect about a hundred of black holes in the Galaxy.Criteria are formulated for the relativistic nature of companions in the binary systems, such as high spatial velocity values and height Z over the galactic plane for OB stars (runaway stars) and for Wolf-Rayet stars. As reported by Tutukov and Yungelson (1973), as well as by van den Heuvel (1976), the presence of ring-type nebulae can serve as another indication of a relativistic nature of companions in the case of Wolf-Rayet stars.Data are collected on Wolf-Rayet stars with low-mass companions (Table I), which can be relativistic objects accreting within a strong stellar wind from Wolf-Rayet stars. Presented are new findings in respect of spectral examination of the runaway OB-stars (Table II), bringing together data on eight OB stars which can represent binary systems with relativistic companions (Table III).A list of 28 OB-stars (Table IV) which offer a good chance for finding relativistic companions is given.     

Some Comments on the Magnetic Braking of CP Stars

The low rotation velocities of magnetic CP stars are discussed. Arguments against the involvement of the magnetic field in the loss of angular momentum are given: (1) the fields are not strong enough in young stars in the stage of evolution prior to the main sequence; (2) there is no significant statistical correlation between the magnetic field strength and the rotation period of CP stars; (3) stars with short periods have the highest fields; (4) a substantial number of stars with very low magnetic fields (B _e < 500 G) have rotation speeds that are typical of other CP stars; (5) simulations of the magnetic fields by Leroy and the author show that the orientation of dipoles inside rotating stars, both slow and fast, is consistent with an arbitrary orientation of the dipoles; and, (6) slow rotators with P>25 days, which form 12% of the total, probably lie at the edge of the velocity distribution for low mass stars. All of these properties conflict with the hypothesis of magnetic braking of CP stars.     

The effects of strong interaction on the observational discrimination between neutron and strange stars

Strange stars are compact objects similar to neutron stars composed of strange matter. This paper investigates the observational effects of the strong interaction between quarks. We believe: 1) that the conversion of a neutron star to a strange star is a large “period glitch” which is determined by the strong interaction; 2) that the strong interaction results in effective damping of oscillation of hot strange stars, which could be a new mechanism of driving supernova explosions; 3) that the strong interaction increases the difference in rotation between strange and neutron stars under high temperatures, making the minimum period for strange stars lower than that for neutron stars.     

A search for unique objects in nearby galaxies

A list of 171 stars in the galaxy M33 is presented. The stars could be considered as candidates for unique objects, such as SS 433, S Dor, P Cyg stars and possibly new kinds of peculiar objects. All these stars have been selected on the basis of the similarity to SS 433, free from interstellar absorption: OB star with strongH emission or with HeII 4686 and CIII, NIII 4630 - 4660 emission lines; a hot star inside a supernovae remnant or radio nebula. The variability of these stars has been used as an additional criterion of the selection. It is important to carry out spectral observations of the presented stars, which will allow us to select stars with intrinsicH emission.     

On the influence of mass loss and convective overshooting on the evolution of massive stars

Evolution of massive stars losing mass with the rateM H L/V C is computed (for =1,2,7). It is shown that observed mass loss rates correspond to 0.3 and, therefore, mass loss by stellar wind cannot play any significant role in the evolution of normal massive stars. However, for several types of massive stars (WR, OH/IR, X-ray sources) enhanced mass loss explains their peculiar features. Computations of evolutionary sequences of massive stars with convective overshooting taken into account (as a formal increase of the convective core) show that a significant broadening of the hydrogen-burning band in the H-R diagram may be obtained.