On steady-state nuclear burning in accreting neutron stars

The properties of the hydrogen burning shell in the envelope of an accreting neutron star have been studied for a range of mass accretion rates, neutron star radii, and metal abundances of the accreted matter. It is found that the hydrogen burning shells lie at densities ranging from 10⁵–6×10⁶ gm cm^–3. For mass accretion rates in excess ofM _c2 hydrogen and helium burn together. ForM _c1MM _c2, the hydrogen burning shell is stabilized by the limited CNO cycle. Implications of these results to the X-ray burst phenomena are briefly discussed.     

Massive fluid spheres with isothermal cores

We can define some adiabatic exponents for neutron star cores. The equality of and ₃ leads to an equation of stateE=P ln(K/P) orP=K exp(–E/P). This equation has been solved alongwith equations for hydrostatic equilibrium for different physical conditions at the centre. The parameters of isothermal neutron star cores have been computed by taking surface densityE _a=2×10¹⁴ g cm^–3. ForP ₀=E ₀ the maximum mass and radius of neutron star core are 3.25M and 17.14 km, respectively.     

The neutrino radiation for a hot neutron star formation and the envelope outburst problem

With the equations of neutrino heat conductivity being used, the neutrino light curve is calculated for the spherically symmetrical collapse of an iron-oxygen 2M star (Figure 1) up to the formation of a hot hydrostatically equilibrium neutron star. The total energy, radiated in the form of muon and electron neutrinos, is 5.8×10⁵³ erg (0.16Mc ²). The mean neutrino particle energy is 12 MeV for all the time the collapse proceeds. The maximum neutrino luminosity value is equal to 3×10⁵³ erg s^–1. For a 10M star collapse, the luminosity maximum 3×10⁵⁴ erg s^–1 takes place just at the moment of the formation of a black hole inside the collapsing star. The total radiated energy in this case is about 0.08Mc ². The set of calculations, allowing for the deposition of momentum by means of neutrino-nuclear coherent scattering, brings us to a conclusion that the envelope outburst is only possible if the scattering cross-section is 50 times larger than the value experimentally accepted (inequality 20)).     

On the interior of the neutron star (II)

With the assumption, the physical 3-spacet = constant in a superdense star is spheroidal and the matter-density on the boundary surface of the configurationa = 2 × 10¹⁴ g cm^–3( the average matter density in a neutron star) Vaidya and Tikekar (1982) proposed an exact relativistic model for a neutron star. They suggested that their model can describe the hydrostatic equilibrium conditions in such a superdense star with densities in the range of 10¹⁴-10¹⁶ g cm^–3. Based on this model Parui and Sarma (1991) estimated the maximum limit of the density variation parameter for a stable neutron star (both for charged and uncharged) which is equal to 0.68, i.e. _max = 0.68.In this paper we have shown variation of central density per unit equilibrium radius (0/a), variation of mass, upper limit of density variation parameter both for charged and uncharged neutron stars at densities 10¹⁵ and 10¹⁶ g cm^–3, respectively. We have obtained _max = 0.68, i.e. the same as before. The important is that the duration of stability among the neutron star's constituents around _max will be shorter and shorter at higher densities as we proceed near the centre of the neutron star. In case of a charged neutron star, once stability among the constituents has been established, then unstability appears gradually maintaining linear relation between change in central density per unit equilibrium radius and change in mass whereas in case of uncharged neutron star, linear relation does not maintain.     

Neutron star models based on an improved equation of state

Using an equation of state for cold degenerate matter which takes nuclear forces and nuclear clustering into account, neutron star models are constructed. Stable models were obtained in the mass range above 0.065M and density range 10^14.08 to 10^15.4 gm/cm³. All of these models were found to be bound. The outer crystalline layer of the star was found to have a thickness of 200 m or more depending on the mass of the model.     

On the X-ray source SCO XR-1

If the assumption of a catastrophic explosion during the formation of a neutron star is correct, the parent systems for klovsky's model of SCO XR-1 seem to have been very short-period white-dwarf binaries. A white dwarf originally in contact with its Roche limit is forced to lose mass. During the ejection of matter the primary may pass the white-dwarf mass limit and become a neutron star. The mass transfer time-scale can change from pulsational to thermal, and a mass flow of 10^–9 M per year needed for SCO XR-1 can be understood, while at the same time the orbital period will increase.     

The accretion of matter by a collapsing star in the presence of a magnetic field. II. Selfconsistent stationary picture

The stationary two-dimensional magnetohydrodynamic solution for the accretion of the matter without pressure into a gravitating centre of a black hole is obtained. It is assumed that the magnetic field far from the collapsed star is homogeneous and its influence on the flow is negligible. Around the star, at the plane perpendicular to the direction of the magnetic field, the dense quasistationary disc is formed, the structure of which in a large extent is determined by dissipation processes. The structure is calculated for (a) a laminar disc with the Coulomb mechanism of dissipation; and (b) a turbulent disc.The estimations of the parameters of the shock which result from the infall of the matter onto the disc are given. In the last section the numerical estimation and approximate character of the radiation spectrum of the disc and the shock are obtained for two cases of 10M and 10⁵ M . The luminosity of collapsed objects withM=10M appears to be about solar, thus its observation is possibly only at the distances less than 300–1000 pc. The collapsed objects in the Galaxy withM=10⁵ M could constitute very bright sources in spectral regions from optical up to X-ray. The spectra of a laminar and a turbulent disc for 10M black hole are very different. The laminar disc radiates primarily in the ultraviolet. The turbulent disc radiates a large part of its flux in the infrared. Therefore, one cannot exclude the possibility that some of the galactic infrared star-like sources are individual black holes in the accretion state.     

Neutron stars and general equation of nuclear matter

It has been shown that the mass of neutron stars obtained from equations of state based on nuclear theory depend upon the number of baryons assembled in it but not on the type of interactions considered. On examining the behaviour of different equations of state based on nuclear theories, a simple polytropic equation of state,P = (K/N)(p –p _s)^N is proposed. The results obtained forN=1.75 cover the entire range of neutron star masses obtained from the equations of state based on nuclear theories and give a maximum mass of 2.8M . Depending upon various mechanisms for energy output the mass of Crab pulsar is estimated to range from 0.32M to 1.5M . The relation connecting the coordinate mass,M, and the rest mass,M ₀, may be written asM/M 0.93 (M ₀/M)^0.9.     

Steady mass-loss from supermassive stars

Structures of Newtonian super-massive stars are calculated with the opacity for Comptor effectK ₀/(1 + T), whereK ₀=0.21(1 +X and =2.2×10^–9K^–1. The track of the Main-Sequence is turned right in the upper part of the HR diagram. Mass loss will occur in a Main-Sequence stage for a star with mass larger than a critical mass. The cause of mass loss and the expansion of the radius is continuum radiation pressure. The critical mass for mass loss is 1.02×10⁶ M for a Population I star, and 1.23×10⁵ M for Population III star. Mass loss rates expected in these stars are 3.3×10^–3 and 4.0×10^–3 M yr^–1, respectively.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.     

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.     

Evolution of massive close binaries and formation of neutron stars and black holes

Main results of computations of evolution for massive close binaries (10M +9.4M , 16M +15M , 32M +30M , 64M +60M ) up to oxygen exhaustion in the core are described. Mass exchange starting in core hydrogen, shell hydrogen and core helium burning stages was studied. Computations were performed assuming both the Ledoux and Schwarzschild stability criteria for semiconvection. The influence of UFI-neutrino emission on evolution of close binaries was investigated. The results obtained allow to outline the following evolutionary chain: two detached Main-Sequence stars — mass exchange — Wolf-Rayet star or blue supergiant plus main sequence star — explosion of the initially more massive star appearing as a supernova event — collapsed or neutron star plus Main-Sequence star, that may be observed as a runaway star — mass exchange leading to X-rays emission — collapsed or neutron star plus WR-star or blue supergiant — second explosion of supernova that preferentially disrupts the system and gives birth to two single high spatial velocity pulsars.Numerical estimates concerning the number and properties of WR-stars, pulsars and X-ray sources are presented. The results are in favour of the existence of UFI-neutrino and of the Ledoux criterion for describing semiconvection. Properties of several well-known X-ray sources and the binary pulsar are discussed on base of evolutionary chain of close binaries.     

Stellar pulsation: (I) analysis of stability of envelope

The life-time of the star on AGB is approximately 6 × 10⁴ yr. We divide it into front half and back half of AGB (including to optical Mira variable and OH/IR star) according to their evolution character. The observations show that the star has non-pulsation, but constant mass loss rate ( 5 × 10^–7 M yr^–1) on front half of AGB. Its circumstellar envelope is formed. When the star has pulsation on back half of AGB, its mass loss rate is relative with time, and increases gradually. In this time the star is on the stage of optical Mira variable. When the mass loss rate reaches the value of 3 × 10^–6 M yr^–1, the star evoluted from the stage of optical variable into the stage of radio bright OH/IR star. On the end of AGB the mass loss rate reaches 10^–4 M yr^–1. (Band and Habing 1983, Hermen and Habing 1985).     

Black holes in cosmic bodies

Possible manifestations of small mass black holes (M _BH<M ) in cosmic bodies (stars, millisecond pulsars, planets, etc.) are considered. The formation of millisecond pulsars in the early proposed pulsar's model goes onto a small black hole in the centre due to accretion of neutron star matter. Within the framework of a model under consideration, the following is predicted: millisecond pulsars withP _min=0.5 ms, single optical and X-ray pulsars with the negative derivative derivative of period. Small black holes can be applied to make models of anomalies in planetary bodies (gravitational, heat, etc.). The vulcan model with radiation of a microblack hole in a magnetic void (M _BH10¹⁵ g) as the source of energy is considered. At the Earth's surface, near a vulcan, the neutrino flow from a microblack hole is estimated.     

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.     

Rapidly rotating supermassive stars in the first post-Newtonian approximation to general relativity

The structure and stability of rapidly uniformly rotating supermassive stars is investigated using the full post-Newtonian equations of hydrodynamics. The standard model of a supermassive star, a polytrope of index three, is adopted. All rotation terms up to and including those of order ⁴, where is the angular velocity, are retained. The effects of rotation and post-Newtonian gravitation on the classical configuration are explicitly evaluated and shown to be very small. The dynamical stability of the model is treated by using the binding energy approach. The most massive objects are found to be dynamically unstable when =1/c ².p _c / _c 2.2 × 10^–3, wherep _c and _c are the central pressure and density, respectively. Hence, the higher-order terms considered in this analysis do not appreciably alter the previously known stability limits.The maximum mass that can be stabilized by uniform rotation in the hydrogen-burning phase is found to be 2.9×10⁶ M , whereM is the solar mass. The corresponding nuclear-generated luminosity of 6×10⁴⁴ erg/sec^–1 is too small for the model to be applicable to the quasi-stellar objects. The maximum kinetic energy of a uniformly rotating supermassive star is found to be 3×10^–5 Mc ², whereM is the mass of the star. Masses in excess of 10¹⁰ M are required if an adequate store of kinetic energy is to be made available to a pulsar like QSO. However such large masses have rotation periods in excess of 100 yr and thus could not account for any short term periodic variability. It is concluded then that the uniformly rotating supermassive star does not provide a suitable base for a model of a QSO.     

Generation of γ-bursts by old magnetic neutron stars

A model of -bursts is considered that treats the flares of neutron stars as a result of convectiveoscillation instability associated with the stars having strong internal magnetic fields ( 10¹³ to 10¹⁴ G). In the context of this model only sufficiently old (10⁴ to 10⁷ yr), drastically cooled-down neutron stars may be sources of -bursts. The paper shows that major characteristics of a -burster in the Supernova N 49 remnant (energy release during burst up to 10⁴⁴ erg, age 10⁴ yr, burst-to-burst interval (I to 3)×10⁶s; rotation period P=8 s) may be explained under the assumption that the mass of the neutron star is about 0.14M _· while its mean magnetic field strength is 1.5×10¹⁴ G abd 10¹³ G within the star and on its surface, respectively. The observational tests of the model discussed conclude the paper.     

The maximum mass of a neutron star

We consider the possibility that gravitational energy may play a local as well as global role in the behavior of matter in strong gravitational fields. A particular idealized equation, suggested as representing uniform energy density in general relativity, is examined, and its stability with respect to oscillatory and convective perturbations shown to be consistent with general relativistic hydrodynamics, subject to a new physical effect predicted for the behavior of fluids moving in strong fields. We calculate from this idealized equation the mass of a non-rotating neutron star, obtaining a maximum surface redshift ofz=2.48 and a maximum core mass of 9.79 ₁₄ ^–1/2 M. This compares withz=2.00 and 11.4 ₁₄ ^–1/2 M for a Schwarzschild star (=const.) and 6.8 ₁₄ ^–1/2 M for a causal star (dP/d1).     

Mass transfer in TV Cassiopeiae

The period variations of TV Cassiopeiae between 1901 and 1977 are discussed in the light of the period change model proposed by Biermann and Hall. During each period decrease 4.0×10^–6 M of mass is transferred from the secondary star to the primary. The average observable mass transfer rate is found to be 4.3×10^–7 M yr^–1. This average rate corresponds to the thermal time-scale of the mass-losing star.     

Theoretical evolution of a hydrogen-helium star of 3M ⊙ from the pre-Main Sequence to the core helium-exhaustion phase

The evolution of a first-generation 3M star from the threshold of stability through the stage of helium exhaustion in the core has been studied. The total time elapsed is 4.174×10⁸ yr and most of this time is spent in the blue-giant region of theH-R diagram. Hydrogen-burning near the Main Sequence occurs at a high central temperature via the proton-proton chain until the triplealpha reactions generate a small amount of C¹² toward the end of the hydrogen-burning phase. The corresponding evolution time is longer than that of a normal population I star with the same mass. The ignition of the triple-alpha processes begins in a mildly degenerate, small convective core while the star still has a high surface temperature. Helium-burning in the core, coupled with hydrogenburning in the shell, occupies a period of about 1.8×10⁷ yr, which is only one-third that of a normal star. The mass of the star interior to the hydrogen shell source has increased to a value of 0.50M near the end of core helium exhaustion. This region maintains an inhomogenous composition composed of helium, carbon and oxygen.     

Identification of a collapsing protostar

The globular molecular cloud B335 contains a single, deeply embedded, far-infrared source. Our recent observations of H₂CO and CS lines toward this source provide direct kinematic evidence for collapse. Both the intensity and detailed shape of the line profiles match those expected from inside-out collapse inside a radius of 0.036 pc. The collapse began about 1.5 × 10⁵ years ago, similar to the onset of the outflow. The mass accretion rate is about 10 times the outflow rate, and about 0.4M should have now accumulated in the star and disk. Because B335 rotates only very slowly, any disk would still be very small (about 3 AU). The accretion luminosity should be adequate to power the observed luminosity. Consequently, we believe that B335 is indeed a collapsing protostar.Paper presented at the Conference onPlanetary Systems: Formation, Evolution, and Detection held 7–10 December, 1992 at CalTech, Pasadena, California, U.S.A.