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.     

Mechanism of thermonuclear burning propagation in a helium layer on a neutron star surface: A simplified adiabatic model

Some thermonuclear X-ray bursters exhibit a high-frequency (about 300 Hz or more) brightness modulation at the rising phase of some bursts. These oscillations are explained by inhomogeneous heating of the surface layer on a rapidly rotating neutron star due to the finite propagation speed of thermonuclear burning. We suggest and substantiate a mechanism of this propagation that is consistent with experimental data. Initially, thermonuclear ignition occurs in a small region of the neutron star surface layer. The burning products rapidly rise and spread in the upper atmospheric layers due to turbulent convection. The accumulation of additional matter leads to matter compression and ignition at the bottom of the layer. This determines the propagation of the burning front. To substantiate this mechanism, we use the simplifying assumptions about a helium composition of the neutron star atmosphere and its initial adiabatic structure with a density of 1.75 × 10⁸ g cm⁻³ at the bottom. 2D numerical simulations have been performed using a modified particle method in the adiabatic approximation.     

Buried Magnetic Field in Accreting Neutron Star

The evolution of the neutron star magnetic field is correlated to the accretion physical process in the binary X-ray phase. It is assumed that the original strong magnetic field is buried by the accreted materials, which is on account of the ferromagnetic physical property of the accreted matter. The obtained theoretical conclusions of our model are that: (1) the magnetic field decays in the X-ray binary phase, and relates inversely to the accreted mass as M^-1, (2) The internal magnetic field strength still remains large although the surface field strength decays.     

The evolution of massive stars with mass loss

The evolution of massive stars is investigated in the phases of hydrogen and helium burning, taking into account the mass-loss due to light pressure in optically thick media. The evolution in the stage of hydrogen burning near the Main Sequence occurs without mass loss. The large inverse density gradient appears in the outer layers of a 30 M star after it goes into the domain of red super-giants in the helium-burning stage. This effect appears as a consequence of an excess of luminosity of the star the ciritical one in sufficiently extensive outer layer, where convection is not so effective. In this way, the conditions for outflow of matter are formed. The sequence of selfconsistent models is constructed, with the core in hydrostatic equilibrium and hydrodynamically outflowing envelope. The amount of mass loss is not a given parameter, but it is found during the calculations as a characteristic number of the problem. The amount of mass loss is very high, of the order of 0.5M yr, the velocity of the flow is 20 km s^–1. The star loses about 7.2M during 15 yr. The amount of mass loss must rapidly decrease or finish altogether when matter near the hydrogen-burning layer begins to flow out, and a transformation of stellar structure must occur.The evolution of a 9M star is calculated. The density in the envelope of this star is sufficiently large and the outer convective zone, which develops on the red giant stage, prevents the outflow of matter. The intensive mass outflow from such star can take place at the carbon burning, or heavier element burning stages. The formation of infrared stars and Wolf-Rayet stars can be possibly explained by such a mechanism of mass loss, so that the infrared stage must precede the Wolf-Rayet stage.     

A polytropic model for the helium shell flash

A model consisting of two polytropes is constructed, to represent a helium core of a star during the helium shell flash occurring at the onset of helium burning in a degenerate core. The maximum temperature reached during the flash can be predicted as a function of core mass and mass inside the helium burning shell. This temperature will generally be too low for the production of neutrons out of¹⁴N. Some additional results on the helium shell flash in a star of 1.3M are also presented.Supported in part by the National Science Foundation [GP-9433] and the Office of Naval Research [Nonr-220(47)].On leave of absence from the Max Planck Institut für Physik und Astrophysik, München.     

The synthesis of26Al during combined hydrogen and helium-burning reactions

We have studied the synthesis of²⁶Al during combined hydrogen and helium-burning processes in high temperature and density conditions. The possible sites for these processes are believed to be the neutron star surfaces where the density ranges from =10⁴–10⁷ g cm^–3 and temperature range from 10⁸–8×10⁸ K. The screening effect which leads to an enhancement of nuclear reaction rates is taken into account whenever necessary. A detailed calculation of the abundances of²⁶Al and²⁷Al isotopes is presented here. Finite amounts of²⁶Al is found to be produced atT=2×10⁸ K and =10⁸ g cm^–3 due to these combined reactions. This situation is likely to be realized during the -ray burst events on neutron star surface. The amount of material processed in the burst sources is very little compared to the amount of material processed in Novae or Supernovae. Thus it is suggested that rather than contributing to the overall amount of²⁶Al, -ray bursts are likely to contribute more significantly to the inhomogeneity of²⁶Al distribution in interstellar medium.     

A two-zone model for the study of nuclear shell burning on accreting white dwarfs

A two-zone model for the analysis of nuclear shell burning on accreting degenerate dwarfs is developed. The model consists of two thin shells in a plane-parallel approximation: an accreted hydrogen zone on the top and a pure helium zone on the bottom, generated by hydrogen burning. The core of the star is isothermal and does not evolve with time. The physical properties (density, temperature, and pressure) of the shells are obtained and an analysis of some correlations between them and the mass accretion rate, the chemical composition of the accreted mass, and the heat flux from core is done. The interaction between both shells is also analyzed.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

Single X-ray Bursts and the Model of a Spreading Layer of Accreting Matter over the Neutron Star Surface

The excess of the rate of type I X-ray bursts over that expected when the matter fallen between bursts completely burns out in a thermonuclear explosion which is observed in bursters with a high persistent luminosity (4 × 10³⁶ ? L_X ? 2 × 10³⁷ erg s^?1) is explained in terms of the model of a spreading layer of matter coming from the accretion disk over the neutron star surface. In this model the accreting matter settles to the stellar surface mainly in two high-latitude ring zones. Despite the subsequent spreading of matter over the entire star, its surface density in these zones turns out to be higher than the average one by 2–3 orders of magnitude, which determines the predominant ignition probability. The multiple events whereby the flame after the thermonuclear explosion in one ring zone (initial burst) propagates through less densematter to another zone and initiates a second explosion in it (recurrent burst) make a certain contribution to the observed excess of the burst rate. However, the localized explosions of matter in these zones, after which the burning in the zone rapidly dies out without affecting other zones, make a noticeably larger contribution to the excess of the burst rate over the expected one.     

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.     

The criterion of appearance of unstable thermonuclear reaction in the helium burning shell of AGB stars

A criterion of the appearance of unstable thermonuclear reaction in the helium burning shell of thermal pulsating AGB (TP-AGB) star is established. The new criterion contains abundant physical information. It involves not only the geometric parameters of the helium burning shell, but also its mechanical, thermal and chemical parameters.The following mechanism of the occurrence and disappearance of unstable thermonuclear reaction in the helium burning shell of TP-AGB star is proposed: The appearance of a region of unstable convection in the helium burning shell of the TP-AGB star triggers unstable thermonuclear reaction which will promote a rapid expansion and a rapid geometric deformation of the shell, thereby removing the unstable thermonuclear reaction.Using the improved program of stellar evolution of Kippenhahn, the evolution of a 5Mo star is followed from the main sequence to the TP-AGB stage. The results show that the new criterion can well reflect the status of the thermonuclear reaction in the helium burning shell of the star. Besides, it is revealed that in the sixth period of thermal pulsation of the star the elements that are dredged up to the surface of the star, are synthesized mainly by thermonuclear reaction under the conditions, temperature lgT₂/K < 8.155 and density 4.0 < lg P2 /9 . CM-3 < 4.6.     

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.     

Multiple X-ray bursts and the model of a spreading layer of accreting matter over the neutron star surface

We report the detection of series of close type I X-ray bursts consisting of two or three events with a recurrence time much shorter than the characteristic (at the observed mean accretion rate) time of matter accumulation needed for a thermonuclear explosion to be initiated on the neutron star surface during the JEM-X/INTEGRAL observations of several X-ray bursters. We show that such series of bursts are naturally explained in the model of a spreading layer of accreting matter over the neutron star surface in the case of a sufficiently high (? ? 1 × 10^?9 M _⊙ yr^?1) accretion rate (corresponding to a mean luminosity L _tot ? 1 × 10³⁷erg s^?1). The existence of triple bursts requires some refinement of the model—the importance of a central ring zone is shown. In the standard model of a spreading layer no infall of matter in this zone is believed to occur.     

Expansion of neutron star matter and its final nuclear composition

The final nuclear composition of the matter expanding from the density of a neutron star is investigated. It is assumed that starquakes cause the cracks which penetrate the neutron star crust and that the neutron star fluid can flow out through the cracks into space. The change with time of the nuclear composition of this matter is calculated by use of the compressible nuclear mass formula, and the hydrodynamics of the system is followed by the effect of nuclear transformation with time of the second fission of heavy neutron-rich nuclei, which is followed by a rapid rise to above 10⁹ K. If the value of the -strength function exceeds about 10^–5.5 MeV^–1 s^–1, the system proceeds to a state of nuclear equilibrium in the later expansion stage and the nuclear composition is reshuffled, finally to be transformed into neutron-excess, stable nuclei within the atomic mass region 80A120. It also becomes clear that if the strength function has a value smaller than the above critical value, then the neutron-rich nuclides withA[200, 400] are copiously produced. These results will also be applied in the cases of a neutron-star-black-hole collision and the explosion of a neutron star associated with the catastrophic phase transition within the neutron star core. The astrophysical implications are briefly discussed.     

Pulsation regime of the thermonuclear explosion of a star's dense carbon core

The hydrodynamical problem of nuclear explosion of a dense carbon core of a star with mass 1.40M _⊙ is solved numerically. In calculation the kinetics of carbon burning at the nuclear reaction C¹²+C¹²→M²⁴+γ rate is included. Thus the inverse effect of hydrodynamical motion on the process of thermonuclear burning is taken into account, as compared with Bruenn's (1972) calculations. The calculations show that a pulsation regime of burning is realized (actually three pulses were obtained) which evolves to the detonation regime with full combustion and disruption of the star only at the third pulse. The effects of disintegration of iron group nuclei, neutronization of matter and neutrino losses in URCA processes have not yet been considered in calculations. The influence of initial conditions (mainly the temperature distributions) and the above mentioned effects, which have not been included in calculation, on the results of the hydrodynamical problem solution are discussed. The conclusion is made on new possibilities of formation of a gravitationally bound remnant of the explosion and a neutron star.     

A possible model of supernovae: Detonation of12C

Stars of intermediate mass (4M M9M ) may ignite the¹²C+¹²C reaction explosively because of the high degree of electron degeneracy in their central regions. After the exhaustion of helium burning in the core of such stars, a helium-burning shell develops which is thermally unstable. Approximating this shell by suitable boundary conditions, the subsequent evolution of the core is examined quantitatively by standard techniques. An explosive instability due to ignition and detonation of¹²C+¹²C develops at a central density _c 2 × 10⁹. Subsequent hydrodynamic expansion is computed; final velocities of expansion up tov20 000 km/sec are found. The star is totally disrupted; no condensed remnant is left. Such an explosion may be a plausible model for a significant fraction of supernovae. Investigation of the relevant nuclear reaction network shows that the entire core (M _core1.37M ) is processed through¹²C burning,¹⁶O burning and silicon burning. Significant amounts of⁵⁶Ni are produced. This nucleosynthesis is critically sensitive to the exact central density at which the¹²C+¹²C reaction ignites; several factors which affect this critical density are discussed. A brief summary of other supernovae thories which have been expounded in detail is presented for comparison.Supported in part by the National Science Foundation [GP-9433, formerly GP-7976], [GP-9114], and the Office of Naval Research [Nonr-220(47)].     

Revisiting Field Burial by Accretion onto Neutron Stars

The surface magnetic field strength of millisecond pulsars (MSPs) is found to be about 4 orders of magnitude lower than that of garden variety radio pulsars (with a spin of \({\sim }\)0.5–5 s and \(B{\sim }10^{12}\hbox { G}\)). The exact mechanism of the apparent reduction of field strength in MSPs is still a subject of debate. One of the proposed mechanisms is burial of the surface magnetic field under matter accreted from a companion. In this article we review the recent work on magnetic confinement of accreted matter on neutron stars poles. We present the solutions of the magneto-static equations with a more accurate equation of state of the magnetically confined plasma and discuss its implications for the field burial mechanism.     

Transport properties of the degenerate electron gas of neutron stars along the quantizing magnetic field

The expressions are derived for thermal and electric conductivities as well as thermopower of a degenerate relativistic electron gas in the surface layers of neutron stars along the magnetic fieldB=4×10¹¹–10¹⁴G for two scattering mechanisms of electrons, namely, for Coulomb scattering on ions in the ion-liquid regime and on high-temperature phonons in the solid regime. The results may be of use to study neutron star cooling rates, nuclear burning of the matter in the surface layers, diffusion of the magnetic field, etc.     

Pulsations of stellar models in H and He burning phases

A study of pulsational properties with evolution has been done for a 15.6M star withX _e =0.90 andY _e =0.08. Pulsational properties in the hydrogen-burning stages have been compared with those in helium-burning stages. A comparison with observed characteristics of Cepheids, classical Cepheids and supergiant variables has been made during the course of its evolution. In addition, models of 5,9 and 15M withX _e =0.708,Y _e =0.272 have also been studied for pulsational properties during the helium burning stage. It is also seen that pulsational instability is sensitive to changes in initial chemical composition and opacity parameters,n ands. A low helium abundance could be a reason for the stability of the models, even when lying in the instability strip of the H-R diagram.     

Nucleosynthesis in supernova outbursts and the chemical composition of the envelopes of neutron stars

The formation of chemical elements in the envelopes of neutron stars is considered at the densities ?=10⁷ to 10¹³ g cm^?3. It is shown, that the compression of cold and hot matter leads to different chemical compositions. The compression of cold matter is accompanied by a decrease of atomic weightA, up to ?≈3×10¹² g cm^?3. One may distinguish the following stages during the compression of hot matter: quasi-equilibrium, when there exists both nuclear equilibrium and kinetic equilibrium in β-processes; and limited equilibrium, when the total number of nuclei is constant. It is shown that a nonequilibrium chemical composition may be formed in the envelopes of neutron stars where there is an excess of neutrons in the presence of superheavy nuclei. The nuclear energy, stored in the neutron star envelope may be sufficient to support neutron star luminosity at a level of ～ 10³⁶ erg s^?1 over a period of ～ 10⁵ yr. Possible applications to the problem of X-ray sources and pulsars are discussed. The formation of the heavy nuclei in Supernovae explosions is considered briefly. Rough estimates are made for the differences in chemical composition of ejected matter during the explosions of stars of different masses and Supernovae of different types.