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)].     

Single close encounters in the planetary problem

We consider a large massM and two small massesm ₁ andm ₂ (m ₁ m ₂;m ₁,m ₂M). The orbit ofm ₁ is initially circular and the motion ofm ₂ hyperbolic with respect toM. The orbital elements of the small masses are strongly modified after a close, single encounter betweenm ₁ andm ₂.An approximative method, similar to the theory of stellar encounters, is used to determine the probabilities of collisions, hyperbolas, direct and retrograde ellipses, as well as the mean values of the semimajor axes and their root mean square deviation after the encounter.The results are close to those which are obtained if the massm ₂ is negligibly small, (Mm ₁m ₂;m ₂ 0), as should be also expected on general grounds.     

Supernova models with slow energy pumping and galactic supernova remnants

The study of supernova (SN) models with slow energy pumping is continued. At maximum luminosity the main characteristics of a SN are shown to be independent of the initial structure of the model (Table I, Figure 1). However, they depend on the massM _e of the envelope, and on the intensity of energy pumpingL , with an increase ofM _e leading qualitatively to the same changes in the SN parameters as a decrease inL (Table I, Figures 2 and 3). A simple relationship connecting the important SN parameters is obtained (Equation (6)). From the inflection of the color indexB-V curve, the possibility of deriving the characteristic time of energy pumping with intensityL 10⁴⁴ erg s^–1 is pointed out. The comparison of the extragalactic type I SN observations with the results of calculations leads to the estimate ofM _e 0.3–0.7M.An investigation of the galactic type I SN remnants is carried out (Table III). The estimate ofM _e 0.2–0.3M is obtained for the remnants of supernovae SN 1006, SN 1572, and SN 1604. It completely fits the results for the extragalactic type I SNs. The total initial mass of SN 1604 presupernova was shown to be at least about 7M .It was established that the Crab nebula resulted from the outburst of a peculiar SN. The unique properties of such SNs, including SN 1054, are due to the low intensity of energy pumping (L 10⁴² erg s^–1). The mass of the envelope of the Crab nebula is evaluated to beM _e 0.7M . SN 1054 was shown to have m _max ^v =–4 _m ^. 0 at maximum luminosity.     

Evidence for iron whiskers near the galactic centre

It is shown that ~ 10² M of iron in the form of long slender whiskers, expelled from supernovae, can explain an observed deficit of line emission in the 157.7µm C II line and in the 205µm N II line from the galactic centre region.     

Type Ia supernovae: An explosion in the regime of a convergent delayed detonation wave

The model of a presupernova’s carbon-oxygen (C-O) core with an initial mass of 1.33 M _⊙, an initial carbon abundance X _C ⁽⁰⁾ =0.27, and a mean rate of increase in mass of 5 × 10^?7 M _⊙ yr^?1 through accretion in a binary system evolved from the central density and temperature ρ_c=10⁹ g cm^?3 and T _c=2.05 × 10⁸K, respectively, by forming a convective core and its subsequent expansion to an explosive fuel ignition at the center. The evolution and explosion equations included only the carbon burning reaction ¹²C+¹²C with energy release corresponding to the complete conversion of carbon and oxygen (at the same rate as that of carbon) into ⁵⁶Ni. The ratio of mixing length to convection-zone size α_c was chosen as the parameter. Although the model assumptions were crude, we obtained an acceptable (for the theory of supernovae) pattern of explosion with a strong dependence of its duration on α_c. In our calculations with sufficiently large values of this parameter, α_c=4.0 × 10^?3 and 3.0×10^?3, fuel burned in the regime of prompt detonation. In the range 2.0×10^?3≥α_c≥3.0×10^?4, there was initially a deflagration with the generation of model pulsations whose amplitude gradually increased. Eventually, the detonation regime of burning arose, which was triggered from the model surface layers (with m ? 1.33 M _⊙) and propagated deep into the model up to the deflagration front. The generation of model pulsations and the formation of a detonation front are described in detail for α_c=1.0 × 10^?3.     

Spin-orbit coupling: A unified theory of orbital and rotational resonances

The dynamics of the spin-orbit interaction of a sphereM ₈ and a rotating asymmetrical rigid bodyM _a are examined. No restrictions are imposed on the masses, on the orientation of the rotation axis to the orbit plane, or on the orbit eccentricity. The zonal potential harmonics ofM _a induce a precession of the spin axis as well as a precession of the orbit plane, the net effect being a uniform precession of the node on an invariant plane normal to the constant total angular momentum of the system. In general, the effect of the tesseral harmonics is to induce short-period perturbations of small amplitude in both the orbital and spin motions. Resonances are shown to exist whenever the orbital and rotational periods are commensurable. In any resonant state a single coordinate is found to represent both orbital and spin perturbations; and the system may be described as trapped in a localized potential well. The resultant spin and orbit librations are in phase with a common period. The relative amplitudes of the spin/orbit modes are determined by the characteristic parameter =M _a M _s a ² /3(M _a +M _s )C, wherea is the semimajor axis of the orbit, andC is the moment of inertia ofM _a about the rotation axis. When ga1, the solutions reduce to those for pureorbital resonance, in whichM _s librates in an appropriate reference frame while the rotation rate of the asymmetrical body remains constant. In the opposite extreme of 1, the solutions are appropriate to purerotational resonance, in which the orbital motion is unperturbed but the spin ofM _a librates. In each of these special cases the equations developed herein on the basis of a single theory are in agreement with those previously determined from separate theories of spin and orbital resonances.     

The effect of convection on the process of carbon burning in a degenerate core

The results of a numerical investigation of the hydrostatic carbon burning in a degenerate carbon core withM=1.4M are presented. Convective heat transfer has been taken into account according to the mixing length formalism. It is shown that for small convection the effective (10^–3) computational results are in agreement with the assumption of a hydrostatic evolution of the core. At 10^–2 the burning times in successive mass zones become less than the hydrodynamic time for the core. In this case carbon burning starts with a rapidly propagating thermal instability. The connection between the convective and neutrino mechanisms of burning propagation is discussed.     

The cooling wave in supernova shells

The cooling wave apparently arises at some phases of the supernova expansion. A number of basic properties of the cooling wave are considered. The dependence of light curve and colour temperature on chemical composition and density distribution law has been investigated in detail. An estimation of total mass ejected by supernovae type II leads to the value of 20M . The necessity of further careful spectroscopic and photometric observations at prolonged postmaximum phases, especially for supernovae type II, is emphasized.     

Relativistic isentropic stellar models

Relativistic, isentropic, homogeneous models are constructed by a method that automatically detects instabilities, and evolutionary tracks of central conditions are shown on a (T, ) diagram. Models heavier than 20M become unstable because of pair creation. Iron photodisintegration causes instability in the mass range between 1.5M and 20M . General relativistic effects bring about the onset of instability in models of 1.2–1.5M when the central density is about 10¹⁰ g/cm³. Lighter models become white dwarfs. It is pointed out that general relativistic instability will prevent the formation of neutron stars through hydrostatic evolution and may be relevant in setting off low-mass supernovae.     

Evolution of binaries with ultra-short periods: Systematic study

A detailed investigation of the evolution of low-mass binaries is performed for the case when the secondary fills its Roche lobe at the stage of core hydrogen exhaustion. The obtained results are compared with observational data for ultra-short periodic X-ray systems MXB 1820-30 and MXB 1916-05. In the frame of the proposed evolutionary scenario it is possible to obtain for MXB 1820-30 its periodP=11.4 min twice (see Figure 2). In the first case the parameters of the system are:M ₂ 0.13–0.15M ,X0.05–0.13, |P/P| (3.6–6.2) } 10^–7 yr^–1, M₂ (4.1–9.6) } 10^–9 M yr^–1, for the second:M ₂ 0.08–0.09M ,X= 0, |P/P| (1.3–1.5) } 10^–7 yr^–1, M₂ (1.4–1.8) } 10^–8 M yr^–1. It is suggested that MXB 1916-05 is the progenitor of the system MXB 1820-30 (M ₂ = 0.1M,X 0.221,M ₂ 1.8 × 10^–10 M yr^–1).     

Carbon deflagration models for type-I supernovae and theoretical optical spectra

A carbon deflagration model in the accreting C+O white dwarf is presented as a plausible model for type-I supernovae (SN I). The evolution of the white dwarf is calculated from the beginning of accretion through complete disruption. The propagation of a carbon deflagration wave from center to the surface and associated nucleosynthesis are calculated. About 0.6M ⁵⁶Ni and substantial amounts of Ca, Ar, S, Si, Mg, and O are synthesized.The synthetic spectrum at maximum light for this carbon deflagration model is calculated and compared to the observed spectrum of SN 1981b in NGC 4536 at maximum light. If the radial stratification of composition in the outer layers of the model is removed by mixing, the theoretical spectrum is in good agreement with the observed spectrum.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.     

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.     

The evolutionary behaviour of population III intermediate mass stars

Assuming the Big-Bang nucleosynthesis was responsible for the formation of helium, the evolution of first-generation intermediate-mass stars of 5, 7, and 9M with no metals have been studied from the threshold of stability through the stage of helium exhaustion in the cores of the stars. Hydrogen Main-Sequence positions are marked at effective temperatures higher than those of normal stars. The evolutionary tracks during the hydrogen burning phase start to be similar to those of normal stars when the CN-cycle reactions, which are controlled by the triple-alpha reactions, become operative for hydrogen depletion. Helium Main Sequence of Population III stars of intermediate mass occurs at the high effective temperature region of the H-R diagram and stars stay as blue stars until the end of the core helium exhaustion phase. The total time elapsed is in the range of 3×10⁷ and 10⁸yr. The stars with the initial masses of 5, 7, and 9M developed a moderately electron degenerate complete hydrogen-exhausted region with masses of 0.77, 1.06, and 1.42M , respectively, in which the most abundant element is carbon.     

Deflagration of white dwarfs as a model for type-I supernovae

Carbon-oxygen white dwarfs may be the progenitors of type-I supernovae. Spherically-symmetric models of such dwarfs have been evolved from an artificial core incineration. The convectively unstable incinerated region was allowed to grow at a velocity prescribed by the mixing-length theory of convection. The mixing length can be varied to give different cases. In all the cases considered the dwarfs exploded and were totally disrupted. The calculations were stopped after the dwarf matter had gone into homologous expansion. The model with the best estimated mixing length incinerated 0.8M . The energy released in burning this amount of carbon-oxygen to⁵⁶Ni provides a disrupted dwarf with velocities suitable for type-I supernovae.Research supported by the Natural Sciences and Engineering Research Council.     

Fourier analysis of the light curves of eclipsing variables,XXIV

The aim of the present paper will be to evaluate numerically Jacobian and other functions which have been discussed in more detail in a previous paper of this series (Edalati, 1978b, Paper XXII), and also choose the most convenient moments to obtain a good determination for the unknown eclipse parametersa andc ₀. More than 12 different pairs ofg-functions for real values ofm have been investigated numerically and diagrammatically. The behaviour ofg-functions depends but very little on different combination of the moments, and related diagrams are approximately the same asg ₂ andg ₄ (Kopal and Demircan, 1978, Paper XIV).The behaviour of the vanishing Jacobian, arising from different pairs ofg-functions for real values ofm1 has been shown diagrammatically in terms ofa andc ₀. Accordingly, we obtain the optimum combination of the moments (i.e.,A ₆,A ₇,A ₈ andA ₉) ing-functionsg ₇ andg ₈. It has been noted that the behaviour of theg-functions which depend on the combinations of the higher order moments (i.e.,m5) have been ruled out, because the proportional error of the momentsA _2m increases with increasing values of realm. The automated method has been tested successfully on the light curve of RT Per (Mancusoet al., 1977; Edalati, 1978a). Finally, a comparison is given of the elements of RT Per arising from two different pairs ofg-functions, i.e.,g ₂,g ₄ (Edalati, 1978a) andg ₇,g ₈ for the light curves analysis.     

Relativistic evolution of 103 M ⊙ star

A fully relativistic evolution of 10³ M is described for initial composition ofY=Z=0. Our results show that (a) a great part of the star is in radiative equilibrium, (b) the maximal red-shift for main-sequence 10³ M stars is significantly less than for isentropic models, and (c) a very low amount of CNO elements (<10^–8 by mass) is formed at any stage before hydrogen is completely consumed and hence such stars cannot be the progenitors of Population II stars.     

On the influence of electronic concentration fluctuations of the dispersion measure and rotation measure

The question of the influence of electronic concentration fluctuations along the line of sight on the dispersion measure (DM) and rotation measure (RM) is under consideration. it is shown that the measuring ofDM andRM enables us to determine the number of electronsN _e =n _e ds and the quantityM _e =n _e H cos ds, respectively, along the line of sight in accordance with the general assertion. Under the conditions considered, the conclusion (Lerche, 1970a, b) that the connection ofDM andRM withN _e andM _e greatly depends on the electronic concentration fluctuations, is found to be incorrect.     

Models of pulsating low-massive yellow supergiants

The nonlinear self-excited oscillations of the envelopes of low-massive highly luminous stars are described. The parameters for these models wereM=0.8M ,M _bol=–5.5, –5.84 mag,T _eff=4500, 5000, 5500 K. The oscillations have been found to consist of the standing wave pulsation near the envelope bottom and running waves in outer layers. The ratio of the standing wave frequency _s to the average frequency of the running waves _r increases with the stellar luminosity: _s / _r =1.7 whenM _bol=–5.5 mag and _s / _r =2.4 whenM _bol=–5.84 mag. The frequency of oscillations near the photosphere is found to be in close agreement with the critical frequency for running waves. Mass loss from these stars is caused by shocks. It has been shown that agreement between FG Sge's period change observed during the last decade and the period-luminosity relation for double shell stars takes place when FG Sge's luminosity isM _bol=–5.96 mag.     

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.     

Numerical simulations of pulsationally unstable accretion disks around supermassive black holes

The innermost region of slim accretion disks with standard viscosity is unstable against axisymmetric radial inertial acoustic perturbations under certain conditions. Numerical simulations are performed in order to demonstrate behaviors of such unstable disks. It is shown that oscillations with the period of 10^–3 (M _BH/M ) s can be excited near the inner edge of the disks, whereM _BH is the mass of the central object. This kind of unstable disks is a possible origin of the periodic X-ray time variabilities with period of 10⁴s observed in a Seyfert galaxy NGC 6814.