On the theory of the light curves of supernovae

An account of the theory of the light curves of supernovae is presented, based on certain assumptions concerning the passage through the stellar atmosphere of powerful shock waves. The investigation is based on numerical integration of appropriate equations of gas dynamics and radiative heat-conductivity. The calculations substantially involve the ionization and recombination of hydrogen in the envelope of a supernova. Changes are traced in the curves arising from the transition from compact stars with small radius (10R ), to stars with very extensive envelopes (10000R ). The light curves for compact stars agree well with observations of the peculiar supernovae in NGC 5457, NGC 6946 and NGC 5236. The characteristics of the light curves with the passage of shock waves through the extended atmosphere coincide within an order of magnitude with observations of the supernovae of type II and type I near their maximum brightness. A powerful heat-wave propagates before the shock-front in the extensive atmosphere which gives rise to a detached supernova envelope in the form of a thin spherical layer. We investigated the condition in an ascending wave of cooling and recombination in the supernova envelope. It is shown that part of the hydrogen may recombine to attain full transparency for radiation passing through it. The observations are compared with the results of the theory of radioactive decay of the elements. This explanation of the light curves by the passage of shock waves requires energies of 10⁵⁰ to 10⁵² ergs, which are in agreement with mechanisms of thermonuclear explosions.Translated from the Russian by E. Budding.     

Local interstellar medium

This paper reviews and analyses various observational data about the local interstellar medium (LISM)-a volume with a radius of about 200 pc near the Sun. There are collected radio, IR, optical, UV, and X-ray observations of the ISM and data on the Sco-Cen association. All available information confirms Weaver's (1979) conclusions that the Sun is located near an edge of a giant cavern with a radius of about 180 pc and the cavern center coincides with the Sco-Cen associated center. The outer rim of the cavern is observed as numerous, very longHi flaments, filaments of the interstellar polarization, and soft X-rays radiated by coronal gas with a temperature of about 10⁶K. Close environment (from 10^–4 to 2–5 pc) of the Sun is filled by warm (about 10⁴ K)Hi with the number density 0.1–0.2 cm^–3, which is a corona of the local cloud of the ISM. The central part of the cloud is observed to the galactical center direction at a distance of 10–20 pc as Sancini and van Woerden's (1970)Hi filament. The cloud blown round by stellar winds has a horseshoe-like shape, bordering the Sun. Tinbergen's (1982) patch of polarization is observational evidence of the shape.Several arguments are given to show that the bright spots of soft X-rays (130–284 eV) near the galactic poles are produced by an interaction of stellar winds with outer edge of the local cloud near the ends of the patch of polarization. Lyman continuum radiation from Sco-Cen stars was shown to be probably the main source of ionization of extendedHii regions of low density in the LISM. Various data evidence that the North Polar Spur is a SNR in the local cavern with the age of about 10⁵ years. Interaction of the local cavern with an interstellar absorption-free tunnel stretched for more than 1 kpc along the galactical longitudel=240° is discussed. In conclusion several actual problems of investigation of the LISM were formulated.     

Origin of low energy cosmic ray positrons at energies ≳2 MeV

It is shown that an appreciable flux of positrons below a few MeV in the cosmic radiation could arise from the decay of cobalt nuclei in the decay chain⁵⁶Ni⁵⁶Co⁵⁶Fe, which occurs in the silicon burning shells of supernovae just after their ejection at relativistic velocities. The equilibrium spectrum of positrons in the interstellar space has been calculated on the assumption that the observed abundance of iron nuclei in the cosmic radiation is the result of the above process. It is found that the observation below about 10 MeV can be well explained with a moderate acceleration of the positrons in the expanding envelope of supernovae prior to their propagation in the interstellar space. The total⁵⁶Ni content in the shells of supernova necessary to account for the observed positrons is in agreement with that required to explain the peak luminosity during the supernova outburst. Since this model deals with positrons created at the time of injection of cosmic rays into the interstellar space, it becomes possible to study the shape of the injection spectrum of cosmic rays.On leave from Tata Institute of Fundamental Research, Bombay, India.     

Unbound planets

Current protostellar theory has determined a lower limit to the mass of a pre-stellar gas cloud fragment of ~0.01 M. This suggests that isolated interstellar bodies in the mass range ~10 M_-710_-2 M must have originated within a planetary system. Two possible mechanisms whereby planets are lost from their parental systems to interstellar space are discussed and the abundance and distribution of such unbound planets within the Galaxy is examined. It is found that, except within the central regions of the Galaxy, unbound planets are expected to be scarce. In the solar neighbourhood for instance, the number density ratio of unbound planets to stars is estimated to range between extremes of ~4 × 10^–4–3 × 10^–2 with a most probable value of ~6 x 10^–3. The faint possibility that the hypothetical Planet X might be of extra-solar origin is also discussed.     

Spectrum of the galactic magnetic fields

The magnetic fields observed in the galactic disc are generated by the differential rotation and the helical turbulent motions of interstellar gas. On the scalesl=2k ^–1 which lie in the intervall ₀<l<l _e (l ₀100 pc is the energy-range scale of the galactic turbulence), the spectral density of the kinetic energy of turbulence (k ^–5/3) exceeds the magnetic energy spectral density (k ^–1). The equipartition between magnetic and kinetic energies is reached atl=l _e 6 pc in the intercloud medium and is maintained down to the scalel=l _d 0.03 pc. In dense interstellar cloudsl _e is determined by the individual cloud size andl _d 0.1 pc.The internal turbulent velocities in Hi clouds (cloud size is assumed to be 10 pc) lie in the range from 1.8 to 5.6km s^–1, fitting well within the observed range of internal rms velocities. Dissipation of the interstellar MHD turbulence leads to creation of temperature fluctuations with amplitudes of 150 K and 65 K in dense clouds and intercloud medium, respectively. The small-scale fluctuations observed in the interstellar medium may arise from such perturbations due to the thermal instability, for instance. Dissipation of the MHD turbulence energy provides nearly half of the energy supply needed to maintain the thermal balance of the interstellar medium.     

Boron cosmochemistry. Part II: Boron nucleosynthesis and condensation temperature

Abstract— The new B solar-system abundance calculated by Zhai and Shaw (1994), 16.9 atoms/10⁶ Si (or 606 atoms/10¹² H) is used to reevaluate the different possibilities of LiBeB (except ⁷Li) nucleosynthesis. The revised abundances support two models: (1) Light elements were formed by continual bombardment of interstellar medium (ISM) by galactic cosmic rays (GCRs), but these galactic cosmic rays should contain a very intense low-energy component, in the form of E^?5 which cannot be observed near the Earth due to solar modulation effects; (2) Light elements are a mixture of two sources. In the first source, light elements were synthesized by continual bombardment of interstellar medium by galactic cosmic rays. In the second source, they were made by the interactions of C and O nuclei ejected from supernovae with the H and He in the surrounding gas. The first source constitutes ～46% of total B. The Si-normalized and CI-meteorite-normalized abundances of common and volatile elements in carbonaceous chondrites show a linear correlation with their condensation temperatures. Using this relationship and the normalized B abundances in CM, CO, and CV meteorites, we can estimate the B condensation temperature to be ～910 K, which is similar to Ga.     

Physical parameters of reflection nebulae in the galaxy

We show how, given observed equivalent widths of Mgii and Mgi absorptions due to an interstellar cloud in which a late-B star is embedded, the basic physical parameters: kinetic temperature, mean density, electron density, and radius can be constrained. Hydrogen ionization by means of cosmic rays and the effect of the stellar radiation field on the magnesium ionization equilibrium are taken into account.The method is applied to the reflection nebula surrounding the star HD 26676. The resulting solutions for the radius and temperature of the nebulosity are comparable to the typical values derived for diffuse interstellar clouds from optical and 21-cm measurements, if a cosmic-ray ionization rate 10^–16s^–1 — in agreement with recent determinations — is assumed. The results are not strongly dependent on the gas pressureP forP varying in a range of values typical of interstellar clouds.     

The prominence radiation theory

The present work is a review of papers related to the theory of prominence radiation. Special attention is paid to stationary equations and the theory of radiation diffusion in the lines and continua of hydrogen, helium and metals.We conclude that prominences are low-temperature formations T _e 7000 K, of low density 10¹² particles per cm³, n _e 10¹¹ cm^–3, effective thickness 10⁹ cm, and that the chemical composition of prominences and that of the Sun's atmosphere are the same. The prominence radiation in the lines of hydrogen, helium and metals is due mainly to quasiresonance scattering of the photospheric radiation.     

Sudden grain nucleation and growth in supernova and nova ejecta

The thermal conditions leading to the rapid nucleation and growth of dust in astronomical explosions are examined. The contribution herein to nucleation physics lies only in the clarification of the ambient conditions where it apparently occurs. In both nova and interior shells of supernovae, dust precipitates in gas densities of order of 10^–14 g cm^–3 a few months after the explosion. The ambient conditions differ widely, however. Supernova condensation occurs in a thermal equilibrium, with photons, ions, electrons and grains having equal temperatures. In novae huge disequilibria exist, with photon and electron temperatures near 5×10⁴ K, photon energy density near 750 K, and forming refractory grains near 1800 K. In neither type of explosion can the condensed matter easily maintain chemical equilibrium with the total system. Interesting isotopic anomalies are trapped in both types of refractory condensate in the interstellar medium. The nova provides the best astronomical laboratory for observing the condensation.Invited contribution to the Proceedings of a Workshop onThermodynamics and Kinetics of Dust Formation in the Space Medium, held at the Lunar and Planetary Institute, Houston, 6–8 September, 1978.     

The abundance of negative hydrogen in small hot interstellar clouds

The observed intensities of the diffuse interstellar absorption band at 4430 have minimum values, for given stellar distances, that are equivalent to the reddening caused by the small Ambarzumian-type clouds studied by B Strömgren. This indicates that there is no negative hydrogen present between these clouds, which are then identified with the hot H I phase of interstellar matter.The equilibrium density of H^– inside such clouds is calculated from mean densities of neutral hydrogen atoms and free electrons, derived from radio observations for the local region outside the large Orion-arm clouds. The filling factor of the small clouds is taken to be the same as that preserved in the structure of the Gum Nebula from before its ionization. An electron temperature of 3375 K corresponding to the local degree of ionization of the small-cloud hydrogen then leads to a mean density of negative hydrogen equal to 2×10¹³ cm^–2 kpc^–1, in agreement with the observed diffuseband intensities.     

Near resonant charge transfer processes at thermal energies

A useful procedure is described for the evaluation of near resonant charge transfer cross-sections at thermal energies. The method is based on a generalization of a semi-classical approach introduced by Bates and Mapleton for the study of symmetric resonant charge transfer processes. The rate coefficient is calculated for the reaction O⁺+HH⁺+O as a function of temperature between 10 and 10⁴ K; the results are compared to those obtained using the orbiting approximation. A brief application of these rates to the interstellar medium is made where it is found that substantial differences emerge between cases where the gas is heated by cosmic rays or by X-Rays.Operated by Associated Universities, Inc., under contract with the National Science Foundation.     

Static spherical configurations of cold matter in the Einstein-Cartan theory of gravitation

We investigate static, spherical configurations of cold catalized matter in the Einstein-Cartan theory of gravitation. Assuming that density of spin is proportional to the number density of baryonsn and using an equation of state of a degenerate, relativistic Fermi gas, we numerically integrated the relativistic equation of equilibrium. We have also studied the stability of those configurations. Configurations with central number densityn _c such that where is the effective pressure, are very similar to general relativistic configurations with the same central density. In the Einstein-Cartan theory there exists another disjoint family of equilibrium configurations for which but . Those configurations have very small masses 10^–6 g and raddi 10^–34 cm and are unstable.Supported in part by Research Grant MR-I-7.     

Effects of suprathermal grains

Grains ejected from stars at velocities of 10⁷ cm s^–1 and/or grains accelerated by the pressure of starlight in the intercloud medium to velocities in the range 2×10⁶–10⁷ cm s^–1 are slowed to velocities of about 2×10⁵ cm s^–1 in a typical interstellar cloud. The interaction of fast grains with gas atoms as they are slowed in clouds could provide (a) the dominant heat source for interstellar clouds; (b) sites for molecule formation; and (c) a mechanism of providing a pressure balance between clouds and the intercloud medium.Paper presented at the Symposium on Solid State Astrophysics, held at the University College, Cardiff, Wales, between 9–12 July, 1974.     

Grain formation in the expanding gas flow around cool luminous stars

We studied grain formation process and flow structure around cool luminous mass-loss stars. The nucleation and growth theory of Yamamoto and Hasegawa was extended to the case of expanding gas flow.The envelope was assumed to be steady, spherically symmetric, in thermal and radiative equilibrium, optically thin, and driven by radiation pressure on grains. For oxygen rich stars, Mg-silicate was found to be the first condensate which can drive the gas effectively. The following stellar parameters were chosen; stellar massM _*=1M , effective temperatureT _*=3000K, stellar luminosityL _* from 7.5×10³ to 2.0×10⁴ L , and mass-loss rate |M| from 1.0×10^–6 to 1.0×10^–4 M yr^–1.Main results of calculations are as follows; (1) grain condensation temperatureT _c9801080 K; (2) total gas pressure at the condensation pointP _t6×10^–116×10^–9 atm; (3) scale parameterA _c10³6×10⁴; and (4) final grain sizer _f=400Å1m. For the smaller |M| or the largerL _*, these values are the smaller. We recognized two types of flow solutions (1) Dust driven flow for large |M|, which reaches the sonic point near the condensation point; and (2) Modified Parker flow for small |M| for which grain sizer _f is almost independent of |M|.A comparison with observational results ofL _* and gas terminal velocityV suggests that Mg-silicate grains are of submicron size, which are effective for interstellar extinction in visible and infrared. Fe-grains condense in the rarefied outflow with a size probably smaller than 100Å, which may contribute for interstellar ultraviolet extinction. The envelope has three-layer structure inner dense region with small outflow velocity, grain formation layer and outer rarefied region with fast outflow velocity.No flow solutions exist forM _* greater than a critical stellar massM _*cr for a given stellar luminosityL _* and mass-loss rate |M|.For example, critical stellar massM _*cr=1.8M forL _*=10⁴ L ,T _*=3000 K, and |M|=10^-5 M yr^-1.     

Accretion and electrostatic interaction of interstellar dust grains; Interstellar grit

This work is divided into 13 sections and 2 appendices, and aims to elucidate the accretion mechanism, which operates via image-theory forces, whenever two interstellar dust grains come close together. Section 1 is an introduction. Section 2 proposes that the distribution of interstellar grains be taken asn(r) r ^–4 to avoid distortion of the 3K microwave background by radiation from spinning grains. Section 3 examines each of three types of image force accretion processes, finding them to be dominant compared to radiation or gravitational forces by at least a factor of 10¹⁹. Section 4 states that only grains made of conducting material (e.g., graphite, ice, iron) are involved in image theory. Section 5 presents reasons for believing that two grains should coalesce on impact. Section 6 examines the motion of charged interstellar grains in Hi and Hii regions. Section 7 demonstrates, by way of four examples involving dust grains ofr=10^–7 cm up tor=10^–4 cm, that the image effects on conducting grains are not trivial, and that the dynamics involved is not to be compared at all with elementary Coulomb interaction of two changes. Section 8 concludes that accretion with not take place in Hi clouds if thermal (equipartition) velocities prevail among the dust particles. section 9 examines grain interactions in Hii regions: here, following an argument due to Spitzer, consideration is given to the case of a population of dust grains all streaming in the direction of the local magnetic field B at velocities of order 0.1 km s^–1. It is shown that accretion takes place effectively, leading to the formation of interstellar grit, meaning grains of mass 10^–8 to 10^–7 gm, radius 0.1 mm; and leaving also a population ofr10^–6 cm grains, which are observed in polarization and extinction measurements. The existence of the latter is now a deduction and not an ad hoc postulate, as previously, and implies a distribution of the general formn(r) r _mean ^–3 , in approximate agreement with that of Section 2. Section 10 considers the accretion mechanism as a cascade process. Section 11 shows that the existence of grains in space ofr 10^–6 cm rules out an origin in supernova or galactic explosions, and supports a passive origin, perhaps in red giants or Mira variables. Section 12 discusses the implications of the results found for polarization observations and cosmogony, the latter being given a new foundation in which planets of different composition form automatically from a solar nebula. Section 13 is a conclusion.     

Cosmic-ray production of deuterium,He3, lithium,beryllium, and boron in the Galaxy

The production of deuterium, He³, lithium, beryllium, and boron by galactic cosmic rays in the interstellar medium, over the life of the Galaxy, is calculated. It is found that high-energy - reactions contribute in an essential way to the observed lithium. When allowance is made for the interchange of material between stars and the interstellar gas and for the change of cosmic-ray intensity with time, the Li⁶, Be⁹, and boron produced turn out to be ample to explain the observed abundances, and with remarkable internal consistency. Deuterium and He³ arenot produced in significant amounts, nor Li⁷ in sufficient amount, however. To explain the Li⁷/Li⁶ ratio measured terrestrially and in chondritic meteorites, we invoke cosmological production of Li⁷. This implies the production of deuterium, He³, and He⁴ as well, in amounts consistent with observation. The theory in its present form cannot explain a solar-system Li⁷/Li⁶ ratio of 12and stellar ratios as low as 3, but additional processes can be adduced to reconcile them. The consistency of the numbers when cosmological production is included lends additional support to the big-bang hypothesis. An incidental result is that the mean luminosity of the Galaxy over its lifetime has been about 3 times its present luminosity.     

The interrelationship between cosmic dust and the microwave background

Attention is given to the radiation of microwaves by charged dust in space. Presently-used particle distributions do not restrict the presence in space of large numbers of small (r<10^–6 cm) silicate grains, but it is shown that such densities (10^–25–10^–26 g cm^–3) of small grains would produce a microwave background with an energy density of the same order of magnitude as the energy density of the (presumed) cosmological 3 K background. Limits set by the isotropy of the latter are: (HI clouds)10^–26, (Galactic plane)10^–30, (Halo)10^–32, (Local Group)10^–34 g cm^–3. These limits imply that either there is a cutoff in particle distributions atr10^–6 cm, or that the density of silicate grains in space has been generally overestimated, or that cosmic rays have broken up a lot of grains so that they now form a population of grains of very small size (10^–7 cm) which are difficult to detect by conventional methods. One way to look for the latter population is by studying expected distortions of the 3 K spectrum to the short wavelength side of the portion hitherto observed (grains may have a size distribution able to give an approximate black-body curve for radiation from larger grains of 10^–6 cm size), and by testing the effective energy density of the 3 K field in other galaxies.     

Large-scale flow of interstellar gas in galactic spiral waves: Effects of thermal balance and self-gravitation

Using the recent observational data on atomic and molecular hydrogen in the Galaxy, we analyse the dynamics of the interstellar gas in a spiral density wave. Within the framework of Marochniket al.'s (1972) model of the galactic spiral structure, the gas flow is obtained, with self-gravitation and thermal processes taken into account.It is shown that: (1) the self-gravitation of gas does not practically affect the galactic shock if the dominant contribution into the gas density comes from atomic hydrogen; (2) the effects of self-gravitation could be essential for both the gas flow and the stellar spiral wave only if the density contribution of H₂ exceeded several times that ofHi, with molecular hydrogen as a continuous medium having the isothermal equation of state; (3) however, regardless of the estimates of H₂ abundance in the Galaxy, its reaction to the density wave is weak, since it forms a collisionless system not dragged by the intercloud gas.It has been found that, if we allow for thermal processes in the interstellar medium, new types of gas flow can develop alongside with a previously-known continuous flow and galactic shock. They are: (1) galactic shock with the phase transition leading to the formation of dense cold clouds; (2) a three-phase flow where hot cavities and dense cold clouds coexist with an initial, moderately dense and cold phase; (3) an accretion wave which is a specific type of nonlinear wave with an amplitude of 11/2 orders of magnitude larger than that of the isothermal galactic shock appearing under the same conditions, but without heating and cooling.     

Modeling chemical growth processes in Titan's atmosphere 2. Theoretical study of reactions between C2H and ethene, propene, 1-butene, 2-butene, isobutene, trimethylethene, and tetramethylethene

Barrierless reactions between unsaturated hydrocarbons and the ethynyl radical (C₂H) can contribute to the growth of organic particulates in the haze-forming regions of Titan's atmosphere as well as in the gas giants and in the interstellar medium. We employed a combination of quantum chemistry and statistical rate theories to characterize reactions between ground state C₂H and seven alkenes of the general structure R₁R₂C^′C^″R₃R₄ containing up to six carbons. The alkenes included ethene (C₂H₄); propene (C₃H₆); 1-butene, 2-butene, and isobutene (C₄H₈); trimethylethene (C₅H₁₀); and tetramethylethene (C₆H₁₂). Density functional theory calculations at the B3LYP/6-31 + G^∗∗ level were used to characterize the adducts, isomers, products, and the intervening transition states for the addition-elimination reactions of all seven species. A multiple-well treatment was then employed to determine the outcome distributions for the range of temperatures and pressures relevant to Titan's atmosphere, the interstellar medium, and the outer atmospheres of the gas giants. Finally, trajectory calculations using an ROMP2 potential energy surface were used to calculate kinetic rates for the ethene + C₂H reaction, where the agreement between the computed and measured values is very good. At low pressure and temperature, vinyl acetylene is a dominant product of several of the reactions, and all of the reactions yield at least one dominant product with both a double and a triple CC bond.     

On the structure and mass of the galactic halo

On the basis of a globular cluster study a crude estimate of the total mass of the galactic halo within 20 kpc from the centre is done. It gives a minimal halo mass of the order of , yielding possibilities for a mass as large as . The content of the interstellar matter in the halo is estimated too. It is found that the gas content is a few percents the minimal mass, the gas temperature is very high — about 1×10⁶ K, the magnetic field weak — about 0.25 nT. A weak nonthermal radio emission might be expected from such a halo.