Equation of state under nuclear statistical equilibrium conditions

We investigate a three-parameter equation of state for stellar matter under nuclear statistical equilibrium conditions in the ranges of temperatures 3×10⁹–10¹¹ K and densities 10⁴–10¹³ g cm^?3 and for various ratios of the total number of neutrons to the total number of protons within the range 1–1.5. These conditions correspond to the initial stages of the gravitational collapse of iron stellar cores that are accompanied by nonequilibrium matter neutronization. We analyze the effect of the excited levels of atomic nuclei on the thermodynamic properties of the matter. We show that this effect is insignificant at low densities, ρ?10¹⁰ g cm^?3, but it leads to an expansion of the instability region, γ<4/3, at higher densities. The incorporated effects of the Fermi degeneracy of free nucleons prove to be insignificant, because their concentrations are low at low temperatures. In the future, we plan to investigate the effects of Coulomb interactions and neutron-rich nuclei on the thermodynamic properties of the matter.     

A numerical model for Type II supernovae — The collapse stage

We use the following numerical model for the collapse stage of a Type II supernova of 15 M_⊙. Our electron capture rate includes the effects of the inverse reaction and the neutron-proton mass difference. This decreases the electron density at the collapse stage and led to rather large values of the maximum inward velocity and of the corresponding mass (Umax = 3.06 × 10⁹cm/s, Mmax=0.76 M_⊙). These larger values are more favourable for the propagation of shock after the rebounce and the triggering-off of a Type-II supernova explosion. For neutrino transport, we use a leakage model and an equilibrium diffusion model, respectively, for the thin and thick stages and a grey atmosphere model to assess the effect of neutrino precipitation on the collapse. We found this effect to be small, the energy precipitation to be not more than 10^?5 the neutrino energy loss and the momentum precipitation not more than 10^?6 the gravitational acceleration.     

The toroidal iron atmosphere of a protoneutron star: Numerical solution

A numerical method presented by Imshennik et al. (2002) is used to solve the two-dimensional axisymmetric hydrodynamic problem on the formation of a toroidal atmosphere during the collapse of an iron stellar core and outer stellar layers. An evolutionary model from Boyes et al. (1999) with a total mass of 25M_⊙ is used as the initial data for the distribution of thermodynamic quantities in the outer shells of a high-mass star. Our computational region includes the outer part of the iron core (without its central part with a mass of 1M_⊙ that forms the embryo of a protoneutron star at the preceding stage of the collapse) and the silicon and carbon-oxygen shells with a total mass of (1.8–2.5)M_⊙. We analyze in detail the results of three calculations in which the difference mesh and the location of the inner boundary of the computational region are varied. In the initial data, we roughly specify an angular velocity distribution that is actually justified by the final result—the formation of a hydrostatic equilibrium toroidal atmosphere with reasonable total mass, M^tot=(0.117–0.122)M_⊙, and total angular momentum, J^tot=(0.445–0.472)×10⁵⁰ erg s, for the two main calculations. We compare the numerical solution with our previous analytical solution in the form of toroidal atmospheres (Imshennik and Manukovskii 2000). This comparison indicates that they are identical if we take into account the more general and complex equation of state with a nonzero temperature and self-gravitation effects in the atmosphere. Our numerical calculations, first, prove the stability of toroidal atmospheres on characteristic hydrodynamic time scales and, second, show the possibility of sporadic fragmentation of these atmospheres even after a hydrodynamic equilibrium is established. The calculations were carried out under the assumption of equatorial symmetry of the problem and up to relatively long time scales (～10 s).     

Boltzmann Equilibrium of Endothermic Heavy Nuclear Synthesis in the Universe and a Quark Relation to the Magic Numbers

As laser–plasma interactions access ever-increasing ranges of plasma temperatures and densities, it is interesting to consider whether they will some day shed light on questions concerning nuclear synthesis. One such open question is the process of endothermic nuclear synthesis for elements with A > 60, thought to have taken place at a point in time during the big bang, or currently in supernovae. We present an explanation based on a Boltzmann equilibrium condition, in combination with the change of the Fermi-statistics from the relativistic branch for hadrons from higher than nuclear densities to the lower density subrelativistic branch. The Debye length confinement of nuclei breaks down at the relativistic change, thus leading to the impossibility of nucleation of the quark-gluon state at higher than nuclear densities. Taking the increment for the proton number Z as Z′ = 10 of the measured standard abundance distribution (SAD) of the elements for a Boltzmann probability for heavy element synthesis, a sequence 3 ⁿ was found with the exponent n for the sequence of the magic numbers. The jump between the magic numbers 20 and 28 does not need then the usual spin-orbit explanation.     

Treatment of pulsating white dwarfs including general relativistic effects

In this paper, pulsating white dwarfs are treated via general relativity. Numerical integration of Einstein's equations was used to find equilibrium white dwarfs models and the fundamental periods of small oscillations about these equilibrium models. In these calculations account was taken of coulomb, Thomas-Fermi, and exchange interactions as well as ion zero point energies. It is shown that general relativity makes not just a quantitative difference in the results but a qualitative differences; pure C¹² models which are stable in Newtonian mechanics can be unstable against collapse (at a central density of 3×10¹⁰ g/cm³) when general relativity is taken into account. The collapsing model may become a neutron star or may continue towards the Schwarzschild radius.More realistic white dwarf models with carbon burning products at the center, also were studied. For these models, the density at which the star becomes unstable against collapse due to electron capture (3×10⁹ g/cm³) was found to be lower than the density at which general relativistic instability occurs.     

Plasma jet and shock formation during current loop coalescence in solar flares

We report on the results of plasma jet and shock formation during the current loop coalescence in solar flares. It is shown by a theoretical model based on the ideal MHD equation that the spiral, two-sided plasma jet can be explosively driven by the plasma rotational motion induced during the two current loop coalescence process. The maximum velocity of the jet can exceed the Alfvén velocity, depending on the plasma (= c _s ² v _A ² ) ratio. The acceleration time getting to the maximum jet velocity is quite short and le than 1 s. The rebound following the plasma collapse driven by magnetic pinch effect can strongly induce super-Alfvénic flow. We present the condition of the shock formation. We briefly discuss the high-energy particle acceleration during the plasma collapse as well as by the shocks.     

A limit for gravitational collapse

Earlier, under certain simplifying assumptions, on the basis of the General Theory of Relativity, it has been concluded by many authors that when the radius of a gravitationally collapsing spherical object of massM reaches the critical value of the Scharzschild radiusR _s=2GM/c ², then, in a co-moving frame, the object collapses catastrophically to a point. However, in drawing this conclusion due consideration has not been given to the nuclear forces between the nucleons. In particular, the very strong ‘hard-core’ repulsive interaction between the nucleons which has the range ～0.4×10^?13 cm has been totally ignored. On taking into account this ‘hard-core’ repulsive interaction, it is found that no spherical object of massM g can collapse to a volume of radius smaller thanR _min=(1.68×10^?6)M ^1/3 cm or to a density larger than ρ_max=5.0 × 10¹⁶ g cm^?3. It has also been pointed out that objects of mass smaller thanM _c～1.21×10³³ g can not cross the Schwarzschild barrier and gravitationally collapse. The only course left to the objects of mass less thanM _cis to reach the equilibrium as either a white dwarf or a neutron star.     

Calculations of the early evolution of Jupiter

The evolution of the protoplanet Jupiter is followed, using a hydrodynamic computer code with radiative energy transport. Jupiter is assumed to have formed as a subcondensation in the primitive solar nebula at a density just high enough for gravitational collapse to occur. The initial state has a density of 1.5 × 10^?11 g cm^?3 and a temperature of 43 K; the calculations are carried to an equilibrium state where the central density reaches 0.5 g cm^?3 and the central temperature reaches 2.5 × 10⁴ K. During the early part of the evolution the object contracts in quasi-hydrostatic equilibrium; later on hydrodynamic collapse occurs, induced by the dissociation of hydrogen molecules. After dissociation is complete, the planet regains hydrostatic equilibrium with a radius of a few times the present value. Further evolution beyond this point is not treated here; however the results are consistent with the existence of a high-luminosity phase shortly after the planet settles into its final quasistatic contraction.     

Stability of a class of non-static axial self-gravitating systems in f(R) gravity

In this paper, we analyze stability regions of a non-static restricted class of axially symmetric spacetime with anisotropic matter distribution. We consider f(R)=R+?R ² model and assume hydrostatic equilibrium of the axial self-gravitating system at large past time. Considering perturbation from hydrostatic phase, we develop dynamical as well as collapse equations and explore dynamical instabilities at Newtonian and post-Newtonian regimes. It is concluded with the help of stiffness parameter, Γ ₁, that radial profile of physical parameters like pressure anisotropy, energy density and higher curvature terms of the f(R) model affect the instability ranges.     

Electron capture in carbon dwarf supernovae

The rates of electron capture on heavier elements under the extreme conditions predicted for dwarf star supernovae have been computed, incorporating modifications that seem to be indicated by present experimental results. An estimate of the maximum possible value of such rates is also given. The distribution of nuclei in nuclear statistical equilibrium has been calculated for the range of expected supernovae conditions, including the effects of the temperature dependence of nuclear partition functions. These nuclide abundance distributions are then used to compute nuclear equilibrium thermodynamic properties. The effects of the electron capture on such equilibrium matter are discussed. The results of supernova numerical hydrodynamics incorporating the computed equilibrium properties and the influence of electron capture are presented. In the context of the ‘carbon detonation’ supernova model, the dwarf central density required to assure core collapse to a neutron star configuration is found to be slightly higher than that obtained by Bruenn (1972) with the electron capture rates of Hansen (1966).     

Theory of superdense matter and degenerate stellar configurations

During the last two decades the theory of degenerate stellar configurations has been developed in works by Ambartsumian and Sahakian, as well as in some other papers. This article is further progress in this direction. Systematic investigations of thermodynamic properties of the ground and metastable states of degenerate plasma have been carried out over the total range of pressures. It was found that in the range of densities 3×10¹⁰???3×10¹⁴ g cm^?3 there exists a pionization effect which plays an important role in the thermodynamics of degenerate plasma. The pion condensate present in nuclear matter promotes the existence of metastable nuclear clusters with the nuclear numberA?10⁶. The equation of state of degenerate stellar matter has been notably revised and, accordingly, the neutron star parameters have been calculated anew. The role of the pion condensate in generating strong magnetic fields observed in the pulsars is discussed.     

A two-dimensional hydrostatically equilibrium atmosphere of a neutron star with given differential rotation

An analytic solution has been found in the Roche approximation for the axially symmetric structure of a hydrostatically equilibrium atmosphere of a neutron star produced by collapse. A hydrodynamic (quasione-dimensional) model for the collapse of a rotating iron core in a massive star gives rise to a heterogeneous rotating protoneutron star with an extended atmosphere composed of matter from the outer part of the iron core with differential rotation (Imshennik and Nadyozhin, 1992). The equation of state of a completely degenerate iron gas with an arbitrary degree of relativity is taken for the atmospheric matter. We construct a family of toroidal model atmospheres with total masses M≈ 0.1?2M _⊙ and total angular momenta J≈(1?5.5)×⁴⁹ erg s, which are acceptable for the outer part of the collapsed iron core, in accordance with the hydrodynamic model, as a function of constant parameters ω₀ and r ₀ of the specified differential rotation law Ω=ω₀exp[?(rsinθ)²/r ₀ ² ] in spherical coordinates. The assumed rotation law is also qualitatively consistent with the hydrodynamic model for the collapse of an iron core.     

Spaceborne ultraviolet 251–384 nm spectroscopy of a meteor during the 1997 Leonid shower

Abstract— We used the ultraviolet to visible spectrometers onboard the midcourse space experiment to obtain the first ultraviolet spectral measurements of a bright meteor during the 1997 Leonid shower. The meteor was most likely a Leonid with a brightness of about‐2 magnitude at 100 km altitude. In the region between 251 and 310 nm, the two strongest emission lines are from neutral and ionized magnesium. Ionized Ca lines, indicative of a hot T ? 10 000 K plasma, are not detected. The Mg and Mg+ line intensity ratio alone does not yield the ionization temperature, which can be determined only by assuming the electron density. A typical air plasma temperature of T = 4400 K would imply a very high electron density: n_e = 2.2 times 10¹⁸ m‐³, but at chondritic abundances of Fe/Mg and Si/Mg ? 1. For a more reasonable local‐thermodynamic‐equilibrium (LTE) air plasma electron density, the Mg and Mg+ line ratio implies a less than chondritic Fe/Mg = 0.06 abundance ratio and a cool non‐LTE T = 2830 K ionization temperature for the ablation vapor plasma. The present observations do not permit a choice between these alternatives. The new data provide also the first spectral confirmation of the presence of molecular OH and NO emission in meteor spectra.     

“Methane on Mars: A product of H2O photolysis in the presence of CO”: Response to V.A. Krasnopolsky

The detection of CH₄ in the martian atmosphere, at a mixing ratio of about 10 ppb, prompted Krasnopolsky et al. [Krasnopolsky, V.A., Maillard, J.P., Owen, T.C., 2004. Icarus 172, 537-547] and Krasnopolsky [Krasnopolsky, V.A., 2006. Icarus 180, 359-367] to propose that the CH₄ is of biogenic origin. Bar-Nun and Dimitrov [Bar-Nun, A., Dimitrov, V., 2006. Icarus 181, 320-322] proposed that CH₄ can be formed in the martian atmosphere by photolysis of H₂O in the presence of CO. We based our arguments on a clear demonstration that CH₄ is formed in our experiments, and on thermodynamic equilibrium calculations, which show that CH₄ formation is favored even in the presence of oxygen at a mixing ratio 1.3×¹⁰⁻³, as observed on Mars. In the present comment, Krasnopolsky [Krasnopolsky, V.A., 2007. Icarus, in press (this issue)] presents his arguments against the suggestion of Bar-Nun and Dimitrov [Bar-Nun, A., Dimitrov, V., 2006. Icarus 181, 320-322], based on the effect of O₂ on CH₄ formation, the absence of kinetic pathways for CH₄ formation and on the inadequacy of thermodynamic equilibrium calculations to describe the martian atmosphere. In this rebuttal we demonstrate that experiments with molecular oxygen at a ratio of O₂/CO₂=(8.9-17)×¹⁰⁻³, exceeding the martian ratio, still form CH₄. Thermodynamic equilibrium calculations replicate the experimental CH₄ mixing ratio to within a factor of 1.9 and demonstrate that CH₄ production is favored in the martian atmosphere, which is obviously not in thermodynamic equilibrium. Consequently, we do not find the presence of methane to be a sign of biological activity on Mars.     

A study of plasmaspheric density distributions for diffusive equilibrium conditions

We have modelled the plasmaspheric density distribution for a range of solar cycle, seasonal and diurnal conditions with a magnetic flux tube dependent diffusive equilibrium model by using experimentally determined values of ionospheric parameters at 675 km as boundary conditions.Data is presented in terms of plasmaspheric H⁺ and He⁺ density contours, total flux tube content and equatorial plasma density for a range of L-values from 1.15 to 3.0. The variation of equatorial density with L-value shows good agreement with the $\text{1}\text{L}{}^4$ dependence observed experimentally.The results show that the model predicts larger solar cycle and diurnal variation in equatorial plasma density than observed using whistler techniques. However, the whistler method requires a model to deduce the equatorial density and is therefore open to interpretation.Seasonal variations are rather artifical since in this general model we have not attempted to match equatorial densities for flux tubes emanating from the winter and summer hemispheres.     

Coulomb losses and the nuclear composition of the solar flare accelerated particles

The influence of Coulomb collisions in two-component plasma on the nuclear composition and the charge-state of accelerated particles is investigated. The main characteristics are the location and value of the two loss maxima. It is shown that the maximum of energy losses on the electron component of plasma for flares is a high energy threshold which prevents the penetration of a large particle flux into the range 10 MeV nucl^–1. The low-energy range up to the maximum is considered in detail. At preliminary or initial stage of acceleration the nuclear composition of accelerated particles is strongly dependent on their energy losses on the proton component of plasma which prevails at low energies. The conditions under which the equilibrium charge is reached are investigated.     

Radiation Induced Dynamics of the Galactic Halo

We show results of numerical simulations of a three component plasma consisting of electrons, ions and dust with external gravitation and radiation fields. We perform simulation runs, starting from an analytic halo equilibrium, balancing pressure, gravitational, and radiative forces. Within these the equilibrium is perturbed by the radiation of a typical OB-star association. The perturbation has a total energy input of 10⁷ L _⊙ and a duration of 30 Myrs. After switching off the perturbation, the simulations are continued to further investigate the dynamics induced. We start with a self consistent one-fluid MHD model without background magnetic field and show for an asymmetric case that the system approaches a new equilibrium after switching on the perturbation. Later it relaxes into the starting configuration again, when the additional radiation is turned off. We then show, first by including a disk-parallel magnetic field and then by redoing the simulations with a full three-fluid code, the influence of magnetic fields and species separation on the plasma dynamics. With our computations we demonstrate that these features can be important for the explanation of the structures of galactic halos and large scale mass flows. This revised version was published online in July 2006 with corrections to the Cover Date.     

A new interpretation of the 1304 Å triplet airglow intensity ratio with the fine structure levels O3Pj) in local thermodynamic equilibrium

The intensity ratios of the 1304 Å triplet airglow of atomic oxygen observed by Fastie and Crosswhite (1964) are interpreted on the basis of the radiative transfer formulation for a model with complete frequency redistribution in a Voigt line profile. A model for the fine structure levels $\text{O(}{}^3\text{P}{}_{\mathrm{j}}\text{)}$ in local thermodynamic equilibrium is favorable to the observed intensity ratios, as far as a Voigt profile is applicable. In view of large cross sections as calculated theoretically by Allison and Burke (1969), the mutual relaxation among the ³P_j levels should occur rapidly enough to allow the population in the ³P_j levels to be in thermodynamic equilibrium with the ambient neutral gases.     

A hibonite‐corundum inclusion from Murchison: A first‐generation condensate from the solar nebula

Abstract— Through freeze‐thaw disaggregation of the Murchison (CM) carbonaceous chondrite, we have recovered a ?90 times 75 μm refractory inclusion that consists of corundum and hibonite with minor perovskite. Corundum occurs as small (?10 μm), rounded grains enclosed in hibonite laths (?10 μm wide and 30–40 μm long) throughout the inclusion. Perovskite predominantly occurs near the edge of the inclusion. The crystallization sequence inferred petrographically‐corundum followed by hibonite followed by perovskite‐is that predicted for the first phases to form by equilibrium condensation from a solar gas for P^tot ≤5 times 10^?3 atm. In addition, the texture of the inclusion, with angular voids between subhedral hibonite laths and plates, is also consistent with formation of the inclusion by condensation. Hibonite has heavy rare earth element (REE) abundances of ?40 × CI chondrites, light REE abundances ?20 × CI chondrites, and negative Eu anomalies. The chondrite‐normalized abundance patterns, especially one for a hibonite‐perovskite spot, are quite similar to the patterns of calculated solid/gas partition coefficients for hibonite and perovskite at 10^?3 atm and are not consistent with formation of the inclusion by closed‐system fractional crystallization. In contrast with the features that are consistent with a condensation origin, there are problems with any model for the formation of this inclusion that includes a molten stage, relic grains, or volatilization. If thermodynamic models of equilibrium condensation are correct, then this inclusion formed at pressures <5 times 10^?3 atm, possibly with enrichments (<1000x) in CI dust relative to gas at low pressures (below 10^?4 atm). Both hibonite and corundum have δ17O ? δ18O ? ?50%, indicating formation from an 16O‐rich source. The inclusion does not contain radiogenic ²⁶Mg and apparently did not contain live ²⁶Al when it formed. If the short‐lived radionuclides were formed in a supernova and injected into the early solar nebula, models of this process suggest that ²⁶Al‐free refractory inclusions such as this one formed within the first ?6 times 10⁵ years of nebular collapse.     

Effects of Temperature Variations with Height on the Nonequilibrium Populations of Vibrational States of Molecules in Planetary Atmospheres

The model of the standard problem of radiative transfer in a vibrational–rotational band that we suggested previously (Shved and Semenov, 2001) for a nonlocal thermodynamic equilibrium (non-LTE) in vibrational molecular states is used to study the populations of these states in a nonisothermal planetary atmosphere. The temperature profile in the atmosphere is specified as a temperature perturbation in the form of a Gaussian function that is superimposed on an isothermal atmosphere. We show that the temperature profile has a complex effect on the state populations, which makes it difficult to analytically represent this effect. We investigate the influence of the peculiar features of the temperature profile in an LTE layer on the non-LTE height and suggest a criterion for determining those features that weakly affect this height. Using the populations of the CO₂ 01¹0 and 00⁰1 states in the atmospheres of the Earth and Mars as examples, we show that the formulas suggested for estimating the non-LTE height are efficient.