Asteroids,comets, meteoric matter: Proceedings of the IAU Colloquium No. 22, held at the University of Nice,France, April 4–6, 1972. Edited by C. Cristescu,W. J. Klepczynski,and B. Milet. Acad. Rep. Soc. Romania,Bucharest, 1974. 333 pp., 27 L

A model is proposed for single close encounters between two small masses, m₁and m₂, which orbit a much larger mass, M. The main new feature of the model is the assumption of conic motion of the center of mass of m₁and m₂ in the gravitational field of M. Comparisons of the model with the three-body equations of motion indicate that the model is a useful approximation for m₁, m₂ ? 10^?5M. The model is therefore applicable for encounters between bodies of the order of an earth mass or smaller in the presence of the sun. Comparisons are also made of outcomes obtained by the model with outcomes of numerical integration for a large variety of close encounters. The above comparisons reveal that for many purposes the model is an adequate approximation for those encounters with ? ≥ 4, where ? is the eccentricity of the hyperbolic orbit of m₁about m₂.     

An Accessible Model of Dynamics and Cycle for Interstellar OH and H2O Maser Associations

An accessible model for interstellar OH/H₂O maser associations is presented. It can be classified into radiative pumping model. It can close the dynamical cycle of H₂O and OH species, and can give an interpretation on interstellar OH/H₂O associations. A reasonable scheme for both regeneration and destruction of interstellar H₂O and OH molecules is argued. Our model has overcome the defects of former radiative models, and is compatible with astronomical conditions. It is shown that the rotational population of H₂O and OH in these regions is much less affected by collisions than by radiation. Some experiments have confirmed our proposal.     

On inhomogeneous scattering models of Titan's atmosphere

The spectrum of Titan from 4800 to 11 000 Å has many CH₄ absorption bands which cover a range of intensities of several orders of magnitude. Yet even the strongest of these bands in Titan's spectrum has considerable residual central intensity. Some investigators have concluded that these strong CH₄ bands must be highly saturated, but recent laboratory measurements of the bands made at room temperature show that curve-of-growth saturation is very small. At the presumed low pressures and temperatures in Titan's atmosphere, we show that saturation is very dependent on the band model parameters. However, in either a simple reflecting layer model or in a homogeneous scattering model saturation cannot be the principal cause of the filling in of these strong CH₄ bands if our best estimates of the band model parameters are correct. We find that an inhomogeneous scattering model atmosphere with fine “Axel dust” above most ot the CH₄ gas is needed to fill in the band centers. The calculated spectrum of one particular model of this class is compared to observations of Titan. Our essential conclusion is that Titan does have most of its scattering particles above most of the CH₄ gas which has an abundance of at least 2 km-am. This large abundance of CH₄ is necessary to produce the 6420-Å feature recently discovered in Titan's spectrum.     

The spectral indices of X-ray and radio producing electrons in solar flares

In the homogeneous model of solar radio burst model, the spectral index of the optically thick part of the spectrum is almost independent of the spectral index of the electron energy, while from the optically thin part, the derived electron index δ_R is far smaller than that derived from the X-ray emission, δ_X. An inhomogeneous model is proposed, in which, by adjusting two parameters within reasonable limits, we can make δ_R, derived from both the optically thick and thin parts, to equal δ_X. The model is exemplified by the 1981 April 27 0800 UT burst.     

Magnetized Stiff Fluid Tilted Universe for Perfect Fluid Distribution in General Relativity

We have investigated magnetized stiff fluid Bianchi Type I anisotropic tilted cosmological model for perfect fluid distribution in General Relativity. It has been assumed that the expansion in the model is only in two directions i.e. one of the Hubble parameter (H₁ = A₄/A); is zero. It has been shown that tilted nature of the model is preserved due to magnetic field. The various physical and geometrical aspects of the model is also discussed.     

Evaluation of the STORM-Time Ionospheric Empirical Model for the Bastille Day event

Recent theoretical model simulations of the ionospheric response to geomagnetic storms have provided the understanding for the development of an empirical storm-time ionospheric model (STORM). The empirical model is driven by the previous time-history of a _p, and is designed to scale the quiet-time F-layer critical frequency (f _o F ₂) to account for storm-time changes in the ionosphere. The model provides a useful, yet simple tool for modeling of the perturbed ionosphere. The quality of the model prediction has been evaluated by comparing with the observed ionospheric response during the Bastille Day (July 2000) storm. With a maximum negative D _st of −290 nT and an a _p of 400, this magnetic perturbation was the strongest of year 2000. For these conditions, the model output was compared with the actual ionospheric response from all available stations, providing a reasonable latitudinal and longitudinal coverage. The comparisons show that the model captures the decreases in electron density particularly well in the northern summer hemisphere. In winter, the observed ionospheric response was more variable, showing a less consistent response, imposing a more severe challenge to the empirical model. The value of the model has been quantified by comparing the root mean square error (RMSE) of the STORM predictions with the monthly mean. The results of this study illustrate that the STORM model reduces the RMSE at the peak of the disturbance from 0.36 to 0.22, a significant improvement over climatology.     

Distribution Law For Particle Fragmentation Times In A Theory For Striated Tails Of Dust Comets: Application To Comet Hale-Bopp (C/1995 O1)

Sekanina and Farrell's model for the striated dust tails of comets describes the formation of striae as a two-step fragmentation process that is characterized by an ejection time t_e of parent particles, by their radiation pressure acceleration β_p, and by their fragmentation time t_f. Of these three, t_f is the weakest parameter in that a range oft_f offers a set of nearly equivalent solutions. In this context, we comment on Nishioka et al.'s finite-lifetime model, which is a modification of the fragmentation model. We propose a truncated Gaussian function as a first-approximation distribution law for particle fragmentation times. We apply this generalized model to a stria in comet Hale-Bopp detected on March 5–15, 1997 and analyzed by Pittichová et al. in a recent paper. We find that in order to fit the stria's estimated width of ∼150 000 km, the fragmentation times cannot be distributed over a period of more than approximately 2 to 3 days. This revised version was published online in July 2006 with corrections to the Cover Date.     

Cylindrically symmetric inhomogeneous universe with electromagnetic field in string cosmology

Cylindrically symmetric inhomogeneous string cosmological model in presence of electromagnetic field is investigated. We have assumed that F ₂₃ is the only non-vanishing component of F _ij . To get the deterministic solution, it has been assumed that the expansion (θ) in the model is proportional to the eigen value σ ¹ ₁ of the shear tensor σ ⁱ _j . The physical and geometric aspects of the model are also discussed.      

Spectrophotometric scan of comet 1973 XII Kohoutek

Photoelectric spectrophotometric scans of Comet 1973 XII Kohoutek were made on November 25.85 and 28.85 UT, 1973. The vibrational temperature of C₂, the total numbers of CN and of C₂, and the production rates for CN and C₂ are derived from the observed fluxes. The temperature of C₂ was 4900 K on 25.85 November and 4300 K on 28.85 November. Mean abundance ratio of C₂ to CN was about 2.7. From the variation of production rates with heliocentric distance, it is shown that there was an outburst on 25.85 November in both CN and C₂ productions. For C₂, the production rates are derived by using two coma models, i.e. the Haser's parent-daughter model and the model relevant to a proposition of Yamamoto (1981b) that C₂ is formed via two-step photodissociation of its parent molecules. By comparing the production rate derived from the two models, it can be supported that C₂ is formed via two-step photodissociation rather than one-step photodissociation. In consequence, it is shown that the variation of the production rate with heliocentric distance is largely modified compared with that derived from the Haser's model.     

The formation of the Ca ii K line in a spinning spicule

The emission of the Ca ii K line from a spinning cylindrical spicule model is considered. In order to reproduce the observed spicule K line profiles, the model must have both radial and axial gradients in N _e and T _e. The rotating spicule model is optically thin at all heights and is hotter and more dense than a stationary model computed in a previous paper. It is proposed that the so-called Type I and Type II spicules may be structurally the same features, with different rotational velocities.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The elliptic restricted problem at the 3 : 1 resonance

Four 3 : 1 resonant families of periodic orbits of the planar elliptic restricted three-body problem, in the Sun-Jupiter-asteroid system, have been computed. These families bifurcate from known families of the circular problem, which are also presented. Two of them, I _c , II _c bifurcate from the unstable region of the family of periodic orbits of the first kind (circular orbits of the asteroid) and are unstable and the other two, I _e , II _e , from the stable resonant 3 : 1 family of periodic orbits of the second kind (elliptic orbits of the asteroid). One of them is stable and the other is unstable. All the families of periodic orbits of the circular and the elliptic problem are compared with the corresponding fixed points of the averaged model used by several authors. The coincidence is good for the fixed points of the circular averaged model and the two families of the fixed points of the elliptic model corresponding to the families I _c , II _c , but is poor for the families I _e , II _e . A simple correction term to the averaged Hamiltonian of the elliptic model is proposed in this latter case, which makes the coincidence good. This, in fact, is equivalent to the construction of a new dynamical system, very close to the original one, which is simple and whose phase space has all the basic features of the elliptic restricted three-body problem.     

Seasonal variations of photochemical tracers at low and middle latitudes on Mars: Observations and models

Mars Express observations give ozone abundances that are smaller than those from the ground-based infrared heterodyne and HST observations at low and middle latitudes. Both ground-based and Mars Express observations of the O₂ dayglow at 1.27 μm, which originates from photolysis of ozone, are in mutual agreement after correction for the local time variability. Therefore a problem appears: whether the MEX ozone data are compatible with (1) the observed O₂ dayglow intensities and (2) the photochemical model by Krasnopolsky [Krasnopolsky, V.A., 2006. Icarus 185, 153-170] within uncertainties of its reaction rate coefficients. That model involves heterogeneous loss of H₂O₂ on water ice and agrees with the observations of the O₂ dayglow, H₂O₂, and the ground-based and HST ozone. The answers are ‘yes’ to both questions. A version of the model is given that fits the MEX ozone as well as the observed O₂ dayglow and H₂O₂. Laboratory studies of two reaction rate coefficients could indicate a preferable version of the model and a preferable set of the ozone data (MEX versus the ground-based and HST). The predicted seasonal behavior of H₂O₂ is different from that in the model by Lefevre et al. [Lefevre, F., Bertaux, J.L., Clancy, R.T., Encrenaz, T., Fast, K., Forget, F., Lebonnois, S., Montmessin, F., Perrier, S., 2008. Nature 454, 971-975], and future observations may help to choose between the models.     

Bianchi type VI1 cosmological model with wet dark fluid in scale invariant theory of gravitation

In this paper, we have investigated Bianchi type VI _h , II and III cosmological model with wet dark fluid in scale invariant theory of gravity, where the matter field is in the form of perfect fluid and with a time dependent gauge function (Dirac gauge). A non-singular model for the universe filled with disorder radiation is constructed and some physical behaviors of the model are studied for the feasible VI _h (h=1) space-time.     

The STAROX stellar evolution code

This paper describes the STAROX stellar evolution code for the calculation of the evolution of a model of a spherical star. The code calculates a model at time t _k , that is the run of pressure, density, temperature, radius, energy flux and related variables on a mesh in mass M _i , given the distribution of chemical elements X _j (i) at t _k and the model at the previous time step t _k?1. It then advances the chemical composition to the next time step t _k+1 and calculates a new model at time t _k+1. This process is iterated to convergence. The model equations are solved by Newton–Raphson relaxation; the chemical equations are solved by an iterative procedure, each element being advanced in turn, and the process repeated to convergence. Convection is modelled by a mixing length model and convective mixing is treated as a diffusive process; chemical overshooting can be incorporated in parametric form. The equation of state is taken from OPAL tables and the opacity from a blend of OPAL and Alexander tables. Nuclear reaction rates are from NACRE but only cover the p–p chain and CNO cycle. The atmospheric layers are incorporated in the model by applying the surface boundary condition at small optical depth (τ≈0.001). The mesh in mass M _i is usually taken as fixed except that there is a moveable mesh point at the boundary of a convective core. Results are given for models of mass 0.9 and 5.0M _⊙ with initial composition X=0.7,Z=0.02 evolved to a state where the central hydrogen abundance is X _c =0.35, and for a model of mass 2.0M _⊙ with initial X=0.72,Z=0.02, evolved to X _c =0.01 and with core overshooting. In this latter case we compute two models one with and one without a moveable mesh point at the boundary of the convective core to illustrate the importance of having such a moveable mesh point for the determination of the Brunt–Väisälä frequency in the layers outside the core.     

Bianchi Type III magnetized massive string cosmological model for perfect fluid distribution in general relativity

Bianchi Type III massive string cosmological model for perfect fluid distribution in the presence of magnetic field, is investigated. It is assumed that the universe is filled with barotropic perfect fluid. We have attempted to investigate Bianchi Type III string cosmological model incorporating perfect fluid with magnetic field. To get the deterministic model in terms of cosmic time, we have assumed that the expansion (θ) in the model is proportional to the shear. We have also assumed that F ₁₂ is the only non-vanishing component of electromagnetic field tensor F _ij . The behaviour of the model in presence and absence of magnetic field together with singularities in these models are also discussed.     

Monte Carlo modeling of neutral gas and dust in the coma of Comet 1P/Halley

The neutral gas environment of a comet is largely influenced by dissociation of parent molecules created at the surface of the comet and collisions of all the involved species. We compare the results from a kinetic model of the neutral cometary environment with measurements from the Neutral Mass Spectrometer and the Dust Impact Detection System onboard the Giotto spacecraft taken during the fly-by at Comet 1P/Halley in 1986. We also show that our model is in good agreement with contemporaneous measurements obtained by the International Ultraviolet Explorer, sounding rocket experiments, and various ground based observations.The model solves the Boltzmann equation with a Direct Simulation Monte Carlo technique (Tenishev, V., Combi, M., Davidsson, B. [2008]. Astrophys. J. 685, 659-677) by tracking trajectories of gas molecules and dust grains under the influence of the comet’s weak gravity field with momentum exchange among particles modeled in a probabilistic manner. The cometary nucleus is considered to be the source of dust and the parent species (in our model: H₂O, CO, H₂CO, CO₂, CH₃OH, C₂H₆, C₂H₄, C₂H₂, HCN, NH₃, and CH₄) in the coma. Subsequently our model also tracks the corresponding dissociation products (H, H₂, O, OH, C, CH, CH₂, CH₃, N, NH, NH₂, C₂, C₂H, C₂H₅, CN, and HCO) from the comet’s surface all the way out to 10⁶ km.As a result we are able to further constrain cometary the gas production rates of CO (13%), CO₂ (2.5%), and H₂CO (1.5%) relative to water without invoking unknown extended sources.     

Refinement of the parameters of three selected model Galactic potentials based on the velocities of objects at distances up to 200 kpc

This paper is a continuation of our recent paper devoted to refining the parameters of threecomponent (bulge, disk, halo) axisymmetric model Galactic gravitational potentials differing by the expression for the dark matter halo using the velocities of distant objects. In all models the bulge and disk potentials are described by the Miyamoto–Nagai expressions. In our previous paper we used the Allen–Santillán (I), Wilkinson–Evans (II), and Navarro–Frenk–White (III) models to describe the halo. In this paper we use a spherical logarithmic Binney potential (model IV), a Plummer sphere (model V), and a Hernquist potential (model VI) to describe the halo. A set of present-day observational data in the range of Galactocentric distances R from 0 to 200 kpc is used to refine the parameters of the listed models, which are employed most commonly at present. The model rotation curves are fitted to the observed velocities by taking into account the constraints on the local matter density ρ_⊙= 0.1 M _⊙pc^?3 and the force K _z=1.1/2πG = 77M _⊙pc^?2 acting perpendicularly to the Galactic plane. The Galactic mass within spheres of radius 50 and 200 kpc are shown to be, respectively, M ₅₀ = (0.409 ± 0.020) × 10¹² M _⊙ and M ₂₀₀ = (1.395 ± 0.082) × 10¹² M _⊙ in model IV, M ₅₀ = (0.417 ± 0.034) × 10¹² M _⊙ and M ₂₀₀ = (0.469 ± 0.038) × 10¹² M _⊙in model V, and M ₅₀ = (0.417 ± 0.032) × 10¹² M _⊙ and M ₂₀₀ = (0.641 ± 0.049)× 10¹² M _⊙ in model VI. Model VI looks best among the three models considered here from the viewpoint of the achieved accuracy of fitting the model rotation curves to the measurements. This model is close to the Navarro–Frenk–White model III refined and considered best in our previous paper, which is shown using the integration of the orbits of two globular clusters, Lynga 7 and NGC 5053, as an example.     

Conservation of both current and helicity in a quadrupolar model for solar flares

A model for a solar flare, involving magnetic reconnection transferring flux and current between current-carrying magnetic loops connecting two pairs of footpoints, is generalized to include conservation of magnetic helicity during reconnection, as well as conservation of current at all four footpoints. For a set of force-free loops, with the ith loop having flux F _i and current I _i, the self and mutual helicities are proportional to the self and mutual inductances with the constant of proportionality determined by α_i=F _i/μ₀ I _i. In a constant-α model, the change in magnetic energy is proportional to the change in helicity, and conservation of helicity implies conservation of magnetic energy, so that a flare cannot occur. In a quadrupolar model, with α₁>α₂ initially, α₁ increases and α₂ decreases when flux and current are transferred from loops 1 and 2 to loops 3 and 4. A model that conserves both current and helicity is constructed; it depends on the initial αs, and otherwise is somewhat simpler than when helicity is neglected.     

A photochemical model of Titan's atmosphere and ionosphere

A global-mean model of coupled neutral and ion chemistry on Titan has been developed. Unlike the previous coupled models, the model involves ambipolar diffusion and escape of ions, hydrodynamic escape of light species, and calculates the H₂ and CO densities near the surface that were assigned in some previous models. We tried to reduce the numbers of species and reactions in the model and remove all species and reactions that weakly affect the observed species. Hydrocarbon chemistry is extended to C₁₂H₁₀ for neutrals and C₁₀H⁺₁₁ for ions but does not include PAHs. The model involves 415 reactions of 83 neutrals and 33 ions, effects of magnetospheric electrons, protons, and cosmic rays. UV absorption by Titan's haze was calculated using the Huygens observations and a code for the aggregate particles. Hydrocarbon, nitrile, and ion chemistries are strongly coupled on Titan, and attempt to calculate them separately (e.g., in models of ionospheric composition) may result in significant error. The model densities of various species are typically in good agreement with the observations except vertical profiles in the stratosphere that are steeper than the CIRS limb data. (A model with eddy diffusion that facilitates fitting to the CIRS limb data is considered as well.) The CO densities are supported by the O⁺ flux from Saturn's magnetosphere. The ionosphere includes a peak at 80 km formed by the cosmic rays, steplike layers at 500-700 and 700-900 km and a peak at 1060 km (SZA = 60°). Nighttime densities of major ions agree with the INMS data. Ion chemistry dominates in the production of bicyclic aromatic hydrocarbons above 600 km. The model estimates of heavy positive and negative ions are in reasonable agreement with the Cassini results. The major haze production is in the reactions C₆H + C₄H₂, C₃N + C₄H₂, and condensation of hydrocarbons below 100 km. Overall, precipitation rate of the photochemical products is equal to 4-7 kg cm⁻² Byr⁻¹ (50-90 m Byr⁻¹ while the global-mean depth of the organic sediments is ∼3 m). Escape rates of methane and hydrogen are 2.9 and 1.4 kg cm⁻² Byr⁻¹, respectively. The model does not support the low C/N ratio observed by the Huygens ACP in Titan's haze.