Vibrational transition probabilities,\bar r-centroids and PE-curves for OH and PN

Vibrational transition probabilities namely Franck-Condon factors and -centroids have been evaluated using an approximate analytical method for theA-X systems of OH and PN. KKRV potential energy curves forX ² _i ,X ¹⁺,A ²⁺, andA ¹ states of OH and PN have been constructed using the latest spectroscopic data. The value of -centroids for the band have been found to increase linearly with the corresponding wavelengths. We show results for six new bands and OH and eight new bands of PN in the spectra of astronomical objects.     

Morse pe-curves of AlH

Morse potential energy curves forC ¹⁺ andC ¹⁺ of AlH have been constructed. The energy values have been found to increase from vibrational levels 0 to 6 and decrease from vibrational levels 7 to 50 with the corresponding centre and half-width in the stateC ¹⁺. InC ¹⁺ state the energy values have been found to increase from vibrational levels 0 to 28 and decrease from vibrational levels 29 to 50 with the corresponding centre and half-width.     

Isothermal neutron star cores

By considering the relativistic expression for isothermal NS cores,T·e ^/2 = constant, we have shown that some of the standard equations of state, when applied to NS cores, correspond to constancy of some adiabatic exponents. It has been shown that the equation of state,P=KE, corresponds to ₁ = to ₂ = ₃ 1 +K and the equation of state, dP/dE=K, corresponds to ₃ 1 +K. The conditions under which different equations of state represent isothermal cores have been obtained: For isothermal NS, the local temperatureT, can be expressed in terms of pressureP, energy densityE, and rest mass density . For example: (a)P =KE :T = constant × (E/); (b)P=KE :T = constant × (P/); (c) dP/dE =K :T ^K ; (d) = ₂ :T = constant × (P/E); and (e) = ₃ :T = constant × (P/)^1/2. Equation of state corresponding to = ₂ is obtained as:P=E/ln(K/E) and the equation corresponding to = ₃ comes out as:E=P ln(K/P). Core-envelope models can be developed for these two cases. When core equation corresponding to = ₂ or = ₃ is used in the core, we can ensure the continuity of dP/dE at the core-envelope boundary, along with the continuity ofP, E, , and . The parameters of isothermal NS cores corresponding to the cases = ₂ and = ₃, have been obtained. The maximum mass of these NS cores comes out to be 2.7 .     

Effects of Hall current on hydromagnetic free-convective flow through a porous medium

An analysis of the effects of Hall current on hydromagnetic free-convective flow through a porous medium bounded by a vertical plate is theoretically investigated when a strong magnetic field is imposed in a direction which is perpendicular to the free stream and makes an angle to the vertical direction. The influence of Hall currents on the flow is studied for various values of .Nomenclature c _p specific heat at constant pressure - e electrical charge - E Eckert number - E electrical field intensity - g acceleration due to gravity - G Grashof number - H ₀ applied magnetic field - H magnetic field intensity - (j _x , j _y , j _z ) components of current densityJ - J current density - K permeability of porous medium - M magnetic parameter - m Hall parameter - n _e electron number density - P Prandtl number - q velocity vector - (T, T _w , T ) temperature - t time - (u, v, w) components of the velocity vectorq - U ₀ uniform velocity - v ₀ suction velocity - (x, y, z) Cartesian coordinates Greek Symbols angle - coefficient of volume expansion - _e cyclotron frequency - frequency - dimensionless temperature - thermal conductivity - coefficient of viscosity - magnetic permeability - kinematic viscosity - mass density of fluid - _e charge density - electrical conductivity - _e electron collision time     

A momentum distribution of high energy particles around Crab pulsar

We determine the momentum distribution of the relativistic particles near the Crab pulsar from the observed X- and -ray spectra (10³10⁹ eV), provided that the curvature radiation is responsible for it. The power law spectrum for the relativistic electrons,f() ^–5, reproduces a close fit to the observed high-energy photon spectrum. The theoretically determined upper limit to the momentum (due to radiation damping), _M 8×10⁶, corresponds to the upper cut-off energy of the -ray spectrum, 10⁹ eV. The lower limit to the momentum, _m 1.8×10⁵, is chosen such that flattening of the X-ray spectrum below 10 keV is simulated. The number density of these electrons is found to be much higher than the Goldreich-Julian density. We also discuss pulse shape and polarization of high-energy photons. The extremely high density of particles and the steep momentum spectrum are difficult to understand. This may imply that another, more efficient, mechanism is in operation.     

A coronal loop model for the production of X-ray and radio flares in the RS CVn binary HR 1099

The RS CVn binary stellar system HR 1099 is a source of both X-ray and radio flares. We present here a model of the system in which the two types of flare are produced by the same population of mildly-relativistic ( 10) electrons, injected into a coronal loop. After reviewing possible radiation mechanisms we conclude that, given the probable conditions in the flaring region, the radio emission is gyrosynchrotron radiation and the X-ray emission is thermal bremsstrahlung. The thermal X-ray source must lie in the stellar chromosphere, but the apparent absence of plasma absorption at radio frequencies indicates that the radio source is located high in the coronal loop. Using the relationships given by Dulk and Marsh (1982) for the radio emission from a power-law electron energy spectrum,N() ( - 1)^–, we conclude that 3 7, with 30% of the electron population trapped in the radio source. Some implications of these results for one particular version of the model are discussed.     

General integral transform of the exponential integrals

General integral transform of the exponential integralsE _n is considered and will be denoted asB _(k) ⁿ (). Different expressions and the equations satisfied byB _(k) ⁿ are developed. Two-term recurrence formula forB _(k) ⁿ (0) and three-term recurrence formula forB _(k) ⁿ (); 0 will be established for a givenk1 andn=2,3, ...,N. The computational algorithms based on these formulae are also constructed for the casesk=1,2,3, andn2. Finally the numerical results fork=2,3 andn=2(1)25 are presented to 15-digit accuracy     

Study of alpha component dynamics in the solar wind using the Prognoz satellite

The analysis of solar wind He⁺⁺ and H⁺ ion distribution functions, collected over five months by the satellite Prognoz 1, shows that these are in general maxwellian but that often tails appear at higher speeds. The existing relation V-T, the observation of ratios of T/Tp 3.83 and V/Vp 1.035 give evidence of preferential He⁺⁺ ion heating and acceleration. The criteria for heating by dissipation of hydromagnetic waves proposed by Barnes and Hung (1973) are tested experimentally. Finally, multifluid models are likely to predict certain observations such as dependence of the velocity ratio V/Vp on the solar wind flux.     

Theory of the Trojan asteroids,IV

In a previous publication (1977) the author has constructed a family () of long-periodic orbits in the Trojan case of the restricted problems of three bodies. Here he constructs the domain of the analytical solution of the problem of the motion, excluding the vicinity of thecritical divisor which vanishes at the exact commensurability of the natural frequencies ₁ and ₂. In terms of thecritical masses m_j(₂), or the associatedcritical energies _j ² (m), is the intersection of the intervals ofshallow resonance, of the form. Inasmuch as the intervals |₂– _j ² |<_j ofdeep resonance aredisjoint, it follows that (1) the disjointed family () embraces the tadpole branch, 0²1, lying in: and (2) despite the clustering of _j ² (m) atj=, the family () includes, for ²=1, an asymptoticseparatrix that terminates the branch in the vicinity of the Lagrangian pointL ₃.In a similar manner, the family () can be extended to the horseshoe branch 1<_{2 2} ² .     

Radio source orientation and the cosmological interpretation of the angular size-redshift relation for double-lobed quasars

The angular size-redshift test for quasars was compared with various cosmological models including non standard models. The possible effects of radio source orientation and relativistic beaming were taken into account in the analysis.It was found that orientation effects alone were not sufficient to explain the observed-z relation in terms of Friedmann models. In addition, linear size evolution of the formD ~ (1 +z)^–n , with 0.75 n 1.2 would be required for 0 1.0, or possibly an inverse correlation between luminosity and linear size. The non-standard cosmological models all gave better fits to the deprojected data than the Friedmann models in the absence of evolutionary effects, with the tired light effect providing the best fit.     

Some applications of Jacobi dynamics to the stellar evolution

The stars in the Main Sequence are seen as a hierarchy of objects with different massesM and effective dynamical radiiR _eff=R/ given by the stellar radii and the coefficients for the inner structure of the stars.As seen in a previous work (Paper I), during the lifetime in the Main SequenceR _eff(t) remains a near invariant when compared to the variation in the time ofR(t) and (t).With such an effectiveR _eff one obtains the amounts of actionA _c(M), the effective densities _eff(M)=(M)³(M), the densities of action and of energy (or mean presures in the stellar interior)a _c(M),e _c(M), and the potential energiesE _p(M).The amounts of action areA _cM ^k withk1.87 for the M stars,k5/3 for the KGF stars, andk1.83 for the A and earlier stars, representing very simples conditions for the other dynamical parameters. For instancek5/3 means a near invariant effective density _eff for the KGF stars, while for such stars the mean densities and coefficients present the strongest variations with masses (M)M ^–1.81, (M)M^0.6.The cases for the M stars (e _c(M)M ^–1) and for the A and earlier stars (betweena _c(M)=constant and _eff(M)M ^–1) and also discussed. These conditions for the earlier stars also represent reasonable mean values for the whole stellar hierarchy in the range of masses 0.2M M25M .With all this, one can build dynamical HR diagrams withA _c(M), E_p(M), _eff M ^–p , etc., whose characteristics are analogous to these in the photometrical HR diagram. A comparison is made betweenA _c(M) from the models here and the HR diagram with the best known stars of luminosity classes IV, V, and white dwarfs.The comparison of the potential energiesE _p(M)M ^–p according to the stellar models used here and the observed frequency function (MM _–q (number of stars in a given interval of masses) from different authors suggests the possibility that the productE _p(M)(M) is a constant, but this must be confirmed with further studies of the function (M) and its fine structure.There are analogies between the formulation used here for the stellar hierarchy and other physical processes, for instance, in modified forms of the Kolmogorov law of turbulence and in the formulation used for the hierarchy of molecular clouds in gravitational equilibrium. Besides, the function of actionA _c(M) for the stars has analogous properties to the relations of angular momenta and massesJ(M) for different types of objects. The cosmological implications of all this are discussed.     

Noise-Storm Continua: Power Estimates for Electron Acceleration

We use a generic stochastic acceleration formalism to examine the power L_in (erg s^-1) input to non-thermal electrons that cause noise-storm continuum emission. The analytical approach includes the derivation of the Greens function for a general second-order Fermi process, and its application to obtain the particular solution for the non-thermal electron distribution resulting from the acceleration of a Maxwellian source in the corona. We compare L_in with the power L_out observed in noise-storm radiation. Using typical values for the various parameters, we find that L_in 10²³–10²⁶ erg s^-1, yielding an efficiency estimate L_out/L_in in the range 10^-10 10^-6 for this non-thermal acceleration/radiation process. These results reflect the efficiency of the overall process, starting from electron acceleration and culminating in the observed noise-storm emission.     

Simultaneous measurements of Ca+ K,Ca+ H,Hα, Hβ, and He D3 emission in prominences

Simultaneously measured line intensities of Ca⁺ K and H, H, H and He D₃ are presented and compared with recent model calculations by Heasley and Milkey (1978). The model calculations are compatible with the observations. There is indication that the observed branching of the relation E(Ca⁺ K and H) E(H) depends on the widths of the Ca⁺-lines.     

B,V surface photometry of the UV continuum galaxy NGC 838

Surface photometry of the UV continuum galaxy NGC 838 has been carried out in theB, V system using photographic plates obtained with the 74 Kottamia telescope, Egypt. Isophotes, luminosity profiles, integrated photographic magnitudes, effective diameters and other photometric parameters are derived.The photoelectrically calibrated total apparent magnitudes areB _T =13.57 with maximum diameters 1.57×1.34 (at threshold _m =27.7 mag.//) andV _T =12.91 with maximum diameters 1.54×1.32 (at threshold _m =27.7 mag./). The integrated colour index(B–V) _T =0.66 and the effective surface brightness _e (B=19.0 mag./) and _e (V=19.7 mag./. The major axis is at position angle =85°±1°.The nucleus of NGC 838 is quite blue (integrated colour(B–V)=0.41 forr ^*<0.1) compared to normal galaxies while the colour becomes redder from the nucleus outwards. The UV excess, H emission and radio continuum emission previously observed from this galaxy by other investigators may be attributed to a recent burst of star formation in the nucleus of the galaxy of duration slightly greater than 2×10⁷ yr.     

Is the ‘superhot’ hard x-ray component in solar flares consistent with a thermal source?

It has been shown by Brown and Emslie (1988) that any optically thin thermal bremsstrahlung source must emit an energy spectrumL () (keV s^–1 keV^–1) which has the property that higher derivatives alternate in sign, i.e., (–) ^j L(^j)() > 0 for allj. In this short note, we apply this test to the superhot component discussed by Linet al. (1981) in order to determine whether a strictly thermal interpretation of this component is valid. We find that all statistically significant higher derivatives do indeed have the correct sign; this strengthens the identification of this component as due to a thermal source.Presidential Young Investigator.     

The significance of spatial curvature for energy output of remote quasars

There is a brightening effect of quasar outputs due to the positive curvature of space in the static Universe, if we use the right expression of distance as an arc³r=R , and not the corrected luminosity distance ofr=Rsin.     

Early Universe in Self-Creation Cosmology

Spatially homogeneous and isotropic Robertson-Walker model of the universe is studied in Barber's second self-creation theory of gravitation in the presence of perfect fluid by using gamma-law equation of state p =(-1). The parameter gamma varies continuously with cosmological time. Exact solutions of the field equations are obtained for inflationary period and radiation-dominated era by using the power law relation R^n-3 = B. Some physical properties of the models are also discussed.     

The proton-proton reaction and related reactions in an intense magnetic field

The reaction rates for the proton-proton reaction and the related electron capture reaction in a strongly magnetized relativistic electron gas of arbitrary degree of degeneracy are computed. The proton-proton reaction rates are unaffected by the presence of the magnetic field for field strengths up to the critical valueH _q =m ² c ³/e=4.414×10¹³G. For fields greater thanH _q , the proton-proton reaction rates are enhanced linearly with (=H/H _q ).The PeP reaction is investigated in detail for a wide range of temperatures, densities and magnetic field strengths that are of interest. The main results are as follows: In the non-degenerate regime the reaction rates are significantly reduced for high temperatures (T ₉5) and low fields (1). For instance, _pep(H)=0.04 _pep(O) at =10^–3,T ₉=10. For relatively high fields (>1) and low temperatures (T ₉2), the reaction rates are enhanced approximately linearly with . In the complete degenerate regime the reaction rates are reduced up to one-third of the field-free value for moderate densities (₆/_e10). At high densities (₆/_e10) the reaction rates are unaffected by the magnetic field.     

Effects of metal abundances on the evolutionary period changes of classical Cepheids

Some peculiarities in the behaviour of a model self-gravitating system described by hydrodynamical equations and isothermal equation of state connected with the presence of thermodynamical fluctuations in real systems were investigated in numerical experiment. The values of density and velocity , , respectively, were computed by numerical code perturbed on each time-step and in each computational cell by random values , for modeling such fluctuations. Perturbed values _i = _i + _i ,v _i = _i + v _i were used to initiate the next step of computations. This procedure is equivalent to an introduction into original hydrodynamical equations of Langevin sources which are random functions. It is shown that these small fluctuations (= v =0,² =v ² = 10^–8) grow many times in marginally-stable state.     

An integrable case of a rotational motion analogous to that of Lagrange and Poisson for a gyrostat in a Newtonian force field

The scope of the present paper is to provide analytic solutions to the problem of the attitude evolution of a symmetric gyrostat about a fixed point in a central Newtonian force field when the potential function isV ⁽²⁾.We assume that the center of mass and the gyrostatic moment are on the axis of symmetry and that the initial conditions are the following: (t ₀)=₀, (t ₀)=₀, (t ₀)=(t ₀)=₀, ₁(t ₀)=0, ₂(t ₀)=0 and ₃(t ₀)= ₃ ⁰ .The problem is integrated when the third component of the total angular momentum is different from zero (B ₁ 0). There now appear equilibrium solutions that did not exist in the caseB ₁=0, which can be determined in function of the value ofl ₃ ^r (the third component of the gyrostatic momentum).The possible types of solutions (elliptic, trigonometric, stationary) depend upon the nature of the roots of the functiong(u). The solutions for Euler angles are given in terms of functions of the timet. If we cancel the third component of the gyrostatic momentum (l ₃ ^r =0), the obtained solutions are valid for rigid bodies.