Zatrikean pre-geometry as a tool for modelling in theoretical astrophysics

In this paper, we present an axiomatic foundation on zatrikean (i.e., chess-like) pre-geometry. Furthermore, we find that rotation can induce such a pre-geometry; and this rotationally induced zatrikean pre-geometry can, in turn, decisively affect all the interrelated physical phenomena, which in their majority are significant for theoretical astrophysics and cosmology.     

Trapping of test particles in static and spherical space-time geometries

Estimates of the pulsation massesM _Q and of massesM _g=gR²/G (g is the surface gravity;R, the mean stellar radius; andG, the gravitational constant) of 89 Delta Scuti-variables have been obtained. An intercomparison of three kinds of masses —M _e, M_g, andM _Q — is performed; the evolutionary massesM _e of the same variables were estimated in a previous paper (Tsvetkov, 1986). It is pointed out that within the limits of the accuracy of determination, the three kinds of masses agree for the majority of the stars under study. For several varaibles, however, there is a considerable discrepancy between the estimates of the pulsation massesM _Q and the estimates of the massesM _e andM _g. Arguments are represented, which may alleviate or even remove this mass discrepancy for some of these stars. It is shown that the results from the comparison between the three kinds of masses of the considered Delta Scuti-stars are not very sensitive to the choice of the system of evolutionary tracks and the adopted chemical composition as well as to the evolutionary phases of the variables (core or shell hydrogen burning). The variations of the chemical composition in most of the stars under study are probably not very large.     

Zatrikean pregeometry: simple cosmological scenarios

In this paper basic cosmological consequences of zatrikean pregeometry are studied. It is shown that many universal quantities can be calculated with simple applications of this theory. An equation directly linking the angular velocity of the universe, the Hubble constantH and the mean density of the universe is derived. The relation between the massM and the radiusR of the universe is examined. This relation leads to various cosmological scenarios, including variations in physical constants and/or violation of the mass conservation and/or variable geometrical properties.     

Accurate masses and radii of normal stars

Summary Binary stars are the main source of fundamental data on stellar masses and radii (M, R). Considerable progress has been made in recent years in the quality and quantity of such data, and stellar masses and radii of high accuracy have led to a number of qualitatively new and interesting results on the properties and evolution of normal stars. This paper reviews the current status of fundamentalM andR determinations which (i) have errors 2%, the limit for non-trivial results in many applications, and (ii) can be presumed valid for single stars. These two conditions limit the discussion to data fromdetached, doublelined eclipsing binary systems.After a brief discussion (Sect. 2) of the main tests for accuracy and consistency which must be met for observational data to be included in the sample, data for 45 binary systems (90 single stars) are presented in Sect. 3 (Table 1 and Figs. 2–5). Spectral types are O8-M1 on the main sequence, with only two stars clearly in the red-giant region. From the review by Popper (1980), data for only 6 systems survive unchanged in the present list, while improved data are given for 18 systems; 21 systems are new additions. Broadband colours, effective temperatures, and luminosities are also given, but are scale-dependent and considerably less reliably determined thanM andR.The observed ranges inM andR for a given colour far exceed the observational errors, primarily due to evolutionary effects within the main sequence. For this reason, single-parameter relations used to predictM andR for single stars are limited to an accuracy of some ±15% inM and ±50% inR, basically independent of the number and accuracy of the data used to establish the relations. Two-parameter calibrations are discussed (Sect. 4) which can eventually reduce these errors to & 5% in bothM andR. At this level, abundance effects become significant and presumably account for the residual scatter.Comparison of the data with stellar evolution models is the topic of Sect. 5. Characteristic features of the data which are crucial in such work are emphasized, rather than attempts to prove the validity of any particular set of models. Already fromM andR alone, some significant constraints can be derived (Fig. 4). When bothM, R, andT _e are known, the initial helium abundanceY can be estimated if the metal-abundance parameter Z is assumed or determined. Studies in which binaries with accurate values ofM, R, and Z are fit by models calculated for the precise observed masses, and withY and mixing length constrained to solar values, provide the most stringent tests of the models. Probing further model refinements such as convective overshooting requires full use of the potential of the data. For example, models may yield general main-sequence limits which are consistent with the observations, but still be unable to fit any single system to the precision of the data. Conditions for critical, informative tests are discussed. Tidal effects in binaries are briefly discussed in Sect. 6. As tidal forces are extremely sensitive to the dimensions and internal structure of the stars, the present sample is well suited for such studies. Recent success in matching computed and observed apsidal-motion parameters for early-type binaries is mentioned. Finally, main priorities for future work are outlined.     

The angle-dependent redistribution functionsR III andR IV: Line absorption probability distribution functions and reemission coefficients

The line absorption probability distribution functions and the reemission coefficients are derived for the non-coherent scattering functionsR _III andR _IV. The appropriate line profile function forR _III is shown to be a simple Voigt function, while forR _IV, the line absorption probability distribution function is more complex involving a linear combination of two Voigt functions and another more complex probability distribution. The structure of the reemission coefficients forR _III andR _IV is then discussed.     

An electron temperature distribution derived from optical and radio measurements of HII regions

Radio measurements of the electron temperature ofHii regions are obtained from the ratio of the brightness temperature of a hydrogen recombination line to that of the adjacent continuum, while optical measurements are obtained from the ratio of [Oiii] forbidden-line intensities. The radio and optical measurements made under the assumption of an isothermalHii region,T _R andT _opt respectively, are combined to derive a temperature distribution for an entire nebula. A sphericalHii region in local thermodynamic equilibrium with constant density which is optically thin in both the line and the continuum is used as a model. Assuming linear temperature gradients withT _R=6000K andT _opt=10000K, it is found thatT=12000K (1–0.74r/R), wherer is the distance from the center andR is the radius of the nebula.     

Photometric calibration of the CCD camera of 1-m telescope at VBO

Calibration of the CCD camera of the 1m telescope at the Vainu Bappu Observatory, Kavalur, to theB V R system is reported here based on the observations of stars in the ‘dipper asterism’ in the open cluster M 67 (NGC 2682). Transformations involvingB andV have negligible colour terms, while those involvingR are slightly colour dependent. The possibility of using scaled-downR band fluxes to estimate the continuum flux at Hα is investigated by comparing the counts inR band with those through an interference filter centred at Hα. The scaling factor is found to remain constant over a wide range of colours. The sensitivity of the telescope-filter-CCD combination is estimated to be 2.0 per cent, 8.3 per cent and 9.7 per cent inB, V andR bands, respectively. The star F117 appears to be a small-amplitude (∼ 0.05 mag) variable.     

Hall effects on thermal hydromagnetic instability of a partially ionized medium

Thermal instability of a finitely conducting hydromagnetic composite medium is considered including the effects of Hall currents and the collisions with neutrals. The equilibrium magnetic field is assumed to be uniform and vertical. For stationary convection, the collissions have no effect, while the Hall currents are found to have a destabilizing effect on the thermal instability. It is further shown that whenM is finite andQ the asymptotic behaviours of the critical Rayleigh number, the critical wave number and the critical temperature gradient remain the same as those obtained by Chandrasekhar whereM is a nondimensional number which includes the Hall current effects andQ stands for the Chandrasekhar number.     

Ages and masses of delta scuti stars in the praesepe cluster

Physical parameters and radial pulsation modes are determined for three Delta Scuti stars in the Praesepe cluster: HD 73345, HD 73712, and HD 73746. Their agest and evolutionary massesM _eare interpolated in the track systems of Iben (1967) and Paczyski (1970). By combining these age estimates with our previous results for nine other Delta Scuti-stars in the Praesepe cluster (Tsvetkov, 1989), the following weighted mean age estimates of this cluster are obtained: (14.2 ± 1.3) × 10⁸ yr (Iben) and (5.4 ± 0.4) × 10⁸ yr (Paczyski). Age and evolutionary mass estimates of the twelve cluster variables are also obtained in the modern track system of Maeder and Meynet (1988), in which the weighted mean cluster age is (15.3 ± 1.0) × 10⁸ yr.Pulsation massesM _Qcalculated from the fitting formulae of Faulkner (1977) and Fitch (1981) as well as massesM _g=gR ² / G were evaluated for the twelve cluster variables by Tsvetkov (1990) or in the present paper. In most cases there is a satisfactory agreement between our estimates of massesM _e,M _g, andM _Q.Due to a large disagreement between the long period and low luminosity of the star HD 73746, its radial pulsation mode and pulsation massM _Qcannot be evaluated.     

Masses and ages of delta scuti stars in eclipsing binary systems

By using data mainly from Frolovet al. (1982) for four Delta Scuti stars in eclipsing binary systems, AB Cas, Y Cam, RS Cha, and AI Hya, their physical parameters, distances, and radial pulsation modes are determined. The evolutionary track systems of Iben (1967), Paczyski (1970), and Maeder and Meynet (1988) are interpolated, in order to estimate evolutionary massesM _eand agest of these variables. Their pulsation massesM _Qare estimated from the fitting formulae of Faulkner (1977) and Fitch (1981). Our estimates of evolutionary massesM _eand pulsation massesM _Qare close to the massesM determined by Frolovet al. (1982) from the star binarity. The only exception is AB Cas, for which there is no agreement between certain star parameters.Another, independent approach is also applied to the stars RS Cha and AI Hya: by using their photometric indicesb — y andc ₁ from the catalogue of López de Cocaet al. (1990) and appropriate photometric calibrations, other sets of physical parameters, distances, modes, ages, evolutionary and pulsation masses of both variables are obtained.     

The transfer of polarized radiation in spectral lines: Solar-type stellar atmospheres

The polarization structure in several spectral lines in solar type stars is computed using the method described by McKenna (1981, 1984a). The frequency redistribution function used for these calculations is a linear combination ofR _II andR _III. The line profiles and polarization structures have been computed for several weak solar resonance lines includingKi 7664 Å, Sri 4607 Å, Baii 4554 Å, for various polar angles along the stellar disk. Both the line profiles and polarization structures as well as the center to limb behavior of the line center polarization agree well with observations.The somewhat stronger resonance line Cai 4227 Å shows a different polarization structure when compared to the weaker solar resonance lines. It is found that for strong resonance lines the proper redistribution function to be used is a linear combination ofR _III andR _v (see McKenna, 1981, 1984b; Heinzel, 1981). The major reason for this is that for strong resonance lines both the upper and lower levels are broadened by collisions. This violates the assumptions upon which the redistribution functionsR _II andR _III are based.     

Effects of partial frequency redistribution functions RII,RIII and RV on source functions

The effects of partial frequency redistribution on the formation of spectral lines have been studied. We considered the angle-averaged R_II, R_III andR _v types of redistribution with isotropic phase function, Transfer equation with plane-parallel geometry is solved in isothermal atmospheres. For an atmosphere with constant thermal sources, the frequency-dependent source function S_L (R _v) lies below S_L (R_III) but above S_L(R _III) in the line wings.     

Plasmon neutrinos emission in a strong magnetic field

The decay of a longitudinal plasmon into two neutrinos is studied in the presence of a strong magnetic field. Contrary to the transverse case, for longitudinal plasmons the existence of a new mode, entirely dependent on the magnetic field, greatly enhances the energy loss at high densities. Denoting byQ _HandQ ₀the neutrino energy losses with and without magnetic field respectively, the situation is as follows: atH10¹¹ G andT10⁹K,Q ₀10⁵ Q _Hfor <10¹¹g cm^–3, WhileQ _H10¹⁰ Q ₀for >10¹¹g cm^–3. A second physically interesting feature is the anisotropic character of the energy loss which is highly peaked along the field lines, giving rise to a shorter cooling time in that direction than in any other.     

Determination and analysis of local seasonal terms of latitude variations

Local seasonal terms of latitude variations were determined on the basis of data of 17 BIH/IPMS stations andx, y, z data of the BIH global solution during the years 1967–1978. Some models for local correctionsR to the latitude introduced by the BIH are created. The correctionsR obtained from the least squares adjustment from one year data appear to be the best. The present study shows that it is necessary to determine these more frequently than once a year or to compute them for all stations simultaneously with the ERP. This will be particularly important in view of the future re-reduction of past astrometric data.     

Ar XIII line ratios in solar flares

Theoretical ArXIII electron-density-sensitive emission line ratios, derived using electron impact excitation rates interpolated from accurateR-matrix calculations, are presented forR ₁ =I(242.22 )/I(236.27 ),R ₂ =I(210.46 )/I(236.27 ), andR ₃ =I(248.68 )/I(236.27 ). Electron densities deduced from the observed values ofR ₁,R ₂, andR ₃ for solar flares obtained with the NRL S082A slitless spectrograph on boardSkylab are in excellent agreement, and furthermore compare favorably with those determined from line ratios in CaXV, which is formed at a similar electron temperature to that of ArXIII. These results provide experimental support for the accuracy of the atomic data adopted in the analysis, as well as for the techniques used to calculate the line ratios.     

Neutron star sequences and the starquake glitch model for the Crab and the Vela pulsars

We construct for the first time, the sequences of stable neutron star (NS) models capable of explaining simultaneously, the glitch healing parameters, Q, of both the pulsars, the Crab (Q≥0.7) and the Vela (Q≤0.2), on the basis of starquake mechanism of glitch generation, whereas the conventional NS models cannot give such consistent explanation. Furthermore, our models also yield an upper bound on NS masses similar to those obtained in the literature for a variety of modern equations of state (EOSs) compatible with causality and dynamical stability. If the lower limit of the observational constraint of (i) Q≥0.7 for the Crab pulsar and (ii) the recent value of the moment of inertia for the Crab pulsar (evaluated on the basis of time-dependent acceleration model of the Crab Nebula), I _Crab,45≥1.93 (where I ₄₅=I/10⁴⁵ g cm²), both are imposed together on our models, the models yield the value of matching density, E _b =9.584×10¹⁴ g cm⁻³ at the core-envelope boundary. This value of matching density yields a model-independent upper bound on neutron star masses, M _max≤2.22M _⊙, and the strong lower bounds on surface redshift z _R ≃0.6232 and mass M≃2.11M _⊙ for the Crab (Q≃0.7) and the strong upper bound on surface redshift z _R ≃0.2016, mass M≃0.982M _⊙ and the moment of inertia I _Vela,45≃0.587 for the Vela (Q≃0.2) pulsar. However, for the observational constraint of the ‘central’ weighted mean value Q≈0.72, and I _Crab,45>1.93, for the Crab pulsar, the minimum surface redshift and mass of the Crab pulsar are slightly increased to the values z _R ≃0.655 and M≃2.149M _⊙ respectively, whereas corresponding to the ‘central’ weighted mean value Q≈0.12 for the Vela pulsar, the maximum surface redshift, mass and the moment of inertia for the Vela pulsar are slightly decreased to the values z _R ≃0.1645, M≃0.828M _⊙ and I _Vela,45≃0.459 respectively. These results set an upper and lower bound on the energy of a gravitationally redshifted electron-positron annihilation line in the range of about 0.309–0.315 MeV from the Crab and in the range of about 0.425–0.439 MeV from the Vela pulsar.     

Patchy structure and selective extinction

Based on diurnal values of the total radio-flux density at 10.7 cm as well as on corresponding Zürich numbers the relation giving the radio-flux as function ofR is established. The behaviour of low and high values ofR andF ₂₈₀₀ during the time interval 1957–1976 is studied. Preliminary conclusions drawn by other investigators are confirmed. A prediction of the total radio-flux for the 22nd solar cycle is given.     

VR c photometry of dwarf cepheids (II)

In this paper, we derived the empirical relationship between stellar surface brightness parameter (F _v) and (V —R _c) colour in Cousins system appropriate to dwarf cepheids. Also theoretical counterpart to this relation has been calculated from model atmospheres. The theoretical relation is in reasonable agreement with the empirical relation but reveals small sensitivities to surface gravity and metallicity. Both relations were used to apply the surface brightness method to estimate the radius of four dwarf cepheids of YZ Boo, AD CMi, XX Cyg, and EH Lib which were observed withV andR band in Cousins photometric system by Kim and Joner (1994). We could obtain the reliable result for AD CMi and it was found that, for three other variables, there are large phase shifts between angular diameter variation and radial displacements.     

Isotropization in bianchi type-I vacuum cosmology

We have found the most general solution for the Bianchi type-I equations in the Brans-Dicke theory (BDT) for the vacuum case. It is shown that forw > 500 the Universe will become isotropic for any amount of initial anisotropy, secondly it is shown that in the extended inflation scenario, the BDT-scalar field can avoid the inflation in one direction,R ₃. In the other scale factorsR ₁ andR ₂ there is inflationary expansion.     

Gas and dust release from comet West (1976VI) nuclear fragments

Emission fluxes of CN, G₂ and C₃ carbon-bearing molecular species observed in the spectra of the nuclear fragment A and D of comet West (1976VI) are analysed in the framework of Haser's two-component model with radial outflow symmetry. Gas production rates have been derived and their ratios obtained. We find these vary as Q r ⁿ (where 1.0r2.6 is the heliocentric distance in AU) with photometric parametern = -4.11 (CN), -2.68 (C₂), -1.89 (C₃) andQ _x /Q _y r ⁿ withn = 2.22 (C₃/CN), 1.42 (C₂/CN), -0.79 (C₂/C₃). The gas-to-dust ratio, dust production rates in arbitrary units, total number of dust particles in the field of view and an effective radius R_eff 2.0 km for the principal nuclear fragmentA is also estimated.