Pitch angle scattering of solar particles: Comparison of ‘particle’ and ‘field’ approach

In the quasi-linear theory of pitch angle scattering the power spectrum of magnetic field fluctuations is related to the shape of the pitch angle diffusion coefficient D(), the absolute value of the mean free path , and the rigidity dependence of the mean free path (R). We discuss these relations in detail during the solar particle event of 11 April, 1978 which was observed on HELIOS-2 at a distance of 0.49 AU from the Sun. Magnetic field measurements obtained during the time of the event are used as a basis for the layer model in which the method of particle trajectories in an actually measured field is used to simulate pitch angle diffusion. The values of D() and based on the trajectory simulation for 100 MeV protons (field approach) are compared with results obtained from solar proton data (particle approach) and with predictions from quasi-linear theory based on the additional assumption of the slab model for magnetic field fluctuations (QLT approach). The time of the event is characterized by a high level of field fluctuations, the observed mean free path of about 0.03 AU for 100 MeV protons is smaller than the average value near 1 AU. Results from the field and particle approaches agree surprisingly well. The remaining difference in the mean free path of about a factor of 2 could be due to tangential discontinuities which are measured by the magnetometer, but not seen by the real particles traveling along the average field. The results from the field and QLT approaches based on the same set of magnetic field measurements differ by about a factor of 4. One of the reasons for this discrepancy is that the conditions for resonance scattering are only marginally valid. In addition, the wave vectors representing Alfvén-type fluctuations may not be totally field aligned. This deviation from the slab model would cause an increase of the theoretically predicted mean free path and lead to better agreement with the other two approaches.     

A model of interplanetary and coronal magnetic fields

A model of the large-scale magnetic field structure above the photosphere uses a Green's function solution to Maxwell's equations. Sources for the magnetic field are related to the observed photospheric field and to the field computed at a source surface about 0.6 R above the photosphere. The large-scale interplanetary magnetic field sector pattern is related to the field pattern at this source surface. The model generates magnetic field patterns on the source surface that compare well with interplanetary observations. Comparisons are shown with observations of the interplanetary magnetic field obtained by the IMP-3 satellite.     

Pulsar nebulae

Several of the exotic supernova remnants are re-interpreted as pulsar-illuminated former windzones. The class of supernova remnants thus splits into (i) (the usual) shell remnants and (ii) pulsar nebulae in which a (fairly young) pulsar blows its relativistic wind into its low-density environs.     

Cosmological models with aG variable gravitational theory

A theory of gravitation with variableG is constructed as a modification of Brans-Dicke's theory. The theory is an attempt to include the effect both of matter and radiation on the inertia of a body, according to Mach's principle. Big Bang cosmological models are computed and the corresponding primordial chemical compositions are found.     

The velocity field in the atmosphere of δ Cephei

Observations related to the photospheric velocity field of Cephei can be interpreted as follows: during the whole cycle of pulsations the only motion form in the atmosphere is a wave motion with a nearly constant full amplitude of approximately 15 km s^–1, and a wavelength of about 10⁶ km (which are quantities, about equal to the amplitudes of pulsational velocity and radius of the star). There are no significant small-scale turbulent velocity components. The microturbulent and macroturbulent velocities, as derived from spectral line observations, are fully compatible with this picture.     

Large-scale structure of the interplanetary medium

We propose that the coronal source longitude and latitude of solar wind plasma can be estimated within 10°. Previous writers have argued that the solar wind in the ecliptic should originate near the equator and that a quasi-radial hypervelocity (QRH) approximation (constant radial flow) is valid beyond the magnetohydrodynamic critical points. We demonstrate that an extension of the QRH approximation (as if the solar wind flowed radially with constant velocity from the center of the Sun) yields a proper estimate of the high coronal source location at the release zone where the solar wind makes its transition to radial interplanetary flow. This extrapolated QRH (or EQRH) approximation succeeds because the two main corrections to this source estimate, coronal corotation and interplanetary acceleration, tend to cancel (the former correcting the source location eastward, the latter westward). Although this ideal spiral approximation was first suggested by Snyder and Neugebauer (1966), only recently has it been demonstrated that it relates a wide range of interplanetary plasma, magnetic field and energetic particle data to observed coronal magnetic structure. We estimate quantitatively the error in the EQRH approximation by comparison with steady-state streamlines predicted by azimuthally independent and dependent theoretical solutions to the steady-state plasma equations. We find the error in both cases 10° in longitude and therefore suggest that the EQRH approximation offers the means to relate observed solar initial conditions in the release zone directly to interplanetary measurements. If, in addition, the EQRH approximation also leads to agreement with low coronal structure, then there should be a straightforward correspondence to otherwise unobservable high coronal structure.     

The ‘naked’ singularity in the scalar-tensor gravitation theory

The complete analysis of possible types of non-relativistic and ultra-relativistic motions in the field of the naked singularity of the STGT is given. The problem of the infall of a monochromatic radiation emitter on the naked singularity is studied. In spite of the absence of a freezing effect in the STGT, the naked singularity is not observable, for the brightness of the falling emitter decreases much faster than in the GTR. Atrr _g , the trajectory of particles and light are quite similar to that of the GTR, and due to this fact the naked singularity is observationally indistinguishable from a black hole.     

On the influence of massless scalar and vector electromagnetic fields on the singularity character in anisotropic cosmology

It is shown that, for the scalar-tensor cosmology (STC) by Jordan-Brans-Dicke (JBD), in general anisotropic solution the oscillatory mixmaster regime near the singularity will be destroyed by the scalar source-free field and replaced by monotonousV ₃-collapse into the point or into the line and plane (only in caseG0) even in the presence of the primordial source-free electromagnetic (EM) field.     

The distribution of quasar absorption line systems — Selection effects

The reported correlation between the absorption-line of emission-line redshifts of quasars is shown to be due to selection effects and thus to favour neither the intrinsic nor intervening hypotheses for the origin of quasar absorption lines.     

Families of three-dimensional axisymmetric periodic orbits in the restricted three-body problem: Sun-Jupiter case

Families of three-dimensional axisymmetric periodic orbits are determined numerically in the Sun-Jupiter case of the restricted three-body problem. These families bifurcate from the vertical-critical orbits (_v = 1,b _v = 0) of the basic plane familiesi andI. Further the predictor-corrector procedure employed to reveal these families has been described and interesting numerical results have been pointed out. Also, computer plots of the orbits of these families have been shown in conical projections.     

High-resolution photography of the solar chromosphere

High-resolution filtergrams of the quiet chromosphere, taken at seven wavelengths in H with the aid of a computer-controlled 1/8 Å filter, have been used to derive the contrast of ten bright and dark mottles as functions of wavelength. The contrast profiles of bright and dark mottles are strikingly different. They disagree with Athay's (1970) velocity model but, with an appropriate choice of parameters, can be brought into good agreement with Beckers' (1964) cloud model. Comparison between observation and theory yields values for the source function S, optical thickness t ₀, line broadening parameter ₀, and line-of-sight velocity V for both bright and dark mottles. The values of S and t ₀ obtained for dark mottles are consistent with Beckers' (1968) spicule model.     

The red shift hypothesis for quasars: Is the earth the center of the universe?

It is shown that the cosmological interpretation of the red shift in the spectra of quasars leads to yet another paradoxical result: namely, that the Earth is the center of the Universe. Consequences of this result are examined.Einstein distinguishes between two main criteria [for a good theory]: (a) theexternal confirmation of a theory, which informs us in experimental checks of the correctness of the theory, and (b) theinner perfection of a theory which judges its logical simplicity or naturalness.     

The distribution of the angular momenta of galaxies

Since the average relation between the angular momentaP and the massesM of galaxies can be represented by a power lawPM , we can define a relative angular momentum =P/M (or a constant timeP/M ). For a random motion picture within protogalaxies, should follow a Maxwellian distribution and consequently the dispersion of log should be 0.210.For the reasonable range of ( to 2), the limited sample of galaxies with known dynamical parameters gives between and 1 times the Maxwellian value. For the plausible special case =2 the reciprocal of the maximum rotational velocityv _m is already a measure of and the larger sample ofv _m-values not only yields the Maxwellian but, moreover, shows the shape of the distribution.

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PM , =constP/M . , (lg )=0.210. 7/42, . =2 v _m- .

     

A power spectrum analysis of granular intensity fluctuations and velocities

An exceptionally highly resolved spectrogram (obtained by W. Livingston at Kitt Peak) has been used to derive rms values for both the intensity fluctuations in the continuum and the granular velocities in the Baii line 5853.69 by means of the power spectrum analysis. The main results are: (1) a corrected rms value for the intensity fluctuations of 3.8%; (2) a nearly constant power level in the one-dimensional power spectrum per unit wave number within the range 0.00018–0.01 km^-1 (34000 km-600km); (3) a corrected rms value for the granular velocities of 1 km/s.The behaviour of the asymmetry of the Ban line in individual bright and dark continuous streaks can be explained by a superposition of two shifted symmetric line profiles originating from pure granular and intergranular regions, respectively. The impurity of dark and bright streaks amounts to be less than 10%, the mean relative velocity of granular and intergranular regions being again 1 km/s. We find indications the microturbulence in the intergranular regions to be larger than in the granular ones.     

Alternating cycle durations in dwarf novae

The cycle durationC in some dwarf novae underwent abrupt significant changes, as was found by using our own photometric data and the published moments of maxima. For the analysis, the DMRT method (Dumontet al., 1978) as well as least-squares (LS) routine were used. The DMRT method is more appropriate for a search for mean period, if the cycle numeration is unknown. Such changes may be possibly explained by a solar-type activity of convective secondary stars in cataclysmic binaries. However, the abrupt character of the changes ofC (i.e., the time of switchings from one cycle to another is sufficiently small as compared with the lifetime of a given cycle) is an observational puzzle which is to be interpreted theoretically.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

The stability parameters of three-body periodic orbits

Formulae containing the elements of the variational matrix are obtained which determine the linear iso-energetic stability parameters of periodic orbits of the general three-body problem. This requires the numerical integration of the variational equations but produces the stability parameters with the effective accuracy of the numerical integration. The procedure is applied for the determination of horizontally critical orbits among the members of sets of vertical-critical periodic orbits of the threebody problem. These critical-critical orbits have special importance as they delimit the regions in the space of initial conditions which correspond to possibly stable three-dimensional periodic motion of low inclination.     

The charge and energy spectra of heavy cosmic-ray nuclei

A charged particle detector array flown on a high altitude balloon has detected and measured some 3×10⁴ cosmic-ray nuclei withZ12. The charge spectrum at the top of the atmosphere for nuclei withE>650 MeV·n^–1 and the energy spectrum for 650E<1800 MeV·n^–1 are reported and compared with previously published results. The charge spectrum at the source of cosmic rays is deduced from these data and compared with a recent compilation of galactic abundances.     

Anisotropic viscous universe with variableG and Λ

An anisotropic model with variableG and and bulk viscosity is considered. The model exhibits an inflationary behavior during which the coefficient of bulk viscosity varies lineraly with the energy density. This allows the anisotropy energy to decrease exponentially with time. Other results overlap with our earlier work with a different ansatz for . The gravitational constant was found to increase during the radiation and matter epochs.     

Reddening map around α Orionis

uvby photometry has been done for early-type stars in the surroundings of the shell star Ori. The reddening maps show the presence of irregularly distributed absorbing material.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

Bifurcations in systems of three degrees of freedom

We study the bifurcations of families of double and quadruple period orbits in a simple Hamiltonian system of three degrees of freedom. The bifurcations are either simple or double, depending on whether a stability curve crosses or is tangent to the axis b=–2. We have also generation of a new family whenever a given family has a maximum or minimum or .The double period families bifurcate from simple families of periodic orbits. We construct existence diagrams to show where any given family exists in the control space (, ) and where it is stable (S), simply unstable (U), doubly unstable (DU), or complex unstable (), We construct also stability diagrams that give the stability parameters b₁ and b₂ as functions of (for constant ), or of (for constant ).The quadruple period orbits are generated either from double period orbits, or directly from simple period orbits (at double bifurcations). We derive several rules about the various types of bifurcations. The most important phenomenon is the collision of bifurcations. At any such collision of bifurcations the interconnections between the various families change and the general character of the dynamical system changes.