Steady wave model of spiral galaxies and its application in cosmogony

The model is based on the assumption that logarithmic spiral arms of most spiral galaxies are due to the totating density wave obeying the steady wave equation . It is shown that this equation accounts also for the so-called Titius-Bode's law in the solar system.     

Identification of Emissions in the Spectrum of Comet C/1989 VI (Skoritchenko–George) Obtained with the 6-m SAO RAS Reflector

The emission spectrum of comet Skoritchenko–George (C/1989 VI), unusual in its information content, was obtained on February 26.7 UT, 1990, with the use of a TV scanner installed on the 6-m BTA reflector of the Special Astronomical Observatory of the Russian Academy of Sciences (SAO RAS) in Nizhni Arkhyz. Detailed identification of the emission lines of this comet was made. The observed spectrum contains 311 emission lines, including those of the molecules. Among others, the lines of the negative carbon C ₂ ^- ion and the lines corresponding to the electron transition in the neutral CO molecule are discovered. The presence of a large number of lines of the neutral CO molecule (the Asundi bands and the triplet bands) in the visible region is one of the uncommon features of the emission spectrum of this comet. The triplet lines : 15–3, 13–2, 11–2, 9–1, 8–1, 7–1, 7–0, 5–0, 4–0; : 7–0, 6–0, 5–0; and a" : 11–1 (K = 3, 4); 16–4 (K= 0, 1, 2, 4); 9-0 (K= 0, 1, 2); 8–0 (K= 0) were identified for the first time. Prior to this work, the lines of CO in the visible range were observed only in the spectrum of comet C/1979 VI (Bradfield) in 1989.     

On the influence of gradients in the angular velocity on the solar meridional motions

If fluctuations in the density are neglected, the large-scale, axisymmetric azimuthal momentum equation for the solar convection zone (SCZ) contains only the velocity correlations and where u are the turbulent convective velocities and the brackets denote a large-scale average. The angular velocity, , and meridional motions are expanded in Legendre polynomials and in these expansions only the two leading terms are retained (for example, where is the polar angle). Per hemisphere, the meridional circulation is, in consequence, the superposition of two flows, characterized by one, and two cells in latitude respectively. Two equations can be derived from the azimuthal momentum equation. The first one expresses the conservation of angular momentum and essentially determines the stream function of the one-cell flow in terms of : the convective motions feed angular momentum to the inner regions of the SCZ and in the steady state a meridional flow must be present to remove this angular momentum. The second equation contains also the integral indicative of a transport of angular momentum towards the equator.With the help of a formalism developed earlier we evaluate, for solid body rotation, the velocity correlations and for several values of an arbitrary parameter, D, left unspecified by the theory. The most striking result of these calculations is the increase of with D. Next we calculate the turbulent viscosity coefficients defined by whereC _ro ⁰ and C _o ⁰ are the velocity correlations for solid body rotation. In these calculations it was assumed that ₂ was a linear function of r. The arbitrary parameter D was chosen so that the meridional flow vanishes at the surface for the rotation laws specified below. The coefficients v _ro ⁱ and v _0o ⁱ that allow for the calculation of C _ro and C _0o for any specified rotation law (with the proviso that ₂ be linear) are the turbulent viscosity coefficients. These coefficients comply well with intuitive expectations: v _ro ¹ and –v _0o ³ are the largest in each group, and v _0o ³ is negative.The equations for the meridional flow were first solved with ₀ and ₂ two linear functions of r ( ₀ ¹ = – 2 × 10 ^–12 cm ^–1) and ( ₂ ¹ = – 6 × 10 ¹² cm ^–1). The corresponding angular velocity increases slightly inwards at the poles and decreases at the equator in broad agreement with heliosismic observations. The computed meridional motions are far too large ( 150m s^–1). Reasonable values for the meridional motions can only be obtained if _o (and in consequence ), increase sharply with depth below the surface. The calculated meridional motion at the surface consists of a weak equatorward flow for gq < 29° and of a stronger poleward flow for > 29°.In the Sun, the Taylor-Proudman balance (the Coriolis force is balanced by the pressure gradient), must be altered to include the buoyancy force. The consequences of this modification are far reaching: is not required, now, to be constant along cylinders. Instead, the latitudinal dependence of the superadiabatic gradient is determined by the rotation law. For the above rotation laws, the corresponding latitudinal variations of the convective flux are of the order of 7% in the lower SCZ.     

The critical and the saturation content of magnetic monopoles in rotating relativistic objects

Both the critical content _c ( N _m /N _B , whereN _m ,N _B are the total numbers of monopoles and nucleons, respectively, contained in the object), and the saturation content _s of monopoles in a rotating relativistic object are found in this paper. The results are:

Meridional flow in thick accretion disks

We have studied the effect of the flow in the accretion disk. The specific angular momentum of the disk is assumed to be constant and the polytropic relation is used. We have solved the structure of the disk and the flow patterns of the irrotational perfect fluid.As far as the obtained results are concerned, the flow does not affect the shape of the configuration in the bulk of the disk, although the flow velocity reaches even a half of the sound velocity at the inner edge of the disk. Therefore, in order to study accretion disk models with the moderate mass accretion rate—i.e.,

A linear theory of electron flow in A Pierce

A procedure exploiting the conventional perturbation theory and the transformation of space variable x through is applied to investigate a case of the electron flow in a Pierce diode. The introduction of such variable simplifies the basic set of equations describing the system, which makes an analytic evaluation of electrode spacing as well as the perturbed electric field, due to electron motion, straightforward.     

Simulations of cosmic-ray particle diffusion

The diffusion of charged particles in a stochastic magnetic field (strengthB) which is superimposed on a uniform magnetic fieldB ₀ k is studied. A slab model of the stochastic magnetic field is used. Many particles were released into different realizations of the magnetic field and their subsequent displacements z in the direction of the uniform magnetic field numerically computed. The particle trajectories were calculated over periods of many particle scattering times. The ensemble average was then used to find the parallel diffusion coefficient . The simulations were performed for several types of stochastic magnetic fields and for a wide range of particle gyro-radius and the parameterB/B ₀. The calculations have shown that the theory of charged particle diffusion is a good approximation even when the stochastic magnetic field is of the same strength as the uniform magnetic field.     

The spherically-symmetrical trajectories of spin particles in the Schwarzschild field

The motion of spin particles in the Schwarzschild field is examined in this paper. It is shown that Mathisson-Papapetrou equations under additional conditions , where is the Lie derivative of the Killing vector _j , permit only radial motion, motion in the equatorial plane and in the equilibrium points. All these types of motion are considered more in detail.     

An approximate solution for the polytropen=3

In general, the Lane-Emden equation for an arbitrary polytropic indexn does not admit of an analytic solution. Simple approximation to the numerical results can, however, be found; and, in particular, affords a hitherto unreported good approximation to then=3 model. This term is accurate to within 10% of the tabulated values over 78% of the polytropic interior.     

Models of galactic mass distribution

Three groups of galactic mass models, each consisting of nine inhomogeneous spheroids of two kinds are described, according to three adopted values of the total density near the Sun: 0.10, 0.15 and 0.20 M pc^–3. Approximately 20% of the total mass of each model is in the halo, constructed to adequately fit recent RR Lyrae star observations. It is shown that the maxima found in the RR Lyrae star densities towards the galactic axis (Plaut, 1970) should not be interpreted as being associated with the galactic nucleus, but as the result of the greater decrease in density with increasingz over the increase in density as the galactic axis is approached. Even at the low galactic latitude of 5° (l=0°), this effect causes a 0.5 kpc correction to the distance to the galactic centre. A basic model for kpc, km s^–1, M pc^–3 is first constructed, mainly to satisfy structural conditions near the sun and in the halo. An attempt to optimize the basic model is made by scaling it so as to retain constant density and angular velocity near the sun, and to best fit kinematic data, including the recent re-examination of the 21-cm data of Simonson and Mader (1972). No unknown matter is required in the models, in accordance with the results of Weistrop (1972b), and, as pointed out earlier (Innanen, 1966b) the faintM-stars must be in a highly flattened spheroid. The optimizing indicates that an adequate fit to kinematics can be achieved for km s^–1. More detailed results are tabulated for a representative model for which . Two new galactic density functions are discussed in the Appendix.     

Intrinsic orbital coordinates on a Hamiltonian surface

A reversible dynamical system with two degrees-of-freedom is reduced to a second-order, Hamiltonian system under a change of independent variable. In certain circumstances, the reduced order system may be integrated following an orthogonal curvilinear transformation from Cartesian x,y to intrinsic orbital coordinates , . Solutions for the orbit position and true time variables are expressed by: % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiabg2 % da9iaadAgacaGGOaGaeqOVdGNaaiilaiabeE7aOjaacMcacaGGSaGa % aeiiaiaadMhacqGH9aqpcaWGNbGaaiikaiabe67a4jaacYcacqaH3o % aAcaGGPaGaaiilaiaabccacaWGKbGaamiDaiabg2da9iabgglaXoaa % dmaabaWaaSaaaeaacaWGibWaa0baaKqaahaacqaH+oaEaeaacaqGYa % aaaOGaam4raiabgUcaRiaadIeadaqhaaqcbaCaaiabeE7aObqaaiaa % ikdaaaGccaWGfbaabaGaaGOmaiaacIcacaWGibGaey4kaSIaamyvai % aacMcaaaaacaGLBbGaayzxaaWaaWbaaSqabKqaGhaacaaIXaGaai4l % aiaaikdaaaGccaWGKbGaeqiXdqhaaa!6498! \[ x = f(\xi ,\eta ),{\rm{ }}y = g(\xi ,\eta ),{\rm{ }}dt = \pm \left[ {\frac{{_\xi ^{\rm{2}} {\ie} + _\eta ^2 }}{{2( + U)}}} \righ \]1446 1040 where U is the potential function, and z is the new independent variable. The functions f, g may be expressed by quadratures when the metric coefficients {\er},{\ie} are specified. Two second-order, partial differential equations specify {\er}, {\ie} and Hamiltonian {\tH}. Auxiliary conditions are needed because the solutions are underdetermined. For example, both sets of curvilinear coordinate lines are orbits when certain dynamical compatibility conditions between U and {\ie} (or {\er}) are satisfied. Alternatively, when orbits cross the parametric curves, the auxiliary condition {\er} = {\ie} specifies a conformal transformation, and the partial differential equation for {\tH} may be reduced to an ordinary differential equation for the orbit curve. In either case, integrability is guaranteed for Lionville dynamical systems. Specific applications are presented to illustrate direct solution for the orbit (e.g., two fixed centers) and inverse solution for the potential.     

Cosmic-ray flow lines and energy changes

In this paper we discuss the particle flow or streaming and energy changes of cosmic rays in the interplanetary region via flow lines in momentum-position space. We consider the steady-state case where particles are released monoenergetically from the Sun or from infinity and study the cosmic-ray traffic pattern in momentum and position arising from monoenergetic sources. The analysis makes extensive use of the result (wherep is the particle momentum,V the solar wind velocity andG the cosmic-ray density gradient) for the mean time rate of change of momentum of cosmic rays reckoned for a fixed volume in a reference frame fixed in the solar system, developed by us in several recent papers.Deceased.     

Possible semi-annual variation of the Newtonian constant of gravitation

A possible semi-annual variation of the Newtonian constant of gravitationG is established. For the aphelion and perihelion points of the Earth's orbit we find, respectively,

The dependence of the frequency spectra of the interplanetary magnetic-field fluctuations on the direction of the mean field

The frequency spectra of the interplanetary magnetic field fluctuations are the projection of their wavenumber spectra onto one dimension. Only the frequency spectra can be measured by spacecrafts. It is studied how their measured size depends on the direction of the mean fieldB ₀, which structures the symmetry of the fluctuations relative to the solar wind system. It is specialized for the slab model, Alfvén waves, magneto-acoustic waves and the isotropic case. For the slab model the frequency spectra are proportional to , whereq is the spectral index and the angle betweenB ₀ and the radial direction. For the diffusion coefficientK _TT the relation holds.     

Gas,dust and molecules in the Galaxy

The relative abundances of cool neutral hydrogen, carbon monoxide and formaldehyde are studied using all the available observational data in the literature. The obtained mean valuesN _{H 1}/ ,N _{H 1}/N _CO,N _CO/ are approximately constant in the dark clouds of the solar neighbourhood and in the distant molecular clouds.The observed correlationsN _CO,A _v and ,A _v show that formaldehyde can also be used as an indicator of molecular hydrogen. The ratioN H₁/A _v depends on densities and decays considerably in the ranges of visual absorptions in which the molecules become detectable (A _v 2 mg); an average of /N _{H 1}10 is calculated for the dense dark clouds.Indications of systematic temperature gradiens T/A _v are found for formaldehyde and neutral hydrogen inside the dark clouds, and qualitative comparisons are made with theoretical quantum mechanics calculations.The observed carbon monoxide and formaldehyde abundances, the free electron layer in the Galaxy, the distribution of neutral hydrogen in different states are only compatible if an ionization rate of 10^–16 is accepted, provided presumably by 2 MeV protons of cosmic radiation.Three main states for neutral hydrogen and dust are identified from different kinds of observational data (21 cm line in emission, absorption in galactic radio sources and self-absorption in the hot gas background): (1) a homogeneous intercloud stratum of tenuous gas and dust with a galactic halfwidth of 350 pc and mean parametersn _H=0.2 atom cm^–3, spin temperatureT _s 10000 K andn _d 0.3 mg kpc^–1; (2) cool gas and dust concentrated in spiral features with a galactic half-width of less than 100 pc, probably forming clouds with diffuse and indefinite limits, with mean parametersn _H2 atom cm^–3,T _s <1100 K (probable average,T _s =135 K) andn _d 3 mg kpc^–1; (3) dense gas and dust clouds with a mean diameter of 7 pc and mean parametersn _H700 atom cm^–3 (90% in a molecular state),T _s 63 K andn _d 1 mg pc^–1 on which molecules as CO and H₂CO are formed.The application of the Jeans criteria for gravitational instability shows that the dense clouds are gravitationally bound while the gas in the intermediate state (2) can be protected against collapse by the total internal energy in the medium increasing due to cosmic rays and the magnetic field in the Galaxy.The observed velocity halfwidths and galacticZ-halfwidths in states (1) and (2) are compatible with a total mass density in the galactic layer of 90M pc^–2 (gas plus stars) according to the barometric equation.The relative abundancesN _{H 1}/N _CO, calculated from C¹²O and C¹³O data and comparisons with studies in the 21 cm emission line, show that the antenna temperatureT _A ⁺ in the 2.6 mm line of C¹²O is a good indicator of the cool gas densities in the Galaxy. The possible application of this for studies in galactic structure is discussed and hypothetical distributions of carbon monoxide in the zones outside the galactic planeB=0° are presented.From a synthesis based on the results obtained, a cycle is postulated for the neutral hydrogen in the Galaxy: condensation and cooling of gas molecular formation gravitational collapse and star formation gas dissipation and heating by cosmic rays and UV radiation.     

The light curved in the CM field

In this paper we introduce the CM field in Sections 2 and 3 based on the paper by Wang and Peng (1985), and calculate the light curved in the CM field in Section 4. The result shows thatP makes _CM larger than _C at , and smaller at . Under a special circumstance which source, CM lens, and observer are in the same line, if we get | ₀₌₀ , and | _=/2 , we can determine theP(M) andQ(M) of the CM lens,M is the mass of the CM lens.     

Tidal effects in the earth–moon system and the earth's rotation

Analytical expressions for tidal torques induced by a tide‐arising planet which perturbs rotation of a nonrigid body are derived. Corresponding expressions both for secular and periodic perturbations of the Euler's angles are given for the case of the earth's rotation. Centennial secular rates of the nutation angle θ and of the earth's angular velocity ω, as well as the centennial logarithmic decrement ν of the Chandler wobble are evaluated:  mas, . In the Universal Time (UT) a large out‐of‐phase (sine) dissipative term with the period 18.6 years and the amplitude 2.3 ms is found. Corrections to nutation coefficients, which presumably have not been taken into account in IAU theory, are given. This revised version was published online in July 2006 with corrections to the Cover Date.     

Velocity-height relation for antimatter meteors

A general velocity-height relation for both antimatter and ordinary matter meteor is derived. This relation can be expressed as % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq% aHfpqDdaWgaaWcbaGaamOEaaqabaaakeaacqaHfpqDdaWgaaWcbaGa% eyOhIukabeaaaaGccqGH9aqpcaqGLbGaaeiEaiaabchacaqGGaWaam% WaaeaacqGHsisldaWcaaqaaiaadkeaaeaacaWGHbaaaiaabwgacaqG% 4bGaaeiCaiaabIcacaqGTaGaamyyaiaadQhacaGGPaaacaGLBbGaay% zxaaGaeyOeI0YaaSaaaeaacaWGdbaabaGaamOqaiabew8a1naaBaaa% leaacqGHEisPaeqaaaaakmaacmaabaGaaGymaiabgkHiTiaabwgaca% qG4bGaaeiCamaadmaabaGaeyOeI0YaaSaaaeaacaWGcbaabaGaamyy% aaaacaqGLbGaaeiEaiaabchacaqGOaGaaeylaiaadggacaWG6bGaai% ykaaGaay5waiaaw2faaaGaay5Eaiaaw2haaiaacYcaaaa!64FD!\[\frac{{\upsilon _z }}{{\upsilon _\infty }} = {\text{exp }}\left[ { - \frac{B}{a}{\text{exp( - }}az)} \right] - \frac{C}{{B\upsilon _\infty }}\left\{ {1 - {\text{exp}}\left[ { - \frac{B}{a}{\text{exp( - }}az)} \right]} \right\},\]where _z is the velocity of the meteoroid at height z, its velocity before entrance into the Earth's atmosphere, is the scale-height, and C parameter proportional to the atom-antiatom annihilation cross- section, which is experimentally unknown. The parameter B (B = DA₀/m) is the well known parameter for koinomatter (ordinary matter) meteors, D is the drag factor, ₀ is the air density at sea level, A is the cross sectional area of the meteoroid and m its mass.When the annihilation cross-section is zero — in the case of ordinary meteors — the parameter C is also zero and the above derived equation becomes % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq% aHfpqDdaWgaaWcbaGaamOEaaqabaaakeaacqaHfpqDdaWgaaWcbaGa% eyOhIukabeaaaaGccqGH9aqpcaqGLbGaaeiEaiaabchacaqGGaWaam% WaaeaacqGHsisldaWcaaqaaiaadkeaaeaacaWGHbaaaiaabwgacaqG% 4bGaaeiCaiaabIcacaqGTaGaamyyaiaadQhacaGGPaaacaGLBbGaay% zxaaGaaiilaaaa!4CF5!\[\frac{{\upsilon _z }}{{\upsilon _\infty }} = {\text{exp }}\left[ { - \frac{B}{a}{\text{exp( - }}az)} \right],\]which is the well known velocity-height relation for koinomatter meteors.In the case in which the Universe contains antimatter in compact solid structure, the velocity-height relation can be found useful.Work performed mainly at the Nuclear Physics Laboratory of the National University of Athens, Greece.     

Optically thick accretion onto black holes

Spherically symmetric, steady-state, optically thick accretion onto a nonrotating black hole with the mass of is studied. The gas accreting onto the black hole is assumed to be a fully ionized hydrogen plasma withn ₀=10⁸ cm^–3 andT ₀=10⁴ K far from the black hole, and a new approximate expression for the Eddington factor is introduced. The luminosity is estimated to beL=1.875×10³³ erg s^–1, which primarily arises from the optical surface (1) ofT10⁴ K. The accretion flow is characterized by 1 and (v/c)10. In the optically thin region, the flow remains isothermal, and the increase of temperature occurs at 1. The radiative equilibrium is strictly realized at (v/c)10.     

K emission-line widths and the solar chromosphere

Closely spaced microphotometer tracings parallel to the dispersion of one excellent frame of a K-line time sequence have been utilized for a study of the nature of the K_2v , K_2R intensities in the case of the solar chromosphere. The frequency of occurrence of the categories of intensity ratio are as follows: per cent; per cent; per cent; per cent; per cent. Two types of absorbing components are postulated to explain the pattern of observed K_2v , k_2R intensity ratios. One component with minor Doppler displacements acting on the normal K₂₃₂ profile, where K_2V >K_2R , produces the cases K_2v K_2R , K_2v = K_2R , K_2v <K_2R . The other component arises from dark condensations which are of size 3500 kms as seen in K_2R . They have principally large down flowing velocities in the range 5–8 km/sec and are seen on K₃ spectroheliograms with sizes of about 5000 kms, within the coarse network of emission. These dark condensations give rise to the situation K_2R = 0.K₂-line widths are measured for all tracings where K_2v , K_2R are measurable simultaneously. The distribution curve of these widths is extremely sharp. The K₂ emission source is identified with the bright fine mottles visible on the surface. Evidence for this interpretation comes from the study of auto-correlation functions of K₂ intensity variations and the spacing between the bright fine mottles from both spectrograms and spectroheliograms. The life time of the fine mottling is 200 sec.The supergranular boundaries which constitute the coarse network come in two intensity classes. A low intensity network has the fine mottles as its principal contributor to the K emission. When the network is bright, the enhancement is caused by increased K emission due to the accumulation of magnetic fields at the supergranule boundary. The K₂ widths of the low intensity supergranular boundary agree with the value found for the bright mottles. Those for the brighter network are lower than this value, similar to the K₂ widths as seen in the active regions.It is concluded that bright fine mottling is responsible for the relation, found by Wilson and Bappu, between K emission line widths and absolute magnitudes of the stars.The paper discusses the solar cycle equivalents that stellar chromospheres can demonstrate and indicates a possible line of approach for successful detection of cyclic activity in stellar chromospheres.