Specificity of Parker instability in polytropic disks

The specificity of the Parker instability in the disks in the presence of the polytropic connection between the equilibrium pressure and density is investigated.It is shown that, in contrary to the caseV _A=const., the even and odd (with reference to the disk perpendicular coordinate) modes consist of non-finite sum of the harmonics, and that the zero (fundamental) harmonic of the even mode, which has the definite wave numberK=K _* will mainly increase. Consequently, this very harmonic will determine the structure, obtained as a result of the Parker instability development.     

Methods of Calculation of Turbulent Diffusivities

Different techniques of calculation and estimation of turbulentdiffusivities D of passive fields in infinite incompressiblemedia showing isotropic, homogeneous and stationary turbulence areconsidered. The numerical comparison of the methods is made mostlyfor two representative limiting models of turbulence – withpeak-like spectrum and for vast Kolmogorov's type spectrum. The timedependence of two-point velocity correlators is assumed to beexponential. The backbone of the comparison is steady-state turbulentdiffusivities calculated in nonlinear DIA-approach with thecorrections due to contribution of four-order velocity correlators.As a result of this comparison the most satisfactory approximatemethods are proposed both for steady-state and time-dependentturbulent diffusivities. The results may be used for the most correctchoice of -dependence in various astrophysical problems.     

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.     

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 ratio of optical to near-infrared emission line strengths inSii as electron density diagnostics for planetary nebulae

EinsteinA-coefficients for transitions inSii, calculated with the atomic structure package CIV3, are used to derive the electron density sensitive emission line ratio

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.,

On the structure and mass of the galactic halo

On the basis of a globular cluster study a crude estimate of the total mass of the galactic halo within 20 kpc from the centre is done. It gives a minimal halo mass of the order of , yielding possibilities for a mass as large as . The content of the interstellar matter in the halo is estimated too. It is found that the gas content is a few percents the minimal mass, the gas temperature is very high — about 1×10⁶ K, the magnetic field weak — about 0.25 nT. A weak nonthermal radio emission might be expected from such a halo.     

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.     

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,

Ultra-high energy neutrino fluxes from supermassive AGN black holes

We compute the ultra-high energy (UHE) neutrino fluxes from plausible accreting supermassive black holes closely linking to the 377 active galactic nuclei (AGNs). They have well-determined black hole masses collected from the literature. The neutrinos are produced via simple or modified URCA processes, even after the neutrino trapping, in superdense proto-matter medium. The resulting fluxes are ranging from: (1) (quark reactions)— $J^{q}_{\nu\varepsilon}/(\varepsilon_{d}\ \mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\,\mathrm{sr}^{-1})\simeq8.29\times 10^{-16}$ to 3.18×10^?4, with the average $\overline{J}^{q}_{\nu\varepsilon}\simeq5.53\times 10^{-10}\varepsilon_{d}\ \mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\,\mathrm{sr}^{-1}$ , where ε _d ～10^?12 is the opening parameter; (2) (pionic reactions)— $J^{\pi}_{\nu\varepsilon} \simeq0.112J^{q}_{\nu\varepsilon}$ , with the average $J^{\pi}_{\nu\varepsilon} \simeq3.66\times 10^{-11}\varepsilon_{d}\ \mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\,\mathrm{sr}^{-1}$ ; and (3) (modified URCA processes)— $J^{URCA}_{\nu\varepsilon}\simeq7.39\times10^{-11} J^{q}_{\nu\varepsilon}$ , with the average $\overline{J}^{URCA}_{\nu\varepsilon} \simeq2.41\times10^{-20} \varepsilon_{d}\ \mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\,\mathrm{sr}^{-1}$ . We conclude that the AGNs are favored as promising pure neutrino sources, because the computed neutrino fluxes are highly beamed along the plane of accretion disk, peaked at high energies and collimated in smaller opening angle θ～ε _d .     

Gamma-ray burst measurements with A 6.3 m2 array

Two flights from Alice Springs, Australia, were achieved in November 1977 and November 1978 with a plastic scintillator -burst detector, effective area 6.3 m², thickness 5 cm, energy response in the range 50 keV to 2 MeV. In 33 hr of good, high altitude data, two bursts were detected, yielding a rate corrected to an isotropic flux of at a size of 8.5×10^–9 erg cm^–2. One event, seen at 22.14 on 15 Nov 1978, was confirmed by spacecraft measurements. The second, too small to be detected by spacecraft, arrived from 0 hr RA, –13.2° Decl. ±12° and possibly comes from a confirmed -burst source location. A galactic origin with a source distribution originating from a relatively thick disk, is favoured by these results.     

Nonlinear newtonian theory and the effect of time dilatation

The fact that the energy density ρ_g of a static spherically symmetric gravitational field acts as a source of gravity, gives us a harmonic function \(f\left( \varphi \right) = e^{\varphi /c^2 } \) , which is determined by the nonlinear differential equation $$\nabla ^2 \varphi = 4\pi k\rho _g = - \frac{1}{{c^2 }}\left( {\nabla \varphi } \right)^2 $$ Furthermore, we formulate the infinitesimal time-interval between a couple of events measured by two different inertial observers, one in a position with potential φ-i.e., dt _φ and the other in a position with potential φ=0-i.e., dt ₀, as $${\text{d}}t_\varphi = f{\text{d}}t_0 .$$ When the principle of equivalence is satisfied, we obtain the well-known effect of time dilatation.     

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.     

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.     

Earth’s precession–nutation motion: the error analysis of the theories IAU 2000 and IAU 2006 applying the VLBI data of the years 1984–2006

The long-term systematic errors of the analytical theories IAU 2000 and IAU 2006 of the Earth’s precession–nutational motion are studied making use of the VLBI data of 1984–2007. Several independent methods give indubitable evidence of the significant quadratic error in the IAU 2000 residuals of the precessional angle while the adopted value of the secular decrease /cy of the Earth’s ellipticity e (derived from Satellite Laser Ranging data) should manifest itself in the residuals of as the negative quadratic trend . The problem with the precession of the IAU 2006 theory adopted as a new international standard and based on the precession model P03 (Capitaine et al., Astron Astrophys 432:355–367, 2005) appears to be even more serious because the above mentioned quadratic term has already been incorporated into the P03 precession. Our analysis of the VLBI data demonstrates that the quadratic trend of the IAU 2006 residuals does amount to the expected value (30.0 ± 3) mas/cy². It means, first, that the theoretical precession rate of IAU 2006 should be augmented by the large secular correction and, second, that the available VLBI data have potentiality of estimating the rate . And indeed, processing these data by the numerical theory ERA of the Earth’s rotation (Krasinsky, Celest Mech Dyn Astron 96:169–217, 2006, Krasinsky and Vasilyev, Celest Mech Dyn Astron 96:219–237, 2006) yields the estimate /cy statistically in accordance with the satellite-based . On the other hand, applying IAU 2000/2006 models, the positive value /cy is found which is incompatible with the SLR estimate and, evidently, has no physical meaning. The large and steadily increasing error of the precession motion of the IAU 2006 theory makes the task of replacing IAU 2006 by a more accurate model be most pressing.     

Determination of Optical Spectra by a Modified Kramers Kronig Integral

A new modified Kramers Kronig Integral is derived and shown to produce excellent results when k data is only known over a limited range. By considering the effect of resonance features simulated using the Dirac-Delta function, the new integral is shown to be more rapidly converging than both the conventional Kramers Kronig integral and a modified (Subtractive Kramers Kronig – SKK) integral introduced by Ahrenkiel (1971). The new integral does not require extensive extrapolation of reflectance data outside the measured region in order to produce reliable results. By extending the above procedure to include n data points, it is shown that at wavelength ₀, \[ n(_0)=\sum_{i=1}^{\rm n}(-1)^{\rm n+1}\prod_{\stackrel{j=1}{j \not=i}}^{\rm n} \frac{(_j^2-_0^2)}{(_i^2- _j^2)}n(_i)+\frac{2}{\pi}P\int_{0}^{\infty}(-1)^{\rm n+1} \frac{\prod_{i=1}^{\rm n}(_i^2-_0^2)}{\prod_{i=0}^{\rm n}(^2-_i^2)} k()d \] with relative error given by, \[ R_n(_0)=\prod_{i=1}^{\rm n}\frac{_i^2- _0^2}{_^2-_i^2} . \] This n^th order expression should prove useful in establishing the internal self-consistency of data sets for which both optical coefficients have been theoretically derived.     

On equivalent widths in a penumbral spectrum (a test of the Moe-Maltby model)

From new observational material we made a curve of growth analysis of the penumbra of a large, stable sunspot. The analysis was done relative to the undisturbed photosphere and gave the following results (⊙ denotes photosphere, * denotes penumbra): $$\begin{gathered} (\theta ^ * - \theta ^ \odot )_{exe} = 0.051 \pm 0.007 \hfill \\ {{\xi _t ^ * } \mathord{\left/ {\vphantom {{\xi _t ^ * } {\xi _t }}} \right. \kern-\nulldelimiterspace} {\xi _t }}^ \odot = 1.3 \pm 0.1 \hfill \\ {{P_e ^ * } \mathord{\left/ {\vphantom {{P_e ^ * } {P_e ^ \odot = 0.6 \pm 0.1}}} \right. \kern-\nulldelimiterspace} {P_e ^ \odot = 0.6 \pm 0.1}} \hfill \\ {{P_g ^ * } \mathord{\left/ {\vphantom {{P_g ^ * } {P_g }}} \right. \kern-\nulldelimiterspace} {P_g }}^ \odot = 1.0 \pm 0.2 \hfill \\ \end{gathered} $$ The results of the analysis are in satisfactory agreement with the penumbral model as published by Kjeldseth Moe and Maltby (1969). Additionally we tested this model by computing the equivalent widths of 28 well selected lines and comparing them with our observations.     

A few observations of and remarks on V1500 Cygni

The development of the post-nova light curve of V1500 Cyg inUBV andHβ, for 15 nights in September and October 1975 are presented. We confirm previous reports that superimposed on the steady decline of the light curve are small amplitude cyclic variations. The times of maxima and minima are determined. These together with other published values yield the following ephemerides from JD 2 442 661 to JD 2 442 674: $$\begin{gathered} {\text{From}} 17 {\text{points:}} {\text{JD}}_{ \odot \min } = 2 442 661.4881 + 0_{^. }^{\text{d}} 140 91{\text{n}} \hfill \\ \pm 0.0027 \pm 0.000 05 \hfill \\ {\text{From}} 15 {\text{points:}} {\text{JD}}_{ \odot \max } = 2 442 661.5480 + 0_{^. }^{\text{d}} 140 89{\text{n}} \hfill \\ \pm 0.0046 \pm 0.0001 \hfill \\ \end{gathered} $$ with standard errors of the fits of ±0 _. ^d 0052 for the minima and ±0 _. ^d 0091 for the maxima. Assuming V1500 Cyg is similar to novae in M31, we foundr=750 pc and a pre-nova absolute photographic magnitude greater than 9.68.     

The motion of the line of apsides of ζ phoenicis

An estimate of the period of the rotation of the line of apsides of the double-star system Phe is obtained by representing the density function as a product of a normal Gaussian distribution and an associated Legendre polynomial .The asymptotic behaviour of this function coincides with the results obtained by Zeldovichet al. (1981).The period of motion of the line of apsides of Phe (about 63 years) obtained in this way comes close to the period determined by an empirical formula for of Batten (1973).     

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: