Al xii line ratios in the Sun

Recent calculations of electron impact excitation rates in He-like Alxii are used to derive the theoretical electron temperature and density sensitive emission line ratios G ( = (f + i)/r and R ( = f/i, where f, i, and r are the forbidden 1s ^{2 1} S – 1s2s ³ S, intercombination 1s ^{2 1} S – 1s2p ³ P and resonance 1s ^{2 1} S – 1s2p ¹ P transitions, respectively. These ratios are found to be significantly different from earlier calculations, and are in much better agreement with X-ray spectral data for two solar flares obtained with the SMM and P78-1 satellites.     

Theoretical emission line ratios for Si XIII compared to solar observations

The electron collision excitation rates recently calculated for transitions in Si xiii by Keenan et al. (1987) are used to derive the electron temperature sensitive ratio G(=(f + i)/r and the density sensitive ratio R(=f/i), where i, f, and r are the intercombination (1s ^{2 1} S – 1s2p ³ P _{1, 2}) forbidden (1s ^{2 1} S – 1s2s ³ S), and resonance (1s ^{2 1} S – 1s2p ¹ P), transitions respectively. Also estimated are the values of R in the low-density limit (R ₀) as a function of electron temperature. The theoretical G ratio at the temperature of maximum emissivity for Si xiii, G(T _m) = 0.70, is in much better agreement with the observed G for the 1985, May 5 flare determined by McKenzie et al. (G = 0.60 ± 0.07) than is the earlier calculation of Pradhan, who derived G(T _m) = 0.85. The error in the observed R ₀ ratio is so large that both our result and Pradhan's fall within the acceptable limits of uncertainty and hence one cannot estimate which of the two is the more accurate.     

Integrability of the Yang-Mills Hamiltonian system

This paper considers the integrability of generalized Yang-Mills system with the HamiltonianH _a (p, q)=1/2(p ₁ ² +p ₂ ² +a ₁ q ₁ ² +a ₂ q ₂ ² )+1/4q ₁ ⁴ +1/4a ₃ q ₂ ⁴ + 1/2a ₄ q ₁ ² q ₂ ² . We prove that the system is integrable for the cases: (A)a ₁=a ₂,a ₃=a ₄=1; (b)a ₁=a ₂,a ₃=1,a ₄=3; (C)a ₁=a ₂/4,a ₃=16,a ₄=6. Our main result is the presentation of these integrals. Only for cases A and B does the Yang-Mills Hamiltonian possess the Painlevé property. Therefore the Painlevé test does not take account of the integrability for the case C.     

Parameter values for stable low-inclination periodic motion in the restricted three-body problem with oblateness

The known intervals of possible stability, on the mgr-axis, of basicfamilies of 3D periodic orbits in the restricted three-body problem areextended into -A₁ regions for oblate larger primary, A ₁ beingthe oblateness coefficient. Eight regions, corresponding to the basicstable bifurcation orbits l1v, l1v, l2v, l3v, m1v, m1v,m2v, i1v are determined and related branching 3D periodic orbits arecomputed systematically and tested for stability. The regions for l1v,m1v and m2v survive the test emerging as the regions allowing thesimplest types of stable low inclination 3D motion. For l1v, l2v,l3v, m1v and m2v oblateness seems to have a stabilising effect,while stability of i1v survives only for a very small range of A ₁values.     

The ratios I(K1)/I(H1) and I(K3)/I(H3) of ca II as diagnostics of the chromosphere above sunspots

The ratios I(K ₁)/I(H ₁) and I(K ₃)/I(H ₃) were calculated from four semi-empirical models of sunspot umbra. We determined the dependencies of both ratios of such parameters as temperature gradient and atmospheric opacity. A certain influence on the expected ratios I(K ₁)/I(H ₁) and I(K ₃)/I(H ₃) can also come from the FIP effect provided it exists in the chromosphere above sunspot umbra. Theoretical and observed values of I(K ₁)/I(H ₁) and I(K ₃)/I(H ₃) are compared. It is shown that for one of the sunspots we observed, the values obtained for the ratio I(K ₁)/I(H ₁) cannot be explained in terms of existing umbra models.     

Single close encounters in the planetary problem

We consider a large massM and two small massesm ₁ andm ₂ (m ₁ m ₂;m ₁,m ₂M). The orbit ofm ₁ is initially circular and the motion ofm ₂ hyperbolic with respect toM. The orbital elements of the small masses are strongly modified after a close, single encounter betweenm ₁ andm ₂.An approximative method, similar to the theory of stellar encounters, is used to determine the probabilities of collisions, hyperbolas, direct and retrograde ellipses, as well as the mean values of the semimajor axes and their root mean square deviation after the encounter.The results are close to those which are obtained if the massm ₂ is negligibly small, (Mm ₁m ₂;m ₂ 0), as should be also expected on general grounds.     

X-rays spectroheliograms in lines of Mg xi and Mg xii

Spectroheliograms in the L Mg xii line and in the Mg xi resonance (R) 1s ²¹ S ₀-1s2p ¹ P ₁ line, intercombination (I) 1s ²¹ S ₀-1s2p ³ P _1,2, line, and the forbidden (F) 1s ²¹ S ₀-1s2s ³ S ₁ line, have been obtained.Two Bragg crystal spectrometers were used mounted with mechanical collimators to obtain a spatial resolution of 1 × 3. The apparatus was launched on a sounding rocket on July 2nd, 1971. A particularly thorough study was made of the brightest active region (MC 11402).Variations in the F to I Mg xi line intensity ratio from one point to another in the active region did not reveal the presence of high electron densities.The observed intensities of the Mg xi R line, Mg xii L line and Mg x 1s ²2s ² S _1/2-1s2p ¹ P 2s × × ² P1_{1/2, 3/2} S line are not well explained by an isothermal model. Good agreement between computed and observed intensities is obtained using the non-isothermal model proposed here.     

On the excitation of lower levels of singlet helium in quiescent prominences

The paper deals with the excitation of the helium singlet level 2¹ P in the homogeneous and filamentary models of quiescent prominences with following parameters: the optical thickness at the limit of helium Lyman continuum _1c ^M = 0.1–100, T _e = 7000 K, n _e = 5 × 10¹⁰ cm^–3. Assuming a model He atom with seven discrete levels (1¹ S, 2³ S, 2¹ S, 2³ P, 2¹ P, 3³ D, 3¹ D) and the continuum the steady state equations for the levels 2³ S, 2¹ P and the continuum have been solved together with the radiative transfer equations for the line 584 Å and the continuum 504 Å. The variations with depth of the functions n ₂ ³ _S /n ₁ ¹ _S (₁ c), n ₂ ¹ _P /n ₁ ¹ _S (_1c ), and n ⁺ _He n _e /n ₁ ¹ S(_1c ) as well as the intensities of the triplet (D₃, 10830 Å) and singlet (16678, 20581 Å) lines have been calculated. Comparison with observations leads to the following conclusions: (1) The line intensities calculated for filamentary models of prominences agree better with observations than those for homogeneous ones. (2) The helium level 2¹ P is excited by diffuse field 584 Å being formed by recombinations and spontaneous transitions 2¹ P – 1¹ S and escaping from the prominence into the space between the filaments and to the surface. (3) Underpopulation of the singlet level 2¹ P may be explained by combination of weak excitation mechanism (recombinations and formation of the diffuse field 584 Å) and strong deexcitation mechanism (spontaneous transitions into the level 1¹ S).     

Variation in Ovii X-ray line-emission from the solar corona

The variation in intensity of the solar X-ray resonance (1s ^{2 1} S ₀ - 1s2p ¹ P ₁), intercombination (1s ^{2 1} S ₀ - 1s2p ³ P ₁), and forbidden (1s^{2 1} S ₀ - 1s2s ³ P ₁) lines of helium-like Ovii with 2800 MHz solar radio flux is presented for three solar rotations. A high correlation (r 0.80) exists between the intensities of all three X-ray lines and the 2800 MHz solar flux. The ratio of the forbidden to the intercombination line intensities is found to be essentially independent of long term solar activity. This ratio is used to determine upper limits on the coronal electron density and to make inferences concerning the change in density with solar activity.     

The extinction curve in the visible and the value of RV: Addendum to AN 333, 160

This paper corrects and completes a previous study of the shape of the extinction curve in the visible and the value of R_V. A continuous visible/infrared extinction law proportional to 1/λ^p with p close to 1 (± 0.4) is indistinguishable from a perfectly linear law (p = 1) in the visible within observational precision, but the shape of the curve in the infrared can be substantially modified. Values of p slightly larger than 1 would account for the increase of extinction (compared to the p = 1 law) reported for λ > 1 μ m and deeply affect the value of R_V. In the absence of gray extinction R_V must be 4.04 if p = 1. It becomes 3.14 for p = 1.25, 3.00 for p = 1.30, and 2.76 for p = 1.40. Values of p near 1.3 are also attributed to extinction by atmospheric aerosols, which indicates that both phenomena may be governed by similar particle size distributions. A power extinction law may harmonize visible and infrared data into a single, continuous, and universal interstellar extinction law (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Elemental abundance analyses with DAO spectrograms: XXXII. HR 6455 (A3 III), δ Aqr (A3 V), η Lep (F2 V), and 1 Boo (A1 V)

We examine the sharp‐lined stars HR 6455 (A3 III, v sin i = 8.7 km s^–1) and η Lep (F2 V, v sin i = 13.5 km s^–1) as well as δ Aqr (A3 V, v sin i = 81 km s^–1) and 1 Boo (A1 V, v sin i = 59 km s^–1) to increase the number consistently analyzed A and F stars using high dispersion and high S/N (≥200) spectrograms obtained with CCD detectors at the long Coudé camera of the 1.22‐m telescope of the Dominion Astrophysical Observatory. Such studies contribute to understanding systematic abundance differences between normal and non‐magnetic main‐sequence band chemically peculiar A and early F stars. LTE fine analyses of HR 6455, δ Aqr, and 1 Boo using Kurucz's ATLAS suite programs show the same general elemental abundance trends with differences in the metal richness. Light and iron‐peak element abundances are generally solar or overabundant while heavy element and rare earth element abundances are overabundant. HR 6455 is an evolved Am star while δ Aqr and 1 Boo show the phenomenon to different extents. Most derived abundances of η Lep are solar (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Tables for the trigonometric series representations of the orbital inclination function

In this paper, tables for the trigonometric series representations of the orbital inclination functionF _lmp (i) in multiples of cosines or sines will be represented forl=2(1)10;m=0(1)l;p=0(1)l.Astrophysics and Space Science Review Article.     

Use of Al xii and Mg xi lines as solar plasma diagnostics

We present three sets of observations of n = 1 to n = 2 lines due to helium-like aluminium (Alxii), made during two solar flares (25 August, 1980 and 19 October, 1986), using the X-Ray Polychromator on the SMM satellite. The observed temperature-sensitive line ratio G is shown to be consistent with the close-coupling calculations of Keenan and McCann (1987), although the ratio R, which is both temperature and density-sensitive for lower-Z elements, is not sufficiently well determined from these data to say more than that the observed values of R are not inconsistent with the theoretical calculations. This region of the spectrum also includes the helium-like magnesium (Mgxi) 1¹ S - 3¹ P line, and it is shown that the ratio of this line to the Alxii resonance (1¹ S - 2¹ P) line is a more sensitive indicator of electron temperature than are the Alxii G and R ratios. We demonstrate that the three ratios may be used together in order to derive values of emission measure, electron temperature and electron density during these flares.     

Non-integrability of Hénon-Heiles system

We show that the Hénon-Heiles system with Hamiltonian H=\frac12(y₁²+y₂²)+\frac12(ax₁²+bx₂²)+\frac13dx₂³+cx₁²x₂{H=\frac12(y_1^2+y_2^2)+\frac12(ax_1^2+bx_2^2)+\frac13dx_2^3+cx_1^2x_2} is integrable in Liouvillian sense (i.e., the existence of an additional first integral) if and only if c = 0; or \frac dc=1, a=b; or \frac dc=6, a, b{\frac dc=1, a=b; {\rm or}\, \frac dc=6, a, b} arbitrary; or \frac dc=16, b=16a{\frac dc=16, b=16a}. Therefore, we get a complete classification of the Hénon-Heiles system in sense of integrability and non-integrability.     

On the relative magnitude of streaming velocities of alpha particles and protons at 1 AU

The occurrence at a heliocentric distance of 1 AU of alpha particle streaming velocities larger than proton streaming velocities,v /v _p >1 (Ogilvie, 1975) is investigated on the basis of the theory suggesting the existence in the solar wind of an accelerating force acting preferentially on the alpha particles.Accurate solution of the three-fluid model equations for the quiet solar wind indicates that anecessary andsufficient condition for (v /v _p )_{1 AU}>1 is the presence of a relativelyweak accelerating forceacting in a limited region in the vicinity of 1 AU. If the force is effectiveonly at small heliocentric distances, the alpha particle streaming velocity excess vanishes at distances less than 1 AU, because of the (equalization) action of the dynamical friction force.     

Methanol 72–81A+ emission and some maser series in Orion KL

Methanol 7₂–8₁ A ⁺ is mapped for the first time in Orion KL. Analysing the observed data and solving the statistical equilibrium and radiative transfer equations, it is concluded that line series ofJ ₂–(J+1)₁ A ⁺ (J=7,8,9) is in quasi-thermal emission rather than the masers in Orion KL. The maser spots of methanolJ ₂–J ₁ E (J=6,7) and 8₀–7₁ A ⁺ are distributed in the northeast part of the contour plot of 7₂–8₁ A ⁺. The physical conditions of the regions of maser seriesJ ₀–(J–1)₁ A ⁺ (J=7,8,9) are discussed. Also from the calculation results another maser seriesJ ₁–(J–1)₂ A ^– (J=10,11,12) that might coexist with maser seriesJ ₂–J ₁ E, is found. The sizes of the 2-dimension Gaussian fit plots of methanol 7₂–8₁ A ⁺ and HCOOCH₃ 10(0,10)–9(0,9)A are almost the same, and the main parts overlap each other.     

New exact solutions for power-law inflation Friedmann models

We consider the spatially flat Friedmann model For a ≈ t^p, especially, if p ≥ 1, this is called power-law inflation. For the Lagrangian L = R^m with p = − (m − 1) (2m − 1)/(m − 2) power-law inflation is an exact solution, as it is for Einstein gravity with a minimally coupled scalar field ϕ in an exponential potential V(ϕ) = exp (μϕ) and also for the higher-dimensional Einstein equation with a special Kaluza-Klein ansatz. The synchronized coordinates are not adapted to allow a closed-form solution, so we write The general solutions reads Q(a) = (a^b + C)^f/b with free integration constant C (C = 0 gives exact power-law inflation) and m-dependent values b and f: f = −2 + 1/p, b = (4m − 5)/(m − 1). Finally, special solutions for the closed and open Friedmann model are found.     

The elliptical three-body problem. Triangular solution

The restricted three-body problem with eccentric orbit is reviewed and the positions of the triangular Lagrangian points (L₄, L₅) are determined. It is put in evidence the fact the fact L₄ and L₅ are situated at the corners of an isoscales triangle: AB = BC = 1 − e²/)1 + e cos ν )4/3 and AC = 1 − e²/)1 + e cos ν )     

New stacked central configurations for the planar 5-body problem

A stacked central configuration in the n-body problem is one that has a proper subset of the n-bodies forming a central configuration. In this paper we study the case where three bodies with masses m ₁, m ₂, m ₃ (bodies 1, 2, 3) form an equilateral central configuration, and the other two with masses m ₄, m ₅ are symmetric with respect to the mediatrix of the segment joining 1 and 2, and they are above the triangle generated by {1, 2, 3}. We show the existence and non-existence of this kind of stacked central configurations for the planar 5-body problem.     

Stable Manifolds and Homoclinic Points Near Resonances in the Restricted Three-Body Problem

The restricted three-body problem describes the motion of a massless particle under the influence of two primaries of masses 1− μ and μ that circle each other with period equal to 2π. For small μ, a resonant periodic motion of the massless particle in the rotating frame can be described by relatively prime integers p and q, if its period around the heavier primary is approximately 2π p/q, and by its approximate eccentricity e. We give a method for the formal development of the stable and unstable manifolds associated with these resonant motions. We prove the validity of this formal development and the existence of homoclinic points in the resonant region. In the study of the Kirkwood gaps in the asteroid belt, the separatrices of the averaged equations of the restricted three-body problem are commonly used to derive analytical approximations to the boundaries of the resonances. We use the unaveraged equations to find values of asteroid eccentricity below which these approximations will not hold for the Kirkwood gaps with q/p equal to 2/1, 7/3, 5/2, 3/1, and 4/1. Another application is to the existence of asymmetric librations in the exterior resonances. We give values of asteroid eccentricity below which asymmetric librations will not exist for the 1/7, 1/6, 1/5, 1/4, 1/3, and 1/2 resonances for any μ however small. But if the eccentricity exceeds these thresholds, asymmetric librations will exist for μ small enough in the unaveraged restricted three-body problem.