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.     

Planar electron-acoustic solitary waves and double layers in a two-electron-temperature plasma with nonthermal ions

A rigorous theoretical investigation of nonlinear electron-acoustic (EA) waves in a plasma system (containing cold electrons, hot electrons obeying a Boltzmann distribution, and hot ions obeying a nonthermal distribution) is studied by the reductive perturbation method. The modified Gardner (MG) equation is derived and numerically solved. It has been found that the basic characteristics of the EA Gardner solitons (GSs), which are shown to exist for α around its critical value α _c [where α is the nonthermal parameter, α _c is the value of α corresponding to the vanishing of the nonlinear coefficient of the Korteweg-de Vries (K-dV) equation, e.g. α _c ≃0.31 for μ=n _h0/n _i0=0.5, σ=T _h /T _i =10, n _h0, n _i0 are, respectively, hot electron and nonthermal ion number densities at equilibrium, T _h (T _i ) is the hot electron (ion) temperature], are different from those of the K-dV solitons, which do not exist for α around α _c , and mixed K-dV solitons, which are valid around α∼α _c , but do not have any corresponding double layers (DLs) solution. The parametric regimes for the existence of the DLs, which are found to be associated with positive potential, are obtained. The present investigations can be observed in various space plasma environments (viz. the geomagnetic tail, the auroral regions, the cusp of the terrestrial magnetosphere, etc.).     

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.     

Stability of motion in the Sitnikov 3-body problem

We study the stability of motion in the 3-body Sitnikov problem, with the two equal mass primaries (m ₁ = m ₂ = 0.5) rotating in the x, y plane and vary the mass of the third particle, 0 ≤ m ₃ < 10⁻³, placed initially on the z-axis. We begin by finding for the restricted problem (with m ₃ = 0) an apparently infinite sequence of stability intervals on the z-axis, whose width grows and tends to a fixed non-zero value, as we move away from z = 0. We then estimate the extent of “islands” of bounded motion in x, y, z space about these intervals and show that it also increases as |z| grows. Turning to the so-called extended Sitnikov problem, where the third particle moves only along the z-axis, we find that, as m ₃ increases, the domain of allowed motion grows significantly and chaotic regions in phase space appear through a series of saddle-node bifurcations. Finally, we concentrate on the general 3-body problem and demonstrate that, for very small masses, m ₃ ≈ 10⁻⁶, the “islands” of bounded motion about the z-axis stability intervals are larger than the ones for m ₃ = 0. Furthermore, as m ₃ increases, it is the regions of bounded motion closest to z = 0 that disappear first, while the ones further away “disperse” at larger m ₃ values, thus providing further evidence of an increasing stability of the motion away from the plane of the two primaries, as observed in the m ₃ = 0 case.     

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.     

Spin-forbidden resonance multiplets in light elements

We present new laboratory data on the multiplets 2s ^{2 1} S -2s2p ³ P, 2s ²2p ² P - 2s2p ^{2 4} P, and 2s ²2p ^{2 3} P - 2s2p ^{3 5} S in nitrogen, oxygen and fluorine, and discuss theZ-dependence of their wave-numbers. These multiplets are very faint in laboratory light sources, but can become prominent in astrophysical sources of low density. Our results confirm the solar identifications of the nitrogen and oxygen multiplets made by Burtonet al. Predicted positions of the corresponding multiplets in neon are given.     

On bridges B(pL, qS) around triangular libration points

When μ is smaller than Routh’s critical value μ ₁ = 0.03852 . . . , two planar Lyapunov families around triangular libration points exist, with the names of long and short period families. There are periodic families which we call bridges connecting these two Lyapunov families. With μ increasing from 0 to 1, how these bridges evolve was studied. The interval (0,1) was divided into six subintervals (0, μ ₅), (μ ₅, μ ₄), (μ ₄, μ ₃), (μ ₃, μ ₂), (μ ₂, μ ₁), (μ ₁, 1), and in each subinterval the families B(pL, qS) were studied, along with the families B(qS, qS′). Especially in the interval (μ ₂, μ ₁), the conclusion that the bridges B(qS, qS′) do not exist was obtained. Connections between the short period family and the bridges B(kS, (k + 1)S) were also studied. With these studies, the structure of the web of periodic families around triangular libration points was enriched.     

The Schwabe and Gleissberg Periods in the Wolf Sunspot Numbers and the Group Sunspot Numbers

Three wavelet functions: the Morlet wavelet, the Paul wavelet, and the DOG wavelet have been respectively performed on both the monthly Wolf sunspot numbers (R_z) from January 1749 to May 2004 and the monthly group sunspot numbers (R_g) from June 1795 to December 1995 to study the evolution of the Gleissberg and Schwabe periods of solar activity. The main results obtained are (1) the two most obvious periods in both the R_z and R_g are the Schwabe and Gleissberg periods. The Schwabe period oscillated during the second half of the eighteenth century and was steady from the 1850s onward. No obvious drifting trend of the Schwabe period exists. (2) The Gleissberg period obviously drifts to longer periods the whole consideration time, and the drifting speed of the Gleissberg period is larger for R_z than for R_g. (3) Although the Schwabe-period values for R_z and R_g are about 10.7 years, the value for R_z seems slightly larger than that for R_g. The Schwabe period of R_z is highly significant after the 1820s, and the Schwabe period of R_g is highly significant over almost the whole consideration time except for about 20 years around the 1800s. The evolution of the Schwabe period for both R_z and R_g in time is similar to each other. (4) The Gleissberg period in R_z and R_g is highly significant during the whole consideration time, but this result is unreliable at the two ends of each of the time series of the data. The evolution of the Gleissberg period in R_z is similar to that in R_g.     

Is the Entropy S q Extensive or Nonextensive?

The cornerstones of Boltzmann-Gibbs and nonextensive statistical mechanics respectively are the entropies S _BG ≡ −k ∑ _{i = 1} ^W p _i ln p _i and S _q ≡ k (1−∑ _{i = 1} ^W p _i ^q )/(q−1) (q∊ℜ S ₁ = S _BG ). Through them we revisit the concept of additivity, and illustrate the (not always clearly perceived) fact that (thermodynamical) extensivity has a well defined sense only if we specify the composition law that is being assumed for the subsystems (say A and B). If the composition law is not explicitly indicated, it is tacitly assumed that A and B are statistically independent. In this case, it immediately follows that S _BG (A+B) = S _BG (A)+S _BG (B), hence extensive, whereas S _q (A+B)/k = [S _q (A)/k]+[S _q (B)/k]+(1−q)[S _q (A)/k][S _q (B)/k], hence nonextensive for q ≠ 1. In the present paper we illustrate the remarkable changes that occur when A and B are specially correlated. Indeed, we show that, in such case, S _q (A+B) = S _q (A)+S _q (B) for the appropriate value of q (hence extensive), whereas S _BG (A+B) ≠ S _BG (A)+S _BG (B) (hence nonextensive). We believe that these facts substantially improve the understanding of the mathematical need and physical origin of nonextensive statistical mechanics, and its interpretation in terms of effective occupation of the W a priori available microstates of the full phase space. In particular, we can appreciate the origin of the following important fact. In order to have entropic extensivity (i.e., lim _N→∞ S(N)/N < ∞, where N≡ numberof elements of the system), we must use (i) S _BG , if the number W ^eff of effectively occupied microstates increases with N like W ^{{eff}}∼ W ∼ μ ^N (μ ≥ 1); (ii) S _q with q = 1−1/ρ, if W ^{{eff}}∼ N^ρ < W (ρ ≥ 0). We had previously conjectured the existence of these two markedly different classes. The contribution of the present paper is to illustrate, for the first time as far as we can tell, the derivation of these facts directly from the set of probabilities of the W microstates.     

Note on the Generalized Hansen and Laplace Coefficients

Recently, Breiter et al. [Celest. Mech. Dyn. Astron., 2004, 88, 153–161] reported the computation of Hansen coefficients X _k ^{γ ,m} for non-integer values of γ. In fact, the Hansen coefficients are closely related to the Laplace b _s ^(m), and generalized Laplace coefficients b _s,r ^(m) [Laskar and Robutel, 1995, Celest. Mech. Dyn. Astron., 62, 193–217] that do not require s,r to be integers. In particular, the coefficients X ₀ ^{γ ,m} have very simple expressions in terms of the usual Laplace coefficients b _{γ +2} ^(m), and all their properties derive easily from the known properties of the Laplace coefficients.     

Emission line ratios for C III in the sun

Theoretical electron-density-sensitive C III emission line ratios are presented forR ₁ =I(2s2p ³ P – 2p ^{2 3} P)/I(2s2p ¹ P – 2p ^{2 1} S) =I(1176 Å)/I(1247 Å),R ₂ =I(2s2p ³ P – 2p ^{2 3} P)/I(2s ^{2 1} S – 2s2p ³ P ₁) =I(1176 Å)/I(1908 Å), andR ₃ =I(2s2p ¹ P – 2p ^{2 1} S)/I(2s ^{2 1} S – 2s2p ³ P ₁) =I(1247 Å)/I(1908 Å). These are significantly different from those deduced previously, principally due to the adoption of improved electron impact excitation rates in the present analysis. Electron densities deduced from the present theoretical line ratios, in conjunction with observed values ofR ₁,R ₂, andR ₃ measured from solar spectra obtained by the Naval Research Laboratory's S082B instrument on boardSkylab, are found to be generally compatible. In contrast, previous diagnostic calculations imply electron densities fromR ₁,R ₂, andR ₃ that differ by up to two orders of magnitude. These results provide observational support for the accuracy of the atomic physics adopted in the present calculations, and the methods employed in the derivation of the theoretical line ratios.     

Presence of LaO, ScO and VO Molecular Lines in Sunspot Umbral Spectra

High-resolution Fourier Transform Spectrometer sunspot umbral spectra of the National Solar Observatory/National Optical Astronomy Observatory at Kitt Peak were used to detect rotational lines from 19 electronic transition bands of the molecules LaO, ScO and VO, in the wavenumber range of 11 775 to 20 600 cm⁻¹. The presence of lines from the following transitions is confirmed: A ² Π _r1/2 – X ² Σ ⁺(0, 0; 0, 1), A ² Π _r3/2 – X ² Σ ⁺(1, 0), B ² Σ ⁺ – X ² Σ ⁺(0, 0; 0, 1; 1, 0) and C ² Π _r1/2 – A′²Δ _r3/2(0, 0; 1, 1) of LaO; A ² Π _r3/2 – X ² Σ ⁺(0, 0), A ² Π _r1/2 – X ² Σ ⁺(0, 0) and B ² Σ ⁺ – X ² Σ ⁺(0, 0) of ScO; and C ⁴ Σ ⁻ – X ⁴ Σ ⁻(0, 1; 1, 0; 0, 2) and (2, 0) of VO. However, the presence of A ² Π _r3/2 – X ² Σ ⁺(0, 0) and C ² Π _r3/2 – A′²Δ _r5/2(0, 0; 1, 1) of LaO and C ⁴ Σ ⁻ – X ⁴ Σ ⁻(0, 0) of VO are found to be doubtful because the lines are very weak, and detections are difficult owing to heavy blending by strong rotational lines of other molecules. Equivalent widths are measured for well-resolved lines and, thereby, the effective rotational temperatures are estimated for the systems for which the presence is confirmed.     

Interstellar Extinction and the Intrinsic Colors of Classical Cepheids in the Galaxy, the LMC, and the SMC

New methods are applied to samples of classical cepheids in the galaxy, the Large Magellanic Cloud, and the Small Magellanic Cloud to determine the interstellar extinction law for the classical cepheids, R _B:R _V:R _I:R _J:R _H:R _K= 4.190:3.190:1.884:0.851:0.501:0.303, the color excesses for classical cepheids in the galaxy, E(B-V)=-0.382-0.168logP+0.766(V-I), and the color excesses for classical cepheids in the LMC and SMC, E(B-V)=-0.374-0.166logP+0.766(V-I). The dependence of the intrinsic color (B-V)₀ on the metallicity of classical cepheids is discussed. The intrinsic color (V-I)₀ is found to be absolutely independent of the metallicity of classical cepheids. A high precision formula is obtained for calculating the intrinsic colors of classical cepheids in the galaxy: (<B>-<V>)₀=0.365(±0.011)+0.328(±0.012)logP.     

The extinction curve in the visible and the value of RV

This article discusses the interstellar extinction curve in the visible and the value of the ratio of absolute to selective extinction R_V = A_V/E (B – V). It is concluded that the visible extinction curve is likely to be linear in the visible and that indirect estimates of R_V from tentative determinations of A_V or from infrared and UV observations are questionable. There is currently no evidence of any variation of R_V with direction. If R_V is close to 3, as it has been inferred from mid‐infrared data, starlight in the visible is extinguished by a factor F /F₀ = (2.5 e^–2μm/λ)^{E (B –V)}. But if the visible wavelength range alone is considered, 4 appears as its most natural and probable value and F /F₀ = e^{–2E (B –V)/λ} (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Existence and uniqueness of stellar equilibrium models

The stellar equilibrium equations for given surface pressureP _* and temperatureT _*, and in the absence of convection, are translated into a nonlinear integral equation, in which the radiusR of the star enters as an eigenvalue. We show that under broad mathematical assumptions on the constitutive equations (equation of state, opacity and energy generation) a global existence and uniqueness property can be formulated. If a valueP _M is selected, which restricts the allowed pressure and temperature range |P(r)–P _*|+E|T(r)–T _*P _M (E, arbitrary constant of dimensions of a pressure over temperature), thenat least one solutionP(r),T(r) exists in the pressure-temperature range chosen, for anyR<R _E . This solution isunique forR<R _c .R _E andR _c are expressed in terms of the constitutive equations, and of the pressure-temperature range adopted. A physical argument in favour of the stability of this solution is presented.     

Meteoroid Stream Searching: The Use of the Vectorial Elements

In this initial study, we propose a new distance function D _V involving heliocentric vectorial orbital elements. The function measures differences between: the orbital energies, the angular momentums vectors and the Laplace vectors. In comparison with the widely used D _SH criterion of Southworth and Hawkins, D _D criterion of Drummond and their hybrid D _H by Jopek, the new function contains one invariant with respect to the principal secular perturbation: the orbital energy. The new function proved to be useful in the classification amongst the IAU2003 meteoroids which we searched for streams by D _V function and also using D _SH and D _N -function given by Valsecchi et al. For major streams, the results agree very well. For minor, and near-ecliptical streams the results sometimes differ markedly.     

MGS electron density profiles: Analysis of the peak magnitudes

We analyze here the behavior of the magnitudes of the F₁ and E peaks of the electron density profiles measured by the Radio Science Subsystem of the Mars Global Surveyor spacecraft, as a function of solar zenith angle χ and solar flux. For each of the 658 days of data in the six occultation seasons in the northern hemisphere, we choose one profile to analyze, which is that for which the F₁ peak is the median value. We assume that the variations of the measured peak densities can be represented as Aa(cosχ) and as Bb(F_10.7), where F_10.7 is the usual solar flux proxy, appropriately shifted to the orbital position of Mars. To minimize the effect of solar activity, we divide the data into 6 F_10.7 bins, fit the data in each bin, and derive the values of the exponent a and the coefficient AF10.7 for each bin. The median values that we derive for the exponent a is 0.46 for the F₁ peak, and 0.395 for the E peak. To minimize the effect of SZA, we divide the data into eight SZA bins, and derive the exponent b and the coefficient Bχ for each SZA bin. We argue that the last three SZA bins should be excluded because the fits were poor, due partly to the small number of data points in each of these bins. If we do so, the median values of b that we derive are 0.27 and 0.40 for the F₁ and E peaks, respectively. Finally we derive a 3-parameter fit to all the data, which expresses the variability of the peak densities as a function of a^′(cosχ) and b^′(F_10.7) simultaneously. The fitted values of the exponents a^′ and b^′ for the F₁ peak are 0.45 and 0.26, respectively; for the E peak, the values are 0.39 and 0.46, respectively. We compare our results to Chapman theory, and to those of other investigators.     

Improved theoretical line ratios for Ciii in the Sun

The recent twelve-state R-matrix calculations of electron excitation rates in Ciii by Berrington are used to derive level populations applicable to the solar transition region. Line ratios R = I(2p ^{2 3} P ^e - 2s2p ³ P ^°)/I(2s2p ¹ P ^° - 2s ^{2 1} S ^e ) and R ₂=I(2p ^{2 1} S ^e - 2s2p ¹ P ^°)/I(2p ^{2 3} P ^e - 2s2p ³ P ^°) deduced from these data in conjunction with the relevent transition probabilities are found to be in much better agreement with the observed quiet Sun values than those determined from the level population calculations of Keenan et al.     

Numerical simulation of the electron capture process in a magnetar interior

In a superhigh magnetic field, direct Urca reactions can proceed for an arbitrary proton concentration. Since only the electrons with high energy E (E>Q, Q is the threshold energy of inverse β-decay) at large Landau levels can be captured, we introduce the Landau level effect coefficient q and the effective electron capture rate Γ _eff . By using Γ _eff , the values of L _X and L _ν are calculated, where L _X and L _ν are the average neutrino luminosity of AXPs and the average X-ray luminosity of AXPs L _X , respectively. The complete process of electron capture inside a magnetar is simulated numerically.     

CCD BV and 2MASS photometric study of the open cluster NGC 1513

We present CCD BV and JHK _s 2MASS photometric data for the open cluster NGC 1513. We observed 609 stars in the direction of the cluster up to a limiting magnitude of V∼19 mag. The star-count method showed that the centre of the cluster lies at α ₂₀₀₀=04 ^h 09 ^m 36 ^s , δ ₂₀₀₀=49°28^′43^″ and its angular size is r=10 arcmin. The optical and near-infrared two-colour diagrams revealed the colour excesses in the direction of the cluster as E(B−V)=0.68±0.06, E(J−H)=0.21±0.02 and E(J−K _s )=0.33±0.04 mag. These results are consistent with normal interstellar extinction values. Optical and near-infrared Zero Age Main-Sequences (ZAMS) provided an average distance modulus of (m−M)₀=10.80±0.13 mag, which can be translated into a distance of 1440±80 pc. Finally, using Padova isochrones we determined the metallicity and age of the cluster as Z=0.015±0.004 ([M/H]=−0.10±0.10 dex) and log (t/yr)=8.40±0.04, respectively.