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.     

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.     

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.     

Density and temperature diagnostics of solar emission lines from NeV/MgV and SiVII/MgVII Ions

We present NeV/MgV and SiVII/MgVII theoretical line intensity ratios as a function of electron densityN _e and temperatureT _e . These are shown in the form of ratio-ratio diagrams, which should in principle allow bothN _e andT _e to be deduced for the emitting region of the solar plasma. We apply these diagnostics in the solar atmosphere, and discuss the available observations made from space. In most cases, however, we deduceN _e andT _e from the computed absolute line intensities in a spherically symmetric model atmosphere of the Sun. Possible future applications of this investigation to spectral data from the Coronal Diagnostic Spectrometer (CDS) on the Solar and Heliospheric Observatory (SOHO) are briefly discussed.     

Evening and morning twilight airglow emissions of 5577 Å and 5893 Å lines at Calcutta and Allahabad and their correlation with flare index

Evening and morning twilight enhancements of 5577 Å and 5893 Å lines were observed by Dunn-Manring type photometer at Calcutta during the period 1983–1985 and that of 5577 Å have been collected from Allahabad observatory. The following paper presents the correlation between the enhanced intensity of airglow lines (A _G ) and solar flare index (I _f ) which is calculated considering all the flares which occurred 24 hr before the times of occurrence of enhancements. It is observed that the intensity of airglow lines varies with the flare index in an oscillatory manner upto a certain limiting value ofI _f . Afterwards intensity of both lines increases with the increase ofI _f . The nature of variation is the same for both sunspot maximum and minimum periods. A possible explanation of such type of variation has also been invoked.     

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.     

Cratering and penetration experiments in aluminum and teflon: Implications for space‐exposed surfaces

Abstract– Whether a target is penetrated or not during hypervelocity impact depends strongly on typical impactor dimensions (D_p) relative to the absolute target thickness (T). We have therefore conducted impact experiments in aluminum₁₁₀₀ and Teflon^FEP targets that systematically varied D_p/T (=D*), ranging from genuine cratering events in thick targets (D_p << T) to the nondisruptive passage of the impactor through very thin films (D_p >> T). The objectives were to (1) delineate the transition from cratering to penetration events, (2) characterize the diameter of the penetration hole (D_h) as a function of D*, and (3) determine the threshold target thickness that yields D_h = D_p. We employed spherical soda‐lime glass (SLG) projectiles of D_p = 50–3175 μm at impact velocities (V) from 1 to 7 km s^?1, and varied target thicknesses from microns to centimeters. The transition from cratering to penetration processes in thick targets forms a continuum in all morphologic aspects. The entrance side of the target resembles that of a standard crater even when the back of the target suffers substantial, physical perforations via spallation and plastic deformation. We thus suggest that the cratering‐to‐penetration transition does not occur when the target becomes physically perforated (i.e., at the “ballistic limit”), but when the shock pulse duration in the projectile (t_p) is identical to that in the target (t_t), i.e., t_p = t_t. This condition is readily calculated from equation‐of‐state data. As a consequence, in reconstructing impactor dimensions from observations of space‐exposed substrates, we recommend that crater size (D_c) be used for the case of t_p < t_t, and that penetration hole diameter (D_h) be used when t_p > t_t. The morphologic evolution of the penetration hole and its size also forms a continuum that strongly depends on both the scaled parameter D* and on V, but it is independent of the absolute scale. The condition of D_h = D_p is approached at D* > 50. The dependence of D_h on T and V, however, is very systematic. This has led to new and detailed calibration curves, permitting the reconstruction of D_p from the measurement of either crater diameter or penetration‐hole size in Al₁₁₀₀ and Teflon^FEP targets of arbitrary thickness. We also placed witness plates behind penetrated targets to intercept the down‐range debris plume, which is generally a mixture of both target and impactor fragments and melts. These witness plates also reveal that the debris plume systematically and diagnostically depends on D*. Thick targets shed spall debris only, and target thickness must be less than crater depth (T_c) to allow projectile material on the witness plate. Concentric plume patterns, accented by characteristic “hole saw” rings, characterize penetrated Al‐targets at D* = 1–10, but they give way to distinctly radial geometries at D* = 10–20. Most of the target debris occupies the periphery of the plume, while the projectile fragments or melts reside in its central parts. The periphery of the plume is also typically more fine‐grained than its center. At D* > 50, the exit plume is dominated by solid projectile fragments that progressively coagulate and overlap with each other, giving rise to compound craters. The latter have irregular crater interiors on account of the heterogeneous mass distribution of a collisionally produced, aggregate impactor. Similarly, complex craters are observed on LDEF and Stardust and they are produced by aggregate cosmic‐dust particles containing large, dense components within a relatively low‐density, fine‐grained matrix. The witness‐plate observations can also be used to address the enigmatic clustering of impact sites observed on Stardust’s aerogel and aluminum surfaces. We suggest that this clustering is difficult to produce by the collision of particles from comet Wild 2 with the Stardust spacecraft, and that it is more likely due to particle disaggregation in the comet’s coma.     

Millimeter and Submillimeter Emissions from Galactic and Extragalactic Photodissociation Regions

The galactic and Extragalactic photodissociation regions are primarily heated by photoelectrons ejected from the surface of interstellar dust grains by Far-ultraviolet (FUV) photons. But there is no direct mechanism to measure the photoelectric heating efficiency. To understand the role of dust grains in processing the Interstellar Radiation Field (ISRF) and heating the gas, we compare the intensities I _CII, I _CO and I _FIR for (² P _3/2→² P _1/2) & (J = 1→ 0) line emission of CII & CO at 158 μm & 2.6 mm and integrated far-infrared from number of photodissociation regions, HII regions, planetary nebulae, reflection nebulae and high latitude translucent clouds (HLCs). It is found that I _CII is linearly correlated with I _FIR. In the cold medium where cloud is exposed to weak radiations temperature is low and most of the cooling is due to [CII] emissions. As a result the ratio of I _CII/I _FIR provide indirect method to evaluate the photoelectric heating efficiency. For the neutral cold medium it is evaluated to be ∼0.028. The FUV radiation field G ₀ are estimated through the model calculation of I _CII and I _CO for different galactic and photodissociation regions. The intensity of FIR radiation I _FIR are well represented as 1.23×10⁻⁴ G ₀(ergs cm⁻² s⁻¹ sr⁻¹) almost same as estimated for HLCs by Ingalls et al (2002). Hydrogen density for each source has also been estimated.     

The theory of relativity and super-luminal-speeds

According to our Paper I (Cao Shenglin, 1988), it could be supposed that the physical space-time is a Finsler space-time, characterized by the metric ds ⁴=g _ijkf dx ⁱ dx ^j dx ^k dx ^f . If so, a new space-time transformation could be found by invariant ds ⁴ and the theory of relativity is discussed on this transformation.The project supported by National Natural Science Foundation of China.     

Quantum vacuum fluctuations and dark energy

It is shown that the curvature of space-time induced by vacuum fluctuations of quantum fields should be proportional to the square of Newton’s constant G. This offers a possible explanation for the success of the formula ρ∼ Gm ⁶ c ² h ⁻⁴, ρ being the dark energy density and m a typical mass of elementary particles.     

Dependence of the U-B and B-V colors of quasars and Seyfert galaxies on their redshifts

We show that the strong emission lines(Mg II, C III, C IV, and Ly and the absorption lineO VI (1035 A) of quasars, when passed through the maximum transmission ofU, B, V, andR light filters, leads to a continuous, and sometimes periodic variation in the dependence ofU-B onB-V. The correlation between the(U-B) and(B-V) colors in quasars with z<1.5 is expressed by the relation(U-B)=–0.92+1.15(B-V). We also give the dependence ofU-B onB-V for Seyfert galaxies of typeS1. We determine the mean variation of the(U-B, B-V) colors due to the strongest emission lines (Mg II, C IV, Ly). It amounts to magnitude0 _. ^m 15.Translated fromAstrofizika, Vol. 38, No. 2, 1995.     

Mg vii and Si ix line ratios in the sun

Recent R-matrix calculations of electron excitation rates for Mg vii and Si ix are used to determine the theoretical density sensitive emission line ratios R ₁= I(2s2p ^{3 1} D ⁰ - 2s ² 2p ^{2 1} D ^e )/I(2s2p ^{3 3} S ⁰ - 2s ² 2p ^{2 3} P ₂ ^e ) and R ₂= I(2s2p ^{3 1} P ⁰ - 2s ² 2p ^{2 1} D ^e )/I(2s2p ^{3 3} S ⁰ - 2s ² 2p ^{2 3} P ₂ ^e ). These are found to be quite similar to the earlier results of Mason and Bhatia. Electron densities derived using observed R ₁ and R ₂ ratios from Skylab NRL XUV spectra of solar flares and active regions are in good agreement, and compare favourably with those deduced from ions formed at similar electron temperatures to Mg vii and Si ix.     

The theory of relativity and super-luminal speeds

According to the different properties between the ds ² and the ds ⁴, it is discussed that the space-time will have the catastrophe nature on the Finsler metric ds ⁴ (see Cao, 1990, Paper II). The space-time transformations and the physical quantities will suddenly change at the catastrophe theory of the space-time. It will be supposed that only the dual velocity of the super-luminal-speed could be observed (see Cao, 1988). If so, a particle with the super-luminal-speedv>c, could be regarded as its anti-particle with the dual velocityv ₁=c ²/v<c.The project was supported by National Natural Science Foundation of China.     

Astrophysical Molecules AlD and CaH: Transition Probabilities and Dissociation Energy

The Franck-Condon (FC) factors and r-centroids for the bands systemC ¹ Σ ⁺ → X ¹ Σ ⁺ of AlD and E ² Π → X ² Σ ⁺ of CaH have been evaluated by means of a reliable numerical integration procedure by using a suitable potential. The dissociation energy, D _e, for the electronic ground states of AlD and CaH have been estimated by the curve fitting method to the RKRV experimental potential curve turning out to be 3.01 eV and 2.32 eV, respectively. This revised version was published online in July 2006 with corrections to the Cover Date.     

The identification of Feix and Nixi in the solar corona

The levels of the configuration 3s ²3 _p ⁵3d of Fe ix have been experimentally determined from their combinations with 3s3 _p ⁶3d ³ D in the region 300–400 Å. Wavelengths can now be accurately predicted for all transitions within 3s ²3 _p 53^d, and eight of these can be identified with coronal lines from 2042 to 4585 Å. Also, identifications of solar lines from 171 to 245 Å with electric-dipole and magnetic-quadrupole transitions to the ground state, 3s ²3p ^{6 1} S, are confirmed and extended. Solar identifications with corresponding transitions in Ni xi, both within 3s ²3 _p ⁵3d and to the ground state, are proposed on the basis of a short extrapolation.     

Radiation forces and nonspherical dust particles

Action of electromagnetic radiation on nonspherical dust particles is discussed. It is stressed that the radiation pressure coefficientQ _PR cannot be considered to be a scalar quantity, as it is used in all calculations for dynamical studies of interplanetary dust particles. Also the equation <Q _PR A> = <Q _PR ><A> (A - area of the particle) holds only for perfectly absorbing convex dust particle (Q _PR = 1) and not even one of these two properties holds for interplanetary dust particles. Plane mirror is discussed in detail - all calculations can be done in this simple case.     

On the identification of Ar x and Ar xiv in the solar corona and the origin of the unidentified coronal lines

A study of theZ-dependence of the² P intervals of 2s ²2p and 2s ²2p ⁵, aided by recent observational results, confirms the identification in the coronal spectrum of λ 4412 with Arxiv, and of λ 5533.4 with Arx. It is further shown that transitions from metastable levels in the configurations 3s ²3p ^k 3d, withk=3, 4 and 5, of Fexi,x, ix, and Nixiii, xiii, xi can well account for the remaining unidentified coronal lines.     

Determining the fundamental parameters of F and G supergiants

A technique for determining the effective temperature T _eff and the acceleration of gravity log g of F and G supergiants is discussed using four bright stars as examples, specifically two F supergiants, α Lep(F0 Ib) and π Sgr (F2 II), and two G supergiants, β Aqr (G0 Ib) and α Aqr (G2 Ib). In all four cases the parameter log g was derived from the high precision parallaxes recently obtained by van Leeuwen in a new reduction of data from Hipparcos. Because of this, the accuracy of the determinations of log g is much greater than before. Estimates of the parameter T _eff were checked using accurate values of T _eff obtained previously by the infrared flux method (IRFM). In the case of the early F supergiants, this method confirms the good accuracy of the T _eff values derived from the Balmer lines and the β-index. Measurements of the Balmer lines for the G supergiants are difficult because of strong blending, so the indices [c ₁] and β serve as indicators of T _eff . It is shown that the indices [c ₁] and β yield a systematic difference in the values of T _eff ; the IRFM confirms that deriving T _eff from the index [c ₁] is more accurate. Based on the values of T _eff and log g that have been found here, with the aid of the evolutionary tracks, we estimate the mass M and age t of each star. The Fe II lines, which are insensitive to departures from LTE, have been used to determine the microturbulence parameter V _t and the iron abundance. The latter is close to the solar iron abundance. Some problems concerning the chemical composition of these stars are discussed using the supergiant α Lep as an example. Translated from Astrofizika, Vol. 52, No. 2, pp. 237–257 (May 2009).     

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)     

Electron-cyclotron maser emission from the sun and stars: Variations with plasma temperature and density

Very bright and highly circularly polarized radio bursts from the Sun, the planets, flare stars, and close binary stars are attributed to the electron-cyclotron maser instability. The mode and frequency of the dominant radiation from the maser instability is shown to be dependent on the plasma temperature and the ratio _p / _e of the plasma frequency to the electron-cyclotron frequency. For the emission from the Sun _p / _e is probably greater than 0.3 and for 0.3 < _p / _e < 2 the emission can be either in the x-mode at the second harmonic or in the o- and/or z-modes at the fundamental. For higher _p / _e , the emission moves to higher harmonics of _e with the emission being predominately in the z-mode when _p / _e > 3.Proceedings of the Workshop on RadioContinua during Solar Flares, held at Duino (Trieste), Italy, 27–31 May, 1985.