Oxygen abundance methods in SDSS: View from modern statistics

Our purpose is to find which is the most reliable one among various oxygen abundance determination methods. We will test the validity of several different oxygen abundance determination methods using methods of modern statistics. These methods include Bayesian analysis and information scoring. We will analyze a sample of ∼ 6000 Hii galaxies from the Sloan Digital Sky Survey (SDSS) spectroscopic observations data release four. All methods that we used drew the same conclusion that the T _e method is a more reliable oxygen abundance determination method than the Bayesian metallicity method under the existing telescope ability. The ratios of the likelihoods between the different kinds of methods tell us that the T _e , P, and O3N2 methods are consistent with each other because the P and O3N2 methods are calibrated by T _e method. The Bayesian and R ₂₃ methods are consistent with each other because both are calibrated by a galaxy model. In either case, the N2 method is an unreliable method.     

PREDICTIONS OF THE FEATURES FOR SUNSPOT CYCLE 23

Smoothed monthly mean Ap indices are decomposed into two components (Ap) _c and (Ap) _n. The former is directly correlated with the current sunspot numbers, while the latter is shown to achieve its maximum correlation with the sunspot numbers after some time lag. This latter property is used to develop a method for predicting the sunspot maximum based on the observed value of (Ap) _n maximum which occurs during the preceding cycle. The value of R _M for cycle 23 predicted by this method is 149.3 ± 19.9. A method to estimate the rise time (from solar minimum to maximum) has been developed (based on analyses of Hathaway, Wilson, and Reichmann, 1994) and yields a value of 4.2 years. Using an estimate that the minimum between cycles 22 and 23 occurred in May 1996, it is predicted that the sunspot maximum for cycle 23 will occur in July 2000.     

Generalized energy balance method for the determination of central star parameters and optical thickness of a planetary nebula

A method is proposed allowing a quick self-consistent determination of both the central star parameters (effective temperature, surface gravity, stellar massetc.) and the optical thickness of a planetary nebula (PN). The method is a generalization of the well-known energy balance method. The method has been calibrated and tested using a photoionization model grid computed for this purpose. The internal accuracy of the method is estimated as 0.038dex for the effective temperature of central star and 0.076dex for the surface gravity.The problem of determination of overall energy losses in the nebula required by any kind of energy balance method is considered thoroughly. Approximate expressions are obtained, relating the overall energy losses to the sum of intensities of collisionally excited lines in the optical and ultraviolet spectral ranges and to some other nebular parameters. It is shown that neglecting the energy losses caused by directly unobservable collisional excitation of neutral hydrogen and helium may underestimate the central star temperature by 0.2 or even 0.5dex. Generalized energy balance method is applied to a sample of 41 PN. Central star temperaturesT _GB found by this method show an agreement withHeII Zanstra temperaturesT _z (HeII) whereasT _z (HI) is always less thanT _GB or equal to it within the accuracy of the method. So, we confirm the explanation that the well-known Zanstra discrepancy is caused merely by low optical thickness of many PN in the Lyman continuum of hydrogen. The value ofT _z (HeII) found with modern model atmospheres can be used as good approximation toT _ef for central stars of overwhelming majority of PN whileT _z (HI) is usually close toT _ef for young nebulae only.     

How the Method of Minimization of Action Avoids Singularities

The method of minimization of action is a powerful technique of proving the existence of particular and interesting solutions of the n-body problem, but it suffers from the possible interference of singularities. The minimization of action is an optimization and, after a short presentation of a few optimization theories, our analysis of interference of singularities will show that:(A) An n-body solution minimizing the action between given boundary conditions has no discontinuity: all n-bodies have a continuous and bounded motion and thus all eventual singularities are collisions;(B) A beautiful extension of Lambert's theorem shows that, for these minimizing solutions, no double collision can occur at an intermediate time;(C) The proof can be extended to triple and to multiple collisions. Thus, the method of minimization of action leads to pure n-body motions without singularity at any intermediate time, even if one or several collisions are imposed at initial and/or final times.This method is suitable for non-infinitesimal masses only. Fortunately, a similar method, with the same general property with respect to the singularities, can be extended to n-body problems including infinitesimal masses.     

Regularization of Motion Equations with L-Transformation and Numerical Integration of the Regular Equations

The sets of L-matrices of the second, fourth and eighth orders are constructed axiomatically. The defining relations are taken from the regularization of motion equations for Keplerian problem. In particular, the Levi-Civita matrix and KS-matrix are L-matrices of second and fourth order, respectively. A theorem on the ranks of L-transformations of different orders is proved. The notion of L-similarity transformation is introduced, certain sets of L-matrices are constructed, and their classification is given. An application of fourth order L-matrices for N-body problem regularization is given. A method of correction for regular coordinates in the Runge–Kutta–Fehlberg integration method for regular motion equations of a perturbed two-body problem is suggested. Comparison is given for the results of numerical integration in the problem of defining the orbit of a satellite, with and without the above correction method. The comparison is carried out with respect to the number of calls to the subroutine evaluating the perturbational accelerations vector. The results of integration using the correction turn out to be in a favorable position.     

AMR Simulations of Magnetohydrodynamic Problems by the CESE Method in Curvilinear Coordinates

The objective of this paper is to present new extensions of the space – time conservation element and solution element (CESE) method for simulations of magnetohydrodynamic (MHD) problems in general curvilinear coordinates by using an adaptive mesh refinement (AMR) grid system. By transforming the governing MHD equations from the physical space (x,y,z) to the computational space (ξ,η,ζ) while retaining the form of conservation, the CESE method is established for MHD in the curvilinear coordinates. Utilizing the parallel AMR package PARAMESH, we present the first implementation of applying the AMR CESE method for MHD (AMR-CESE-MHD) in both Cartesian and curvilinear coordinates. To show the validity and capabilities of the AMR-CESE-MHD code, a suite of numerical tests in two and three dimensions including ideal MHD and resistive MHD are carried out, with two of them in both Cartesian and curvilinear coordinates. Numerical tests show that our results are highly consistent with those obtained previously by other authors, and the results under both coordinate systems confirm each other very well.     

Study of the June 30, 1973 trans-polar coronal hole

Radially and tangentially polarized pictures of the solar corona obtained near 4500 Å during the 30 June, 1973 solar total eclipse have been used to derive a model of a trans-polar coronal hole. The hole is identified by using OSO-7 EUV spectroheliograms. The line of sight coincides with the privileged plan of the hole over the N-polar region. A new method of absolute calibration is used. The Saito (1970) method is applied to determine the electron densities. Extrapolated values of densities down to the surface are lower than have ever been observed although derived hydrostatic temperatures are certainly not: N _e × 10⁷ cm^–3 and T = 2 × 10⁶ K. The morphological peculiarities of polar regions are considered.On leave from Institut d'Astrophysique, CNRS, Paris as NRC Research Associate.     

Solving Kepler’s Equation using Bézier curves

This paper presents a non-iterative approach to solve Kepler’s Equation, M = E − e sin E, based on non-rational cubic and rational quadratic Bézier curves. Optimal control point coordinates are first shown to be linear with respect to orbit eccentricity for any eccentric anomaly range. This property yields the development of a piecewise (e.g., 3, 4) solving technique providing accuracies better than 10⁻¹³ degree for orbit eccentricity e ≤ 0.99. The proposed method does not require large pre-computed discretization data, but instead solves a cubic/quadratic algebraic equation and uses a single final Halley iteration in only a few lines of code. The method still provides accuracies better than 10⁻⁵ degree for the near parabolic worst case (e = 0.9999) with very small mean anomalies (M < 0.0517 deg). The complexity of the proposed algorithm is constant, independent of the parameters e and M. This makes the method suitable for extensive orbit propagations. Presented at the 7th Dynamics and Control of Systems and Structures in Space Conference, July 18–22, 2006, Greenwich, England.     

Dissipative cylindrical fast magnetoacoustic waves in planetary magnetospheres

Nonlinear cylindrical fast magnetoacoustic waves are investigated in a dissipative magnetoplasma comprising of electrons, positrons, and ions. In this regard, cylindrical Kadomtsev-Petviashvili-Burgers (CKPB) equation is derived using the small amplitude perturbation expansion method. Furthermore, cylindrical Burgers-Kadomtsev-Petviashvili (Cyl Burgers-KP) for a fast magnetoacoustic wave is derived, for the first time, for spatial scales larger than the electron/positron skin depths, c/ω _p(e,p). Using the tangent hyperbolic method, the solutions of both planar KPB and Burgers-KP equations are obtained and then subsequently used as an initial profile to solve their respective counterparts in the cylindrical geometry. The effect of positron concentration, kinematic viscosity, and plasma β are explored both for the KPB and the Burgers-KP shock waves and the differences between the two are highlighted. The temporal evolution of the cylindrical fast magnetoacoustic wave is also numerically investigated. The present study may be beneficial to study the propagation characteristics of nonlinear electromagnetic shock waves in planetary magnetospheres.     

Phenomenological Nucleon-nucleon Potentials and the Equation of State of Neutron Star Matter

We have calculated the equation of state of the neutron star matter and some of its properties for a wide range of nucleon-nucleon potentials using the lowest order constrained variational (LOCV) method. It turns out that for the UV ₁₄+TNI potential, the proton fraction exhibits a peak and falls off at high densities. The equation of state with the UV ₁₄+TNI potential is seen to be much harder than those with other potentials. The polytropic behaviour of the neutron star matter with various potentials are discussed. Compared with the other methods, the LOCV results show good agreement for densities below 0.7 fm _-3. Above this density, however, the differences with other methods are appreciable.     

Techniques For Measuring Radar Meteor Speeds

We compare the results from the application of four different methods to determine the speed of meteoroids from single station radar data. The methods used are the pre-t ₀ amplitude, post-t ₀ amplitude, pre-t ₀ phase and the Fresnel transform (FT) methods. Speeds from the first three methods are compared to the FT method since, requiring the use of the entire records of both the amplitude and phase data, this method is the most accurate of the four.     

Abundance calibration and evolution of GiantHii Regions

We present a self-consistent method to determine abundance and evolutionary status for GiantHii Regions (GHR) as well as the nominal temperature of the ionizing cluster and the ionization parameter. We define the ionization parameter-free plane [,R ₂₃] (Vilchez and Pagel, 1988) where observations are compared with the prediction of photoionization models, in order to obtain the abundance and evolutionary status for a given GHR. This new method allows us to re-calibrate the empirical relationship (R ₂₃, O/H) by Pagelet al. (1979) up to abundances three times solar. The effects of evolution of GHR on their observed spectra are explained in terms of the cooling down of the ionizing population and some evolutionary tracks are presented.     

Dynamic evolution of nearby galaxy clusters

A study of the evolution of 377 rich ACO clusters with redshift z < 0.2 is presented. The data concerning galaxies in the investigated clusters were obtained using FOCAS packages applied to Digital Sky Survey I. The 377 galaxy clusters constitute a statistically uniform sample to which visual galaxy/star reclassifications were applied. Cluster shape within 2.0 h^–1 Mpc from the adopted cluster centre (the mean and the median of all galaxy coordinates, the position of the brightest and of the third brightest galaxy in the cluster) was determined through its ellipticity calculated using two methods: the covariance ellipse method (hereafter CEM) and the method based on Minkowski functionals (hereafter MFM). We investigated ellipticity dependence on the radius of circular annuli, in which ellipticity was calculated. This was realized by varying the radius from 0.5 to 2 Mpc in steps of 0.25 Mpc. By performing Monte Carlo simulations, we generated clusters to which the two ellipticity methods were applied. We found that the covariance ellipse method works better than the method based on Minkowski functionals. We also found that ellipticity distributions are different for different methods used. Using the ellipticity‐redshift relation, we investigated the possibility of cluster evolution in the low‐redshift Universe. The correlation of cluster ellipticities with redshifts is undoubtly an indicator of structural evolution. Using the t‐Student statistics, we found a statistically significant correlation between ellipticity and redshift at the significance level of α = 0.95. In one of the two shape determination methods we found that ellipticity grew with redshift, while the other method gave opposite results. Monte Carlo simulations showed that only ellipticities calculated at the distance of 1.5 Mpc from cluster centre in the Minkowski functional method are robust enough to be taken into account, but for that radius we did not find any relation between e and z. Since CEM pointed towards the existence of the e (z) relation, we conclude that such an effect is real though rather weak. A detailed study of the e (z) relation showed that the observed relation is nonlinear, and the number of elongated structures grows rapidly for z > 0.14 (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Determination of the mass-ratio distribution,I: Single-lined spectroscopic binary stars

For single-lined spectroscopic binary stars (SBI), the mass ratioq=M _sec/M _prim is calculated from the mass functionf(m), which is determined from observations. For statistical investigations of the mass-ratio distribution, the term sin³ i, that remains in the cubic equation from whichq is solved, has to be dealt with.This paper compares the common practise of taking an average value for sin³ i to a deconvolution scheme that takes into account the precise (expected) behaviour ofP (sin³ i) d sin³ i. The behaviour ofP(sin³ i) d sin³ i depends on how orbital planes of binary stars are oriented in space. For a random orientation of orbital planes,P _i(i) di=sini di. For the average value method, it is generally assumed thatP _i(i) di=(4/) sin² i di.For verification purposes, the deconvolution scheme is applied to an observed sample of double-lined spectroscopic binary stars (SBII), and to a synthetic sample of SBI systems, produced by a numerical model. In both cases, the scheme produces better results with the assumption thatP _i(i) di=(4/gp) sin² i di, rather than a purely random orientation of orbital planes. In the case of the synthetic sample of SBI systems, the deconvolution scheme does not produce better results than the method that assumes an average value for sin³ i.Application of the deconvolution method to the double-lined spectroscopic binary systems in theEighth Catalogue of the Orbital Elements of Spectroscopic Binary Stars, provides results which are compatible with the assumption that the orbital planes of these systems are oriented randomly in space.     

The extended phase space formulation of the Vinti problem

The Vinti problem, motion about an oblate spheroid, is formulated using the extended phase space method. The new independent variable, similar to the true anomaly, decouples the radius and latitude equations into two perturbed harmonic oscillators whose solutions toO(J ₂ ⁴ ) are obtained using Lindstedt's method. From these solutions and the solution to the Hamilton-Jacobi equation suitable angle variables, their canonical conjugates and the new Hamiltonian are obtained. The new Hamiltonian, accurate toO(J ₂ ⁴ ) is function of only the momenta.     

The effective temperatures,radii and masses of Dwarf Cepheids

Using the flux values determined with the infrared flux method (IRFM) developed by Blackwell and Lynas-Gray (1993), we derived the empirical relationship between flux (F _v ) and (V — K) colour appropriate to Dwarf Cepheids. For three Dwarf Cepheids CY Aqr, YZ Boo and SZ Lyn where both VK photometry and radial velocities were available from the literature, effective temperatures were determined using the intrinsic Strömgren indices, model atmosphere grids for (V — K) and the relation between temperature and (V — K) colour. Then, by applying the infrared surface brightness method, radii and distances and hence masses and absolute magnitudes were estimated with effective temperatures determined by three different methods. It was found that the average mass of these variables is about 0.5 solar mass and this result supports the hypothesis that Dwarf Cepheids are pre-white dwarf objects. It was also confirmed that the temperatures determined with the IRFM are most successful in the application of the surface brightness method to the radius estimation of Dwarf Cepheids.     

The characteristics of ion acoustic shock waves in non-Maxwellian plasmas with (G′/G)-expansion method

Korteweg-de-Vries-Burger (K-dVB) equation is derived for ion acoustic shock waves in electron-positron-ion plasmas. Electrons and positrons are considered superthermal and are effectively modeled by a kappa distribution in which ions are as cold fluid. The analytical traveling wave solutions of the K-dVB equation investigated, through the (G′/G)-expansion method. These traveling wave solutions are expressed by hyperbolic function, trigonometric functions are rational functions. When the parameters are taken special values, the shock waves are derived from the traveling waves. It is observed that the amplitude ion acoustic shock waves increase as spectral index κ and kinematic viscosity η _i,0 increases in which with increasing positron density β and electron temperature σ the shock amplitude decreases. Also, numerically the effect different parameters on the nonlinearity A and dispersive B terms and wave velocity V investigated.     

Control of chaos in the vicinity of the Earth‐Moon L5 Lagrangian point to keep a spacecraft in orbit

The concept of Space Manifold Dynamics is a new method of space research. We have applied it along with the basic idea of the method of Ott, Grebogi, and York (OGY method) to stabilize the motion of a spacecraft around the triangular Lagrange point L₅ of the Earth‐Moon system. We have determined the escape rate of the trajectories in the general three‐ and four‐body problem and estimated the average lifetime of the particles. Integrating the two models we mapped in detail the phase space around the L₅ point of the Earth‐Moon system. Using the phase space portrait our next goal was to apply a modified OGY method to keep a spacecraft close to the vicinity of L₅. We modified the equation of motions with the addition of a time dependent force to the motion of the spacecraft. In our orbit‐keeping procedure there are three free parameters: (i) the magnitude of the thrust, (ii) the start time, and (iii) the length of the control. Based on our numerical experiments we were able to determine possible values for these parameters and successfully apply a control phase to a spacecraft to keep it on orbit around L₅. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Determination of the orbits of near-Earth asteroids from observations at the first opposition

Observations at the first opposition are used to determine the orbits of 16 near-Earth asteroids with two or more observed oppositions. The orbits are improved by the differential method. This paper considers two modifications of the improvement technique, which are compared to the classical method based on the principle of the least square method (LSM). The first modification uses the principle of least absolute deviations (LAD). In the second modification, the differences O - C (between the observed and calculated positions) are transformed to fit into a new coordinate system whereby the axes go parallel and perpendicular to the asteroid’s apparent path (the modified differential method (MDM)). The orbits determined from one opposition by the classical LSM, LAD, and MDM are compared to a more accurate orbit calculated by the LSM from all the available oppositions. The calculations show that in 13 cases out of 16, the asteroid orbits calculated by LAD are more accurate than those calculated by the classical LSM. The improvement by the modified differential method, which includes the O - C transformation, does not produce any perceptible increase in accuracy when compared to the orbits calculated by the classical method.     

Possible meteoroid streams associated with (69230) Hermes and 2002 SY50

The orbits of (69230) Hermes and 2002 SY₅₀ are similar and the Earth approaches both of them twice: at the end of October the local orbital minimum distances are smaller than 0.007 AU, and at the end of April the distances are smaller than 0.04 AU. This gives us opportunities to observe the meteors associated with these asteroids. Using the geocentric parameters of the orbital close encounters (the theoretical radiants) and our D _N distance function (Valsecchi et al. Mon. Not. R. Astron. Soc. 304 (1999) 743), we searched for meteoroids originated by Hermes and 2002 SY₅₀. A search among 1830 good quality photographic meteors gave negative results: we found no meteor dynamically similar to Hermes or 2002 SY₅₀. In a second search, done in a set of 62150 radio meteors, we applied two methods (M1, M2) and in both cases we found two streams; the streams found with the M1 method had 43 and 30 members, those found with the M2 method had 39 and 14 members. However, these results do not look convincing, due to the small number of common members in the corresponding streams. We therefore conclude that amongst the IAU meteors used in our search there are no compact streams associated with Hermes and 2002 SY₅₀.