A method of measuring the [α/Fe] ratios from the spectra of the LAMOST survey

The [α/Fe] ratios in stars are good tracers to probe the formation history of stellar populations and the chemical evolution of the Galaxy. The spectroscopic survey of LAMOST provides a good opportunity to determine [α/Fe] of millions of stars in the Galaxy. We present a method of measuring the [α/Fe]ratios from LAMOST spectra using the template-matching technique of the LSP3 pipeline. We use three test samples of stars selected from the ELODIE and MILES libraries, as well as the LEGUE survey to validate our method. Based on the test results, we conclude that our method is valid for measuring [α/Fe]from low-resolution spectra acquired by the LAMOST survey. Within the range of the stellar parameters Teff= [5000, 7500] K, log g = [1.0, 5.0] dex and [Fe/H]= [onsistent with values derived from high-resolution spectra,-1.5, +0.5] dex, our [α/Fe] measurements are c and the accuracy of our [α/Fe] measurements from LAMOST spectra is better than 0.1 dex with spectral signal-to-noise higher than 20.     

Analysis of periodic orbits in the Saturn-Titan system using the method of Poincare section surfaces

We explore the periodic orbits and the regions of quasi-periodic motion around both the primaries in the Saturn-Titan system in the framework of planar circular restricted three-body problem. The location, nature and size of periodic and quasi-periodic orbits are studied using the numerical technique of Poincare surface of sections. The maximum amplitude of oscillations about the periodic orbits is determined and is used as a parameter to measure the degree of stability in the phase space for such orbits. It is found that the orbits around Saturn remain around it and their stability increases with the increase in the value of Jacobi constant C. The orbits around Titan move towards it with the increase in C. At C=3.1, the pericenter and apocenter are 358.2 and 358.5 km, respectively. No periodic or quasi-periodic orbits could be found by the present method around the collinear Lagrangian point L ₁ (0.9569373834…).     

Computing periodic orbits of the three-body problem: Effective convergence of Newton’s method on the surface of section

We consider Newton’s method for computing periodic orbits of dynamical systems as fixed points on a surface of section and seek to clarify and evaluate the method’s uncertainty of convergence. Several fixed points of various multiplicities, both stable and unstable are computed in a new version of Hill’s problem. Newton’s method is applied with starting points chosen randomly inside the maximum possible—for any method—circle of convergence. The employment of random starting points is continued until one of them leads to convergence, and the process is repeated a thousand times for each fixed point. The results show that on average convergence occurs with very few starting points and non-converging iterations being wasted.     

Diagnostics of the solar atmosphere by the Non-LTE inversion method: Line of Ba II λ 455.403 nm

The inverse problem of nonequilibrium radiative transfer in the Ba II λ 455.403 nm line is solved taking into account the hyperfine structure and isotopic splitting. Diagnostic capabilities of this line for the study of the solar atmosphere are investigated based on the three-dimensional hydrodynamic model. It is shown that the use of inversion methods for the analysis of the observed Ba II λ 455.403 nm line makes it possible to reproduce physical conditions in the layers of the photosphere and the lower chromosphere (0 < h < 600 km) with a correlation coefficient of 0.9.     

The influence of the correlations between an asteroid’s orbital parameters on the estimation of the probability of planetary collision by the Monte Carlo method

The probability of an asteroid colliding with a planet can be estimated by the Monte Carlo method, in particular, through the statistical simulation of the possible initial conditions for the motion of an asteroid based on the probability density distribution set by the respective covariance matrix to be further projected with the orbital model onto the supposed time point of the collision. Hence, the collision probability is calculated as the ratio between the number of projected (virtual) asteroids striking the planet and their total number. The main problem is that different elements of the initial conditions (orbit or state vector) are correlated and, therefore, cannot be simulated independently. These correlations are reflected in the nondiagonal covariance matrix of the solution. The matrix is diagonalized by an orthogonal transformation. In the uncertainty domain constructed from the diagonal matrix elements, the initial values for each of the six orbital elements are simulated independently from the other elements, but with the accounting for their normal distribution. The program for calculating the normal distribution is based on the central limit theorem. Each sample of the initial values for the six orbital elements is transferred to the initial reference frame using an inverse transformation. Then, numerical integration is used to track the asteroid’s motion along the respective orbit to predict a possible impact event. Asteroids 99942 Apophis and 2007 WD5 are used as examples to show that disregarding the correlations when diagonalizing the covariance matrix to set the initial conditions may seriously distort the collision probability estimates. The paper gives the probabilities of the collisions of Apophis with the Earth and asteroid 2007 WD5 with Mars calculated by the author from observation sets showing nonzero collision probabilities. The author’s estimates are compared to those calculated by NASA.     

Periodicity of flare index revisited using the Hilbert–Huang transform method

Using the Hilbert–Huang Transform (HHT) method, we investigate the periodicity in the monthly mean flare indices from 1966 to 2007 (corresponding to almost four complete solar cycles), calculated by T. Atac and A. Ozguc. The results show as following. (1) The periods of 9.37 ± 2.53, 11.8 ± 0.172 and 23.6 ± 0.316 years are found to be statistically significant in the flare index. The most eminent period is 9.37 ± 2.53 years. (2) Other periods of 0.237 ± 0.196 years (86.6 ± 71.6 days), 0.525 ± 0.0508 years (191 ± 18.5 days), 1.05 ± 0.478 years (383 ± 174 days) and 2.37 ± 0.395 years are below the 99% confidence level line, suggesting they are due to stochastic random noise.     

Multiple Poincaré sections method for finding the quasiperiodic orbits of the restricted three body problem

A new fully numerical method is presented which employs multiple Poincaré sections to find quasiperiodic orbits of the Restricted Three-Body Problem (RTBP). The main advantages of this method are the small overhead cost of programming and very fast execution times, robust behavior near chaotic regions that leads to full convergence for given family of quasiperiodic orbits and the minimal memory required to store these orbits. This method reduces the calculations required for searching two-dimensional invariant tori to a search for closed orbits, which are the intersection of the invariant tori with the Poincaré sections. Truncated Fourier series are employed to represent these closed orbits. The flow of the differential equation on the invariant tori is reduced to maps between the consecutive Poincaré maps. A Newton iteration scheme utilizes the invariance of the circles of the maps on these Poincaré sections in order to find the Fourier coefficients that define the circles to any given accuracy. A continuation procedure that uses the incremental behavior of the Fourier coefficients between close quasiperiodic orbits is utilized to extend the results from a single orbit to a family of orbits. Quasi-halo and Lissajous families of the Sun–Earth RTBP around the L2 libration point are obtained via this method. Results are compared with the existing literature. A numerical method to transform these orbits from the RTBP model to the real ephemeris model of the Solar System is introduced and applied.     

Apparatus Weighting Functions in measuring the line-of-sight velocities by the ‘center of gravity’ method

The conception of the Apparatus Weighting Function (AWF), numerically characterizing the contributions of different layers of the solar atmosphere to indications of the apparatus used is introduced. For the detection of line-of-sight velocities, measuring the shifts of the center of gravity of a spectral line profile, AWFs have been calculated for several single lines used by the authors in their observations of the photospheric velocity field. A comparison of AWFs is given for instruments, based on the principles of measuring both the center of gravity shifts and intensity differences in the line wings.     

Imaging of an unknown sector of Mercury (260–350°W) at the Special Astrophysical Observatory of the Russian Academy of Sciences using the short-exposure method

A series of observations of Mercury were performed at the Special Astrophysical Observatory using the short-exposure method to image a hitherto unknown part of the Hermean surface. Several thousand electronic frames of the planet were taken during its morning elongation in the period from November 20–24, 2006. The phase angle of Mercury varied from 103° to 80°, and the interval of planetocentric longitudes observed spanned from 260 to 350°W. Observations were made with a CCD camera attached to the 1-m Zeiss-1000 Ritchey-Chretien telescope operating with a KS-19 filter (short-wavelength border at 700 nm). The Hermean surface is known to be almost impossible to resolve on ordinary images. A reduction of a large number of frames taken with millisecond-long exposures made it possible to obtain a rather sharp image of the observed part of the Hermean surface. One of the primary aims of new observations was to have a general outline of the basin earlier found by one of the authors (L. Ksanfomaliti). We are the first to image this giant feature. The size of its inner part exceeds that of the largest lunar Mare — Mare Imbrium, however, unlike the latter the studied basin is of impact origin. The synthesized images reveal a number of large impact craters of various ages, as well as smaller features. The highest resolution achieved corresponds to the diffraction limit for the instrument employed, or about 100 km on the Hermean surface.     

Predicting monthly sunspot numbers of solar cycle 23 by the method of “similar cycles”

We briefly describe the concept and method of “similar cycles” to be used in sunspot prediction. We have checked on the reliability of this method and made the comparison of the predictions and observations for the 23rd solar activity cycle.     

The Hori–Deprit method for averaged motion equations of the planetary problem in elements of the second Poincaré system

We consider an algorithm to construct averaged motion equations for four-planetary systems by means of the Hori–Deprit method. We obtain the generating function of the transformation, change-variable functions and right-hand sides of the equations of motion in elements of the second Poincaré system. Analytical computations are implemented by means of the Piranha echeloned Poisson processor. The obtained equations are to be used to investigate the orbital evolution of giant planets of the Solar system and various extrasolar planetary systems.     

Periodicity of the solar radius revisited by using empirical mode decomposition and the Lomb–Scargle method

Using the Hilbert–Huang transform and the Lomb–Scargle method, we investigate periodicities in the daily solar radius data during the time interval from February 1978 to October 1999 derived from Calern Observatory. The following prominent periods are found:(1) the rotation cycle signal;(2) several mid-term periods including 122, 162.9 and 225 days, annual-variation periodicities(319 and 359days), quasi-triennial oscillations(3.46 and 3.94 years);(3) the 11-year Schwabe cycle, which is in anti-phase with solar activity. This result indicates that the strong magnetic field associated with the Sun has a greater inhibitive effect on the radius variation.     

Automated estimation of stellar fundamental parameters from low resolution spectra： the PLS method

PLS （Partial Least Squares regression） is introduced into an automatic estimation of fundamental stellar spectral parameters. It extracts the most correlative spectral component to the parameters （Teff, log g and [Fe/H]）, and sets up a linear regression function from spectra to the corresponding parameters. Considering the properties of stellar spectra and the PLS algorithm, we present a piecewise PLS regression method for estimation of stellar parameters, which is composed of one PLS model for Teff, and seven PLS models for log g and [Fe/H] estimation. Its performance is investigated by large experiments on flux calibrated spectra and continuum normalized spectra at different signal-to-noise ratios （SNRs） and resolutions. The results show that the piecewise PLS method is robust for spectra at the medium resolution of 0.23 nm. For low resolution 0.5 nm and 1 nm spectra, it achieves competitive results at higher SNR. Experiments using ELODIE spectra of 0.23 nm resolution illustrate that our piecewise PLS models trained with MILES spectra are efficient for O ～ G stars： for flux calibrated spectra, the systematic offsets are 3.8%, 0.14 dex, and -0.09 dex for Teff, log g and [Fe/H], with error scatters of 5.2%, 0.44 dex and 0.38 dex, respectively; for continuum normalized spectra, the systematic offsets are 3.8%, 0.12dex, and -0.13 dex for Teff, log g and [Fe/H], with error scatters of 5.2%, 0.49 dex and 0.41 dex, respectively. The PLS method is rapid, easy to use and does not rely as strongly on the tightness of a parameter grid of templates to reach high precision as Artificial Neural Networks or minimum distance methods do.     

Moment method for multiple scattering of solar Lα radiation in the nearby interstellar medium

The problem of solar L (1216 Å) photons scattered coherently by interplanetary medium is solved for a realistic density distribution using a simple three-stream division of the radiation field.     

A two-color CCD survey of the North Celestial Cap: I. The method

We describe technical aspects of an astrometric and photometric survey of the North Celestial Cap (NCC), from the Pole (δ=90°) to δ=80°, in support of the TAUVEX mission. This region, at galactic latitudes from ∼17° to ∼37°, has poor coverage in modern CCD-based surveys. The observations are performed with the Wise Observatory one-meter reflector and with a new mosaic CCD camera (LAIWO) that images in the Johnson–Cousins R and I bands a one-square-degree field with sub-arcsec pixels. The images are treated using IRAF and SExtractor to produce a final catalogue of sources. The astrometry, based on the USNO-A2.0 catalogue, is good to ∼1 arcsec and the photometry is good to ∼0.1 mag for point sources brighter than R=20.0 or I=19.1 mag. The limiting magnitudes of the survey, defined at photometric errors smaller than 0.15 mag, are 20.6 mag (R) and 19.6 (I). We separate stars from non-stellar objects based on the object shapes in the R and I bands, attempting to reproduce the SDSS star/galaxy dichotomy. The completeness test indicates that the catalogue is complete to the limiting magnitudes.     

On the elimination of the critical terms of a first order theory of Jupiter perturbed by Saturn carried out through Hori's method and Poincaré canonical variables

The elimination of the critical terms inside the Hamiltonian of a first order theory of Jupiter perturbed by Saturn is carried out through the Poincaré canonical variables and the Hori's procedure. Powers of the eccentricities and the sines of inclinations which are>3 are neglected. The Poincaré variablesL ₁,H ₁,P ₁, ₁,K ₁,Q ₁ of Jupiter which result from a previous elimination of the short period terms are expressed in terms of the Poincaré canonical variablesL _u ,H _u ,P _u , _u ,Q _u ;u=1, 2; index 1 Jupiter, index 2 Saturn resulting from the elimination of the short period and critical terms. The differential equations inH _u ,P _u ,K _u ,Q _u are solved through the method of Lagrange and the analytical expressions ofL ₁,H ₁,P ₁, ₁,K ₁,Q ₁ as functions of timet are finally obtained.     

Searching for r-process-enhanced stars in the LAMOST surveyⅠ:the method

The abundance patterns of r-process-enhanced stars contain key information required to constrain the astrophysical site(s)of r-process nucleosynthesis,and to deepen our understanding of the chemical evolution of our Galaxy.To expand the sample of known r-process-enhanced stars,we have developed a method to search for candidates in the LAMOST medium-resolution(R7500)spectroscopic survey by matching the observed spectra to synthetic templates around the EuⅡline at 6645.1 A.We obtain a sample of 13 metal-poor(-2.35<[Fe/H]<-0.91)candidates from 12209 unique stars with 32774 mediumresolution spectra.These candidates will be further studied by high-resolution follow-up observations in the near future.We describe some extensions of this effort to include larger samples of stars,in particular at lower metallicity,using the strength of the BaⅡline at 6496.9 A.     

Exact solution of the equation for the problem of diffuse reflection and transmission with a scattering function ω0(1 +x cos⊙) by the method of laplace transform and theory of linear singular integral equation

Neutrinos couple through a weak neutral current to the density of matter, in particular to the neutron density. Density fluctuations, or phonons, in the neutron fluid may be emitted or absorbed by neutrinos passing through the matter. At high densities, temperatures and neutrino energies the neutrino mean free paths for phonon emission and absorption can be 10⁶ cm. Significant changes in the neutrino momentum and energy accompany these processes. We present a model calculation for neutrino scattering by phonons, and representative numerical results for the neutrino mean free path and mean energy and momentum changes fork _B T andE _v both ranging from 1 to 27 MeV.Research supported by the National Research Council of Canada.