Time elements in rectangular coordinates

In a paper by the second author (Nacozy, 1981), various time elements are presented for use with the Sundman time transformation. In that paper, the time elements are given in terms of Keplerianorbital elements. We give here the corresponding time elements in terms ofrectangular coordinates. Extensive references are given in the previous paper and will be omitted here.We present additional numerical experiments comparing the use of time elementsand time transformationstogether with the use of time transformationsalone. The results indicate a reduction in computational error when time elements are used.     

Applications to stellar and galactic dynamics

Computation and a wealth of new observational techniques have reinvigorated dynamical studies of galaxies and star clusters. These objects are examples of the gravitationaln-body problem withn in the range from a few hundred to 10¹¹. Relaxation effects dominate at the low end and are completely negligible at the high end. The gravitationaln-body problem is chaotic, and the principal challenge in doing physics where that problem is involved (whether computationally or with analytic theory) is to ensure that chaos has not vitiated the results. Enforcing a Liouville theorem accomplishes this with collision-free large-n problems, but equivalent recipes are not in common use for smallern. We describe some important insights and discoveries that have come from computation in stellar dynamics, discuss chaos briefly, and indicate the way the physics that comes up in different astronomical contexts is addressed in numerical methods currently in use. Graphics is a vital part of any computational approach. The long range prospects are very promising for continued high scientific productivity in stellar dynamics.     

Dust attenuation in starburst galaxies determined by measuring the dependence of the optical color indices on galaxy inclination

We use optical color indices (colors) from the SDSS database to study the effect of dust in starburst galaxies by mea‐suring the dependence of colors on galaxy inclination. Starburst galaxies with ongoing star formation, are rich with metals/dust and are, therefore, an excellent objects for studying the effect of dust in galaxies. They are selected using the [O III ]λ 5007/Hα vs. [N II ]λ 6584/Hβ diagram, that is, the BPT‐diagram. We use Kauffmann's empirical demarcation line in the BPT‐diagram to exclude galaxies with active galactic nuclei (AGN) from the sample because they have different physical and dust properties from normal galaxies. The sample is divided into bins according to galaxy stellar mass and 4000 Å break (which is a coarse measure of a galaxy star formation history; SFH) and the reddening with inclination is studied as a function of these two physical parameters. Assuming that the dust effect is negligible in the SDSS z ‐band, we derive the attenuation curves for these galaxies. We fit the attenuation curves with a simple power law and use power law index to interpret the relative distribution of dust and stars in the starburst galaxies (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Elemental abundance analyses with DAO spectrograms: XXXIII. β UMa (A0mA1 IV‐V), α Dra (A0 III), π Dra (A2 IIIs), and κ Cep (B9 III)

This paper presents extended analyses of β UMa (A0mA1 IV‐V), α Dra (A0 III), π Dra (A2 IIIs), and κ Cep (B9 III) which have previously been studied in this series. α Dra is a metal‐poor star while κ Cep has solar abundances. Both β UMa and π Dra are Am stars. Whenever possible, more accurate and precise gf values replace older values. High S/N (200+) and high dispersion Dominion Astrophysical Observatory spectrograms to the red of previously obtained spectra supplement the observations. The derived rotational velocities are 45, 25, 26, and 23 km s^–1, respectively. These LTE fine analyses use the ATLAS9 and the WIDTH9 programs of R. L. Kurucz. The results of the extended and the previous analyses are in good agreement. Thus in the past decade a significant improvement in the system of gf values has not been achieved although for many lines there have been changes. The use of additional regions has increased the quality of some results (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Eclipsing Binary bx Andromedae and its Orbital Period Behaviour

The orbital period variations of the eclipsing binary BX And are examined analysing its (O–C) diagram 1) with the standard method, in which the minima times are fitted by the quadratic ephemeris combined with an assumed light-time effect, and 2) with the first continuous method. The results from the use of the two methods are, as was expected, different.     

An exact solution of transfer equations for interlocked multiplets

The transfer equations for non-coherent scattering arising from interlocking of principal lines without redistribution is exactly solved in a very simple way by Laplace tranform and Wiener-Hopf technique which are easily applied by the use of the new representation ofH-functions obtained recently by the author (1977). The emergent intensity in therth line is expressed in terms of anH-function and a Cauchy type integral admitting of closed form evaluation.     

Superconducting critical field in cold magnetic white dwarfs and in neutron stars

For an evaluation of the superconducting critical fieldH _c as a function of the mass-density in the external layers of cold magnetic white dwarfs and in the superconducting proton fluid in neutron stars, we use the solution of a differential equation involvingH _c as a function of the pressure. The differential equation and its solution are obtained by pure thermodynamic way.Finally other thermodynamic quantities are calculated for the above superconducting astrophysical systems.     

Some spectroscopic observations of visual binaries

The use of a coudé spectrograph for securing the high-resolution spectrograms necessary to follow the slow variations of radial velocity exhibited by visual binaries is discussed. Recent observations, using the spectrograph at the coudé focus of the Dominion Astrophysical Observatory's 48-in. reflector, are then presented for the systems ofα UMa,ɛ Hya,β LMi andγ Leo.     

An analytic satellite theory using gravity and a dynamic atmosphere

An analytical solution is given for the motion of an artifical Earth satellite under the combined influences of gravity and atmospheric drag. The gravitational effects of the zonal harmonicsJ ₂,J ₃, andJ ₄ are included, and the drag effects of any arbitrary dynamic atmosphere are included. By a dynamic atmosphere, we mean any of the modern empirical models which use various observed solar and geophysical parameters as inputs to produce a dynamically varying atmosphere model. The subtleties of using such an atmosphere model with an analytic theory are explored, and real world data is used to determine the optimum implementation. Performance is measured by predictions against real world satellites. As a point of reference, predictions against a special perturbations model are also given.     

Magnetic fields and quasi-periodic oscillations of black hole radiation

Various relations are found between the key parameters of black holes and active galactic nuclei. Some have a statistical property, others follow from the theoretical consideration of the evolution of these objects. In this paper we use a recently discovered empirical relation between the characteristic frequency of quasi-periodic oscillations of radiation ν _br of black holes, their masses and matter accretion rates to determine the magnetic field strength B _H at the black hole event horizon. Since the characteristic frequency can be determined from observations, the use of a new relation for the estimations of magnetic field B _H can yield more definite results, since we are decreasing the number of the unknown or poorly-determined parameters of objects (it especially concerns the accretion rate Ṁ). The typical values which we have found are B _H ≃ 10⁸G for the stellar mass black holes, and B _H ≃ 10⁴G for the supermassive black holes. Besides, we demonstrate that if the linear polarization of an object is caused by the radiation of a magnetized accretion disk, then the degree of observable polarization is p ∼ ν _br ^−1/2.     

The Spectrum of Torsional Oscillations of the Moon

The diagnostic potentialities of the torsional oscillations for probing the structure of the interiors of the Moon are investigated. Models with no core, a liquid core, and a solid core are considered. The profiles of compressional and shear wave velocities V _P and V _S for the lunar interior estimated by Bills and Ferrari (1977), Goins et al. (1981), and Nakamura (1983) from the Apollo lunar seismic network are used. For all these models, the periods of torsional oscillations for n = 2–100 and four overtones have been calculated. The derivatives of the dimensionless eigenfrequency with respect to the dimensionless shear modulus and density are calculated and tabulated for use. These data can be used to determine corrections to the model density and shear modulus distributions due to their small change. The damping of torsional oscillations is studied. Several trial radial distributions of the dissipative function Q are considered.     

Formal Integrals and Nekhoroshev Stability in a Mapping Model for the Trojan Asteroids

A symplectic mapping model for the co-orbital motion (Sándor et al., 2002, Cel. Mech. Dyn. Astr. 84, 355) in the circular restricted three body problem is used to derive Nekhoroshev stability estimates for the Sun–Jupiter Trojans. Following a brief review of the analytical part of Nekhoroshev theory, a direct method is developed to construct formal integrals of motion in symplectic mappings without use of a normal form. Precise estimates are given for the region of effective stability based on the optimization of the size of the remainder of the formal series. The stability region found for t=10¹⁰ yrs corresponds to a libration amplitude D_p=10.6°. About 30% of asteroids with accurately known proper elements (Milani, 1993, Cel. Mech. Dyn. Astron. 57, 59), at low eccentricities and inclinations, are included within this region. This represents an improvement with respect to previous estimates given in the literature. The improvement is due partly to the choice of better variables, but also to the use of a mapping model, which is a simplification of the circular restricted three body problem.     

Non-integrability of first order resonances in Hamiltonian systems in three degrees of freedom

The normal forms of the Hamiltonian 1:2:ω resonances to degree three for ω = 1, 3, 4 are studied for integrability. We prove that these systems are non-integrable except for the discrete values of the parameters which are well known. We use the Ziglin–Morales–Ramis method based on the differential Galois theory.     

Photometric study of MM Cas

TheU, B, andV photometric observations of the eclipsing binary MM Cas have been presented and discussed. The photometric elements have been derived. By use of the colour indicesU-B andB-V, the spectral types of the systemic components are estimated. An examination of all available times of minimum light of MM Cas does not reveal any change in its orbital period.     

Search for Optical Identifications in the 5C1 Radio Survey

Identifications of 5CI radio sources with optical objects are given. The identification rates amount to 44 and 30 per cent up to the limiting magnitude of about 21^m in R and B, respectively. The objects are to about equal parts galaxies, blue starlike objects, and “unclassified objects” (presumably mostly faint galaxies and less pronounced blue objects). For every proposed identification a reliability and for the identification samples the reliability and the completeness are given. Some inaccuracies in the use of a statistical method, proposed in a previous paper, have been removed; two additional means of statistical treatment have been applied to discuss the data.     

The maximum temperatures of interstellar grains

The maximum temperature a typical interstellar grain will attain upon absorption of a photon or chemical band formation of molecules on its surface is calculated by considering the exact Debye theory of dielectrics. Other contributions to the specific heats of solids are discussed. It is shown that the use of the approximate Debye theory whereC _v is proportional toT will lead to serious errors in the calculation of velocities of desorption of molecules from grain surfaces.     

Use of the FITS World Coordinate System by STEREO/SECCHI

The World Coordinate System (WCS) is a standard for embedding coordinate information in a Flexible Image Transport System (FITS) header. Its first extensive use within solar physics is by the Sun Earth Connections Coronal and Heliospheric Investigation (SECCHI) telescope suite onboard the Solar Terrestrial Relations Observatory (STEREO). The WCS formalism assists in SECCHI data analysis in several ways: First of all, the spherical effects associated with the extremely wide fields-of-view of the Heliospheric Imager (HI) telescopes can be handled in a completely unambiguous and standard fashion. Of particular importance is that WCS positional keywords allow spacecraft-ephemeris information to be embedded within the FITS header without depending on mission-specific keywords. Ephemeris data is critical to the three-dimensional analysis that the STEREO mission is designed for. We also show how the WCS software in SolarSoft\textsf{SolarSoft} can be used to relate STEREO data to other missions such as the Solar and Heliospheric Observatory (SOHO). The ability of WCS to support a parallel celestial right ascension (R.A.)/declination (Dec) coordinate system and the use of WCS for COR1 synoptic maps are also discussed. The advantages that STEREO derived from WCS can equally be applied to other solar missions, in particular Solar Orbiter, and should be adopted by all future missions.     

Inhomogeneities in the circumstellar envelope of the A0E herbig star AB aur

Simultaneous high-resolution spectroscopy in H andUBVRI polarimetric observations are proposed as an effective method for the search for circumstellar inhomogeneities in A0-type Herbig stars. The new results for AB Aur are presented as a successful example of the use of this method. The analysis of about 100 CCD H profiles (R = 30 000) and more than 150 polarimetric measurements obtained in January, 1994 allowed to discover a long-lived stream-like inhomogeneity in the circumstellar gaseous envelope.     

Galaxy clustering in two dimensions: Some analytic results

The key results of Fall, Saslaw, and Kandrup regarding the early stages of galaxy clustering are reformulated here for the model problem of two-dimensional gravity with anr ^–1-interaction force. This should lead to new insights into the various physical processes involved and, more importantly, may prove of some use in interpreting numerical results obtained from two-dimensionalN-body simulations. The calculations suggest that, for a two-, rather than three-dimensional system, the correlational energy density should grow more rapidly with time, but should exhibit only a weak logarithmic dependence upon the typical particle speed. Various other measures of the clustering are independent of the dimensionality.     

An implementation ofN-body chain regularization

The chain regularization method (Mikkola and Aarseth 1990) for high accuracy computation of particle motions in smallN-body systems has been reformulated. We discuss the transformation formulae, equations of motion and selection of a chain of interparticle vectors such that the critical interactions requiring regularization are included in the chain. The Kustaanheimo-Stiefel (KS) coordinate transformation and a time transformation is used to regularize the dominant terms of the equations of motion. The method has been implemented for an arbitrary number of bodies, with the option of external perturbations. This formulation has been succesfully tested in a generalN-body program for strongly interacting subsystems. An easy to use computer program, written inFortran, is available on request.