General planetary theory in elliptic functions

It is shown that the first-order general planetary theory, i.e. the theory without secular terms, developed in (Brumberg and Chapront, 1973) may be re-constructed and presented by the series in powers of the eccentricity and inclination variables with the closed form coefficients expressed in terms of elliptic functions. The intermediate solution of the zero degree in eccentricities and inclinations has been given explicitly with the aid of elliptic functions and the Hansen type quadratures with trigonometric function kernels. In determining the first and higher degree terms in eccentricities and inclinations one meets the Hansen type quadratures with elliptic function kernels. The secular evolution is described by the autonomous polynomial differential system.     

A third-order intermediate orbit for planetary theory

By use of a new canonical transformation procedure, a third-order intermediary for planetary motion is developed. The intermediary contains all contributions that arise from the assumption of circular, coplanar orbits for the disturbing masses. The results are expressible in terms of elliptic integrals of the first, second, and third kinds.Proceedings of the Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets. Facultés universitaires Notre Dame de la Paix, Namur, Belgium, 28–31 July, 1980.     

Precession/nutation solution consistent with the general planetary theory

In the present paper the equations of the translatory motion of the major planets and the Moon and the Poisson equations of the Earth’s rotation in Euler parameters are reduced to the secular system describing the evolution of the planetary and lunar orbits (independent of the Earth’s rotation) and the evolution of the Earth’s rotation (depending on the planetary and lunar evolution). Hence, the theory of the Earth’s rotation is presented by means of the series in powers of the evolutionary variables with quasi-periodic coefficients.     

Planetary theories with the aid of the expansions of elliptic functions

For coplanar circular orbits, the mutual perturbations between two bodies can be expressed in term of the argument of Jacobian elliptic functions instead of the difference of the mean longitudes. For a given pair of planets, such a change of time variable improves the convergence of the developments. At the first order of planetary masses an integration of Lagrange's equations for the osculating elements is performed. When compared to classical developments the results are reduced by an important factor. The method is then extended to the mutual perturbations of Jupiter and Saturn, at any order of planetary masses, either with Fourier series with two arguments, or with one argument solely, taking advantage of the close commensurability of the mean motions.     

Helium recombination spectra as temperature diagnostics for planetary nebulae

Electron temperatures derived from the He  i recombination line ratios, designated T _e(He  i ), are presented for 48 planetary nebulae (PNe). We study the effect that temperature fluctuations inside nebulae have on the T _e(He  i ) value. We show that a comparison between T _e(He  i ) and the electron temperature derived from the Balmer jump of the H  i recombination spectrum, designated T _e(H  i ), provides an opportunity to discriminate between the paradigms of a chemically homogeneous plasma with temperature and density variations, and a two-abundance nebular model with hydrogen-deficient material embedded in diffuse gas of a 'normal' chemical composition (i.e. ∼solar), as the possible causes of the dichotomy between the abundances that are deduced from collisionally excited lines and those deduced from recombination lines. We find that T _e(He  i ) values are significantly lower than T _e(H  i ) values, with an average difference of  〈 T _e(H  i ) − T _e(He  i )〉= 4000 K  . The result is consistent with the expectation of the two-abundance nebular model but is opposite to the prediction of the scenarios of temperature fluctuations and/or density inhomogeneities. From the observed difference between T _e(He  i ) and T _e(H  i ), we estimate that the filling factor of hydrogen-deficient components has a typical value of 10⁻⁴. In spite of its small mass, the existence of hydrogen-deficient inclusions may potentially have a profound effect in enhancing the intensities of He  i recombination lines and thereby lead to apparently overestimated helium abundances for PNe.     

Orientation of planetary nebulae within the Galaxy

Narrow-band CCD images of 209 axially symmetrical planetary nebulae (PNe) have been examined in order to determine the orientation of their axes within the disc of the Galaxy. The nebulae have been divided into the bipolar (B) and elliptical (E) PNe morphological types, according to the scheme of Corradi &38; Schwarz. In both classes, contrary to the results of Melnick &38; Harwit and Phillips we do not find any strong evidence for non-random orientations of the nebulae in the Galaxy. Compared with previous work in this field, the present study takes advantage of the use of larger and morphologically more homogeneous samples and offers a more rigorous statistical analysis.     

Accurate coordinates of planetary nebulae

Accurate optical coordinates of 734 PNe, measured on the charts of the Digitized Palomar Sky Survey, are presented. As a result of the discussion about the external accuracy the constants –0.8″ in RA and +0.8″ in DEC should be added to the coordinates measured by us. They were used but rounded off already in CGPN(2000). The list and measurements of new 31 candidates of central stars are given which might be interesting for stellar evolution.     

The low-excitation structures of planetary nebulae

The low excitation properties of the planetary nebula (PN) NGC 6720 are known to be unusual, and to imply large ring/core emission ratios. We point out that such characteristics are by no means confined to this source alone, and that high ratios may occur in a large fraction of elliptical and circular PNe. Such trends may arise because of the presence of thin low-excitation emission sheets 'wrapped' within and around the primary outflows. The widths of such shells are required to be exceedingly small, and may (for certain cases) be of order ≪10⁻² pc. Such a mechanism appears capable of explaining most of the observed emission properties, and may arise through shock interaction between differing envelopes. Alternative explanations in terms of bipolar or cylindrical outflows are shown to be implausible.     

FLAIR observations of planetary nebulae in the Large Magellanic Cloud

This paper presents new observations of 97 planetary nebulae in the Large Magellanic Cloud (LMC) obtained using the FLAIR system on the UK 1.2-m Schmidt Telescope. These nebulae are mostly at the fainter end of the known population, and about 75 per cent have not been observed before in spectroscopic mode. Radial velocities have been measured using cross-correlation techniques, and represent an increase of 66 per cent in the sample of LMC planetary nebulae with known radial velocities. The major line ratios are given, and are analysed in conjunction with published data. One-quarter of the faint nebulae are Type I objects with very strong [N II ] and [S II ] lines; most of the other faint nebulae have low density, low excitation and relatively strong [S II ] lines.     

The optical spectrum of the planetary nebula NGC 6543

With the Hamilton echelle spectrograph at the Lick Observatory, emission-rich spectral lines of the planetary nebula NGC 6543 were secured in the wavelength range from 3550 to 10 100 Å. We chose two bright regions, ∼8 arcsec east and ∼13 arcsec north of the central star, the physical conditions and chemical abundances of which may differ as a result of the different physical characteristics involving the mass ejection of different epochs. By combining Hamilton echelle observations with archive UV data secured with the International Ultraviolet Explorer ( IUE ), we obtain improved diagnostics and chemical compositions for the two observed regions. The diagnostic diagram gives the average value of T _e=8000∼8300 K, and the electron number density near N _e∼5000 cm⁻³ for most ions, while some low-excitation lines indicate much higher temperatures, i.e. T _e∼10 000 K. With the construction of a photoionization model, we try to fit the observed spectra in a self-consistent way: thus, for most elements, we employ the same chemical abundances in the nebular shell; and we adopt an improved Sobolev approximation model atmosphere for the hydrogen-deficient Wolf–Rayet type central star. Within the observational errors, the chemical abundances do not seem to show any positional variation except for helium. The chemical abundances of NGC 6543 appear to be the same as in average planetary nebulae. The progenitor star may have been an object of one solar mass, most of the heavier elements of which were less plentiful than in the Sun.     

Dynamical and ionization structure of planetary nebulae in three dimensions. A simulation for NGC3132

Using a numerically accurate radiation-gas dynamical method we investigate the winds scenario for aspherical planetary nebulae (PNe). Our model includes the interaction of two winds: as low high mass-loss rate wind (a `super wind'); and a fast wind; low mass-loss rate wind. Our model also includes the evolution of the UV spectrum of the PNe centeral star. As stated in the section3 of Paper I (Ganbari and Khesali, 2001), we consider a three dimensional density distribution ρ(r,θφ for the super wind, in this way we enter the effects of cooling and heating mechanisms in our model. Taking into account the above assumptions, we introduce the code (DIS3D) and numerically we study the dynamical and ionization properties of the planetary nebula NGC3132. We show that it is possible by simulations to reproduce the shape of PNe in three dimensions, and calculating the physical quantities throughout the entire nebula. This revised version was published online in July 2006 with corrections to the Cover Date.     

Detecting planets in planetary nebulae

We examine the possibility of detecting signatures of surviving Uranus/Neptune-like planets inside planetary nebulae. Planets that are not too close to the stars (orbital separation larger than ∼5 au) are likely to survive the entire evolution of the star. As the star turns into a planetary nebula, it has a fast wind and strong ionizing radiation. The interaction of the radiation and wind with a planet may lead to the formation of a compact condensation or tail inside the planetary nebula, which emits strongly in H α , but not in [O  iii ]. The position of the condensation (or tail) will change over a time-scale of ∼10 yr. Such condensations might be detected with currently existing telescopes.     

Eccentricity generation in hierarchical triple systems: the planetary regime

In previous papers, we developed a technique for estimating the inner eccentricity in hierarchical triple systems, with the inner orbit being initially circular. We considered systems with well-separated components and different initial setups (e.g., coplanar and non-coplanar orbits). However, the systems we examined had comparable masses. In the present paper, the validity of some of the formulae derived previously is tested by numerically integrating the full equations of motion for systems with smaller mass ratios (from 10⁻³ to 10³, i.e. systems with Jupiter-sized bodies). There is also discussion about HD 217107 and its planetary companions.     

The determination of progenitor masses for planetary nebulae

We have evaluated the likely progenitor masses M _PG of nebulae having elliptical, circular and bipolar morphologies, using observed ratios between the populations of these sources, and deduced central star mass functions. We find that most bipolar nebulae (BPNe) are likely to arise from progenitors having mass M _PG>2.3 M_⊙ and spectral types earlier than A3.2, whilst circular sources are associated with progenitors of mass 1.0 M_⊙< M _PG<1.2 M_⊙ and spectral range G1.9–F7.8 . Elliptical sources arise from intermediate-mass progenitors. The procedures employed to determine these values are relatively insensitive to uncertainties in scaleheights and population ratios, and completely insensitive to uncertainties in the distance scale. They are, however, dependent upon the precise forms adopted for the initial–final and central star mass functions, and we discuss the sensitivity of M _PG to uncertainties in these functions.