Interacting Winds in Eclipsing Symbiotic Systems – The Case Study of EG Andromedae

We report the mathematical representation of the so called eccentric eclipse model, whose numerical solutions can be used to obtain the physical parameters of a quiescent eclipsing symbiotic system. Indeed the nebular region produced by the collision of the stellar winds should be shifted to the orbital axis because of the orbital motion of the system. This mechanism is not negligible, and it led us to modify the classical concept of an eclipse. The orbital elements obtained from spectroscopy and photometry of the symbiotic EG Andromedae were used to test the eccentric eclipse model. Consistent values for the unknown orbital elements of this symbiotic were obtained. The physical parameters are in agreement with those obtained by means of other simulations for this system.     

The importance of the Lie algebra so (4, 2) for the Kepler problem

It is shown that the Lie algebra so(4, 2) is characteristic for the three dimensional Keplerian motion provided the eccentric anomaly is used as the independent variable. This algebra generates all the integrals of motion and yields the guiding principle for reformulating all the Keplerian formulas.Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.     

Spectroscopic binaries near the North Galactic Pole paper 16: HD 116093

Photoelectric radial-velocity measurements show that HD 116093 is a double-lined spectroscopic binary in a very eccentric 53-day orbit. Very little else is known about the system, but circumstantial evidence is consistent with the hypothesis that the components’ types are near to F3 V and F8 V. If that is so, the orbit must be seen very nearly edge-on; a search for eclipses is warranted and an ephemeris for them is given.     

The formation of an eccentric gap in a gas disc by a planet in an eccentric orbit

We investigate the effect of a planet on an eccentric orbit on a two-dimensional low-mass gaseous disc. At a planet eccentricity above the planet's Hill radius divided by its semimajor axis, we find that the disc morphology differs from that exhibited by a disc containing a planet in a circular orbit. An eccentric gap is created with eccentricity that can exceed the planet's eccentricity and precesses with respect to the planet's orbit. We find that a more massive planet is required to open a gap when the planet is on an eccentric orbit. We attribute this behaviour to spiral density waves excited at corotation resonances by the eccentric planet. These act to increase the disc's eccentricity and exert a torque opposite in sign to that exerted by the Lindblad resonances. The reduced torque makes it more difficult for waves driven by the planet to overcome viscous inflow in the disc.     

The eccentricities of the barium stars

We investigate the eccentricities of barium (Ba  ii ) stars formed via a stellar wind accretion model. We carry out a series of Monte Carlo simulations using a rapid binary evolution algorithm, which incorporates full tidal evolution, mass loss and accretion, and nucleosynthesis and dredge-up on the thermally pulsing asymptotic giant branch. We follow the enhancement of barium in the envelope of the accreting main-sequence companion and dilution into its convective envelope once the star ascends the giant branch.
The observed eccentricities of Ba  ii stars are significantly smaller than those of an equivalent set of normal red giants but are nevertheless non-zero. We show that such a distribution of eccentricities is consistent with a wind accretion model for Ba  ii star production with weak viscous tidal dissipation in the convective envelopes of giant stars. We successfully model the distribution of orbital periods and the number of observed Ba  ii stars. The actual distribution of eccentricities is quite sensitive to the strength of the tides, so that we are able to confirm that this strength is close to, but less than, what is expected theoretically and found with alternative observational tests. Two systems – one very short-period but eccentric, and one long-period and highly eccentric – still lie outside the envelope of our models, and so require a more exotic formation mechanism. All our models, even those which were a good fit to the observed distributions, overproduced the number of high-period barium stars, a problem that could not be solved by some combination of the three parameters: tidal strength, tidal enhancement and wind accretion efficiency.     

Chaotic zone boundary for low free eccentricity particles near an eccentric planet

We consider particles with low free or proper eccentricity that are orbiting near planets on eccentric orbits. Through collisionless particle integration, we numerically find the location of the boundary of the chaotic zone in the planet's corotation region. We find that the distance in semimajor axis between the planet and boundary depends on the planet mass to the 2/7 power and is independent of the planet eccentricity, at least for planet eccentricities below 0.3. Our integrations reveal a similarity between the dynamics of particles at zero eccentricity near a planet in a circular orbit and with zero free eccentricity particles near an eccentric planet. The 2/7th law has been previously explained by estimating the semimajor at which the first-order mean motion resonances are large enough to overlap. Orbital dynamics near an eccentric planet could differ due to first-order corotation resonances that have strength proportional to the planet's eccentricity. However, we find that the corotation resonance width at low free eccentricity is small; also the first-order resonance width at zero free eccentricity is the same as that for a zero-eccentricity particle near a planet in a circular orbit. This accounts for insensitivity of the chaotic zone width to planet eccentricity. Particles at zero free eccentricity near an eccentric planet have similar dynamics to those at zero eccentricity near a planet in a circular orbit.     

Properties of the solar nebula and the origin of the moon

The basic geochemical model of the structure of the Moon proposed by Anderson, in which the Moon is formed by differentiation of the calcium, aluminium, titanium-rich inclusions in the Allende meteorite, is accepted, and the conditions for formation of this Moon within the solar nebula models of Cameron and Pine are discussed. The basic material condenses while iron remains in the gaseous phase, which places the formation of the Moon slightly inside the orbit of Mercury. Some condensed metallic iron is likely to enter the Moon in this position, and since the Moon is assembled at a very high temperature, it is likely to have been fully molten, so that the iron can remove the iridium from the silicate material and carry it down to form a small core. Interactions between the Moon and Mercury lead to the present rather eccentric Mercury orbit and to a much more eccentric orbit for the Moon, reaching past the orbit of the Earth, establishing conditions which are necessary for capture of the Moon by the Earth. In this orbit the Moon, no longer fully molten, will sweep up additional material containing iron oxide. This history accounts in principle for the two major ways in which the bulk composition of the Moon differs from that of the Allende inclusions.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April 1973.     

Spectral observations of 19 weathered and 23 fresh NEAs and their correlations with orbital parameters

Results of our visible to near-infrared spectrophotometric observations of 41 near-Earth asteroids (NEAs) are reported. These moderate-resolution spectra, along with 14 previously published spectra from our earlier survey [Hicks, M.D., Fink, U., Grundy, W.M., 1998. Icarus 133, 69-78] show a preponderance of spectra consistent with ordinary chondrites (23 NEAs with this type of spectrum, along with 19 S-types and 13 in other taxonomic groups). There exists statistically significant evidence for orbit-dependent trends in our data. While S-type NEAs from our survey reside primarily in (1) Amor orbits or (2) Aten or Apollo orbits which do not cross the asteroid main-belt, the majority of objects with spectra consistent with ordinary chondrites in our survey are in highly eccentric Apollo orbits which enter the asteroid main-belt. This trend toward fresh, relatively unweathered NEAs with ordinary chondrite type spectra in highly eccentric Apollo orbits is attributed to one or a combination of three possible causes: (1) the chaotic nature of NEA orbits can easily result in high eccentricity orbits/large aphelion distances so that they can enter the collisionally enhanced environment in the main-belt, exposing fresh surfaces, (2) they have recently been injected into such orbits after a collision in the main-belt, or (3) such objects cross the orbits of several terrestrial planets, causing tidal disruption events that expose fresh surfaces.     

Eccentric discs in binaries with intermediate mass ratios: superhumps in the VY Sculptoris stars

We investigate the role of the eccentric disc resonance in systems with mass ratios q ≳1/4, and demonstrate the effects that changes in the mass flux from the secondary star have upon the disc radius and structure. The addition of material with low specific angular momentum to the outer edge of a disc restricts that disc radially. Should the mass flux from the secondary be reduced, it is possible for the disc in a system with mass ratio as large as 1/3 to expand to the 3:1 eccentric inner Lindblad resonance and for superhumps to be excited.     

Tilted accretion discs in cataclysmic variables: tidal instabilities and superhumps

We investigate the growth of tidal instabilities in accretion discs in a binary star potential, using three-dimensional numerical simulations. As expected from analytic work, the disc is prone to an eccentric instability provided that it is large enough to extend to the 3:1 resonance. The eccentric disc leads to positive superhumps in the light curve. It has been proposed that negative superhumps might arise from a tilted disc, but we find no evidence that the companion gravitational tilt instability can grow fast enough in a fluid disc to create a measurable inclination. The origin of negative superhumps in the light curves of cataclysmic variables remains a puzzle.     

The MOA catalogue of eclipsing binary stars in the Small Magellanic Cloud

We present a catalogue of 167 eclipsing binary stars in the Small Magellanic Cloud (SMC) derived from the data base of time-series photometry for 400 000 SMC stars acquired by the Microlensing Observations in Astrophysics (MOA) project during 1997. We print coordinates, ephemerides, magnitudes and light curves for the 35 new detections; similar data and finding charts are available electronically for the whole catalogue. The majority of periods lie within the range 0.4 to 20 d; six systems are possibly eccentric while 14 are probably or certainly so. The majority of the newly identified systems lie in the outer regions of the SMC.     

Decay of a highly eccentric satellite

The re-entry phase of a highly eccentric satellite is discussed. Numerical simulations allowing the prediction of the exact date of re-entry of a highly eccentric satellite are exposed.It is shown that under very particular circumstances the life of the satellite can be extended by a few days. The number of final revolutions of the rapidly contracting orbit depends critically on the air density between 70 km and 100 km.Re-entry of the European scientific satellite HEOS-1 predicted for 28 October, 1975 is near such a situation.     

Warp and eccentricity propagation in discs around black holes

We consider the inward propagation of warping and eccentric disturbances in discs around black holes under a wide variety of conditions. In our calculations, we use secular theories of warped and eccentric discs and assume the deformations to be stationary and propagating in a disc model similar to regions (a) and (b) of Shakura & Sunyaev discs. We find that the propagation of deformations to the innermost regions of the disc is facilitated for low viscous damping and high accretion rate. We relate our results to the possible excitation of trapped inertial modes, and to the observations of high-frequency quasi-periodic oscillations (QPOs) in black hole systems in the very high spectral state.     

Convergence of the expansions of the disturbing functions in the planar three-body planetary problem

In the framework of the planar three-body planetary problem, conditions are found for the absolute convergence of the expansions of the disturbing functions in powers of the eccentricities, with coefficients represented by trigonometric polynomials with respect to the mean, eccentric, or true anomaly of the inner planet. It is found that using the eccentric or true anomaly as the independent variable instead of the mean anomaly (or time) extends the holomorphy domain of the principal part of the perturbation functions. The expansions of the second parts converge in open bicircles, which admit values of the eccentricity of the inner planet in excess of the Laplace limit.     

PSR J1753−2240: a mildly recycled pulsar in an eccentric binary system

We report the discovery of PSR J1753−2240 in the Parkes Multibeam Pulsar Survey data base. This 95-ms pulsar is in an eccentric binary system with a 13.6-d orbital period. Period derivative measurements imply a characteristic age in excess of 1 Gyr, suggesting that the pulsar has undergone an episode of accretion-induced spin-up. The eccentricity and spin period are indicative of the companion being a second neutron star, so that the system is similar to that of PSR J1811−1736, although other companion types cannot be ruled out at this time. The companion mass is constrained by geometry to lie above 0.48 solar masses, although long-term timing observations will give additional constraints. If the companion is a white dwarf or a main-sequence star, optical observations may yield a direct detection of the companion. If the system is indeed one of the few known double neutron star systems, it would lie significantly far from the recently proposed spin-period/eccentricity relationship.     

Non-linear fluid dynamics of eccentric discs

A new theory of eccentric accretion discs is presented. Starting from the basic fluid-dynamical equations in three dimensions, I derive the fundamental set of one-dimensional equations that describe how the mass, angular momentum and eccentricity vector of a thin disc evolve as a result of internal stresses and external forcing. The analysis is asymptotically exact in the limit of a thin disc, and allows for slowly varying eccentricities of arbitrary magnitude. The theory is worked out in detail for a Maxwellian viscoelastic model of the turbulent stress in an accretion disc. This generalizes the conventional alpha viscosity model to account for the non-zero relaxation time of the turbulence, and is physically motivated by a consideration of the nature of magnetohydrodynamic turbulence. It is confirmed that circular discs are typically viscously unstable to eccentric perturbations, as found by Lyubarskij, Postnov & Prokhorov, if the conventional alpha viscosity model is adopted. However, the instability can usually be suppressed by introducing a sufficient relaxation time and/or bulk viscosity. It is then shown that an initially uniformly eccentric disc does not retain its eccentricity as had been suggested by previous analyses. The evolutionary equations should be useful in many applications, including understanding the origin of planetary eccentricities and testing theories of quasi-periodic oscillations in X-ray binaries.     

Tidal evolution of Dysnomia, satellite of the dwarf planet Eris

The past tidal evolution of the satellite Dysnomia of the dwarf planet Eris can be inferred from the current physical and orbital properties of the system. Preliminary considerations, which assumed a circular orbit for the satellite, suggested that the satellite formed close to the planet, perhaps as a result of a giant impact, and that it is thus unlikely that smaller satellites lie further out. However, if the satellite's orbit is eccentric, even if the eccentricity is very small, a qualitatively different past tidal evolution may be indicated. Early in the Solar System's history, the satellite may have been on a highly eccentric orbit much farther from the planet than it is now, suggestive of a capture origin. Additional satellites farther out cannot be ruled out.     

Book Review

The aim of this book is to present techniques for the study of motion of solar system objects in highly eccentric orbits. Instead of using the usual anomalies (mean, true, eccentric), the authors define and use a new kind of anomaly, the elliptic anomaly.In this way, it is possible, in a theory using perturbation series expansions, to make the ratio: (accuracy)/(number of needed terms), higher than in the classical techniques. The book consists of six chapters. The first chapter deals with the elliptic anomaly in the two-body problem and the second chapter presents the general technique to construct first-order perturbation theory in elliptic function expansions. The next three chapters deal with applications of the new technique to artificial satellites and asteroids, in highly eccentric orbits. The last chapter describes the basic algorithms of the theory.The tools developed in the book demand the use of computer algebra, which is implemented by means of Mathematica 3.0.The book is well written and the new technique is clearly presented and related to the existing techniques, making it useful to all those who use analytical or semi-analytical methods for the study of highly eccentric motion. Celestial Mechanics at High Eccentricities, Gordon and Breach Publishers, US$95, GBP 59, EUR 79, ISBN 90-5699-212-0     

On the evolution of giant protoplanets forming in circumbinary discs

We present the results of hydrodynamic simulations of Jovian mass protoplanets that form in circumbinary discs. The simulations follow the orbital evolution of the binary plus protoplanet system acting under their mutual gravitational forces, and forces exerted by the viscous circumbinary disc. The evolution involves the clearing of the inner circumbinary disc initially, so that the binary plus protoplanet system orbits within a low density cavity. Continued interaction between disc and protoplanet causes inward migration of the planet towards the inner binary. Subsequent evolution can take three distinct paths: (i) the protoplanet enters the 4 : 1 mean motion resonance with the binary, but is gravitationally scattered through a close encounter with the secondary star; (ii) the protoplanet enters the 4 : 1 mean motion resonance, the resonance breaks, and the planet remains in a stable orbit just outside the resonance; (iii) when the binary has initial eccentricity   e _bin≥ 0.2  , the disc becomes eccentric, leading to a stalling of the planet migration, and the formation of a stable circumbinary planet.
These results have implications for a number of issues in the study of extrasolar planets. The ejection of protoplanets in close binary systems provides a source of 'free-floating planets', which have been discovered recently. The formation of a large, tidally truncated cavity may provide an observational signature of circumbinary planets during formation. The existence of protoplanets orbiting stably just outside a mean motion resonance (4 : 1) in the simulations indicate that such sites may harbour planets in binary star systems, and these could potentially be observed. Finally, the formation of stable circumbinary planets in eccentric binary systems indicates that circumbinary planets may not be uncommon.     

Some investigations into the atmospheric drag problem

This paper calls into question the validity of the well-known formulae for the perturbations in the Keplerian elements, over one revolution of an orbit, for the motion of a drag-perturbed artificial satellite. These formulae are derived from Gauss's form of the planetary equations, by averaging over a single revolution of the orbit, and using the eccentric anomaly as the independent variable.It is shown that for light balloon-type satellites in near-circular orbits neither the eccentric anomaly nor the true longitude is a suitable choice of independent variable for the averaging procedure. Under these circumstances, it would seem that simple formulae for the variations in the elements cannot be derived from Gauss's equations.