Tidal friction in triple stars

Tidal friction in close binaries, with periods of a few days, is expected to circularize the orbit on a time-scale long compared with human observation but shorter than, or comparable to, the lifetimes of main-sequence stars. In a hierarchical triple star, however, the perturbing effect of the distant third star may decircularize the inner orbit significantly on a time-scale of the order of days (as in λ Tau) or centuries (as in β Per). If the inner pair is observed to be semidetached, however, it is plausible to assume that the eccentricity is small. This may be because tidal friction is operating on a comparably short time-scale, and so it is in principle amenable to observation. We attempt to determine a lower limit to the strength of tidal friction in λ Tau and β Per, on the basis of this consideration. Tidal friction will also lead to a secular transfer of angular momentum from the inner orbit to the outer orbit. Too rapid a transfer may lead to orbital shrinkage that is fast compared with the nuclear time-scales of the inner systems, and this can also be ruled out on observational grounds. Thus we may be able to set an upper as well as a lower limit to the strength of tidal friction, on the basis of observations. In a young hierarchical triple, provided that the orbits are fairly nearly orthogonal, tidal friction can serve to reduce the inner orbital period from months to days within a fairly short period of time, of order P ²_out/ P _in. This may be a significant mechanism for producing young short-period binaries.     

On the stability of high inclination Trojans

Numerical integrations have been performed for orbits of Venus', Earth's and Mars' Trojan-asteroid test particles in a self consistent model of the solar system to study the stability of inclined Trojan orbits. In the case of Mars low inclination orbits tend to be unstable while the contrary seems to apply to Venus and Earth, although the stability of some very high inclination orbits may not be excluded on the basis of these computations.     

A nitrogen fixation estimate for the Baltic Sea based on continuous pCO2 measurements on a cargo ship and total nitrogen data

Organic matter production and nitrogen fixation in the central Baltic Sea were studied on the basis of high-resolution CO₂ partial pressure data that were obtained from an automated measurement system deployed on a cargo ship. The net organic carbon (OC) production was calculated from a surface water CO₂ mass balance and used to estimate the nitrogen uptake by organic matter during the period March to August 2005. It was shown that the net OC production continued despite the exhaustion of dissolved inorganic nitrogen (DIN) after the spring bloom in April. The nitrogen demand for this production was calculated on the basis of the C/N ratio of organic matter. It was of the same order of magnitude than the winter DIN concentration that fuelled the spring bloom. Since the atmospheric DIN deposition was negligible and no indications of alternative DIN sources were found, it was assumed that N₂ fixation had taken place despite the low temperatures (4–8 °C) in April/May. This “cold fixation” amounted to 74 mmol m^?2 whereas a value of 99 mmol m^?2 was obtained for the summer N₂ fixation during June/July. Due to the contribution of the April/May N₂ fixation, a total annual rate (173±35 mmol m^?2) was obtained for 2005 which is considerably higher than presently accepted estimates. These findings were confirmed by a nitrogen budget based on long-term data (1993–2006) for total nitrogen and total phosphorus concentrations. Furthermore, these data revealed a 30% increase in N₂ fixation during the years 1994–2006.     

Adaptive management to climate change for Norway spruce forests along a regional gradient in Finland

We hypothesized that the responses of boreal Norway spruce (Picea abies) forests to climate change would be region-specific due to regional differences in temperature and water availability. In this context, we analyzed the adaptive effects of varied thinning intensities on the gross primary production (GPP), total stem wood growth, and timber yield over a 100-year period using a process-based ecosystem model. Our simulations represented Norway spruce forests for five different bioclimatic zones spanning southern to northern Finland (61–67^oN). Ten thinning regimes with thinning intensities ranging from 5 to 50 %, as well as an unthinned regime, were included in the calculations. The results showed that at the southern sites without thinning, the cumulative GPP and total stem wood growth were lower under the changing climate than in the current climate over the simulation period due to greater water depletion via evapotranspiration and reduced soil water availability. At the central and the northern sites, the climate changes increasingly enhanced the GPP and total stem wood growth due to the mitigation of low-temperature limitation and the improved soil water availability. Thinning generally mitigated the soil water deficit by reducing water evaporation and led to a reduction of the natural mortality. At the southern sites, light and moderate thinning intensities increased the GPP and total stem wood growth relative to sites with a changing climate that experienced no thinning. Moreover, moderate thinning resulted in the greatest timber yield. Heavy thinning, in which a large proportion of standing trees were removed, reduced the GPP and total stem wood growth despite allowing increased soil water availability. At the northern sites, all levels of thinning, including light thinning, decreased the GPP and stem wood growth, indicating that soil water availability was not a limiting factor for growth prior to thinning.     

Dynamical evolution of fragmenting gas clouds

Previous numerical simulations have shown that under certain conditions rotating gas clouds break up in two equal parts. We explore the consequences, if this process continues and a planar, equal mass four-body system forms. The results of the four-body calculations are used in Monte Carlo simulation of fragmentation of a rotating gas cloud in a galactic nucleus. Then it appears possible that clusters of large numbers of objects form; the dynamical evolution of these clusters have been calculated. The results were applied to ejection of supermassive objects from galactic nuclei. We find that several statistical properties of double radio sources may be understood as resulting from the fragmentation process.     

Discovery of an asteroid and quasi‐satellite in an Earth‐like horseshoe orbit

Abstract— The newly discovered asteroid 2002 AA₂₉ moves in a very Earth‐like orbit that relative to Earth has a unique horseshoe shape and allows transitions to a quasi‐satellite state. This is the first body known to be in a simple heliocentric horseshoe orbit, moving along its parent planet's orbit. It is similarly also the first true co‐orbital object of Earth, since other asteroids in 1:1 resonance with Earth have orbits very dissimilar from that of our planet. When a quasi‐satellite, it remains within 0.2 AU of the Earth for several decades. 2002 AA₂₉ is the first asteroid known to exhibit this behavior. 2002 AA₂₉ introduces an important new class of objects offering potential targets for space missions and clues to asteroid orbit transfer evolution.     

Monte Carlo Simulations of Comet Capture from the Oort Cloud

There is a very large number of small bodies in the Solar System and their orbits are varied and complicated. Some types of orbits and events are so rare that they occur in numerical simulations only when millions or billions of orbits have been calculated. In order to study these orbits or events an efficient Monte Carlo simulation is useful. Here we describe a new Monte Carlo simulation method and test it against some existing simulations of orbits of small bodies which have been obtained by different methods. We find good agreement with many earlier calculations, and study briefly the possibility of the Oort Cloud capture origin of short period comets. This revised version was published online in July 2006 with corrections to the Cover Date.     

Symplectic Tangent map for Planetary Motions

Equations are presented for the computation of tangent maps for use in nearly Keplerian motion, approximated by use of a symplectic leapfrog map. The resulting algorithms constitute more accurate and efficient methods to obtain the Liapunov exponents and the state transition matrix, and can be used to study chaos in planetary motions, as well as in orbit determination procedures from observations. Applications include planetary systems, satellite motions and hierarchical, nearly Keplerian systems in general. This revised version was published online in July 2006 with corrections to the Cover Date.     

A numerical investigation of the one-dimensional newtonian three-body problem

Numerical orbit integrations have been conducted to characterize the types of trajectories in the one-dimensional Newtonian three-body problem with equal masses and negative energy. Essentially three different types of motions were found to exist. They may be classified according to the duration of the bound three-body state. There are zero-lifetime predictable trajectories, finite lifetime apparently chaotic orbits, and infinite lifetime quasi-periodic motions. The quasi-periodic orbits are confined to the neighbourhood of Schubart's stable periodic orbit. For all other trajectories the final state is of the type binary + single particle in both directions of time. The boundaries of the different orbit-type regions seem to be sharp. We present statistical results for the binding energies and for the duration of the bound three-body state. Properties of individual orbits are also summarized in the form of various graphical maps in a two-dimensional grid of parameters defining the orbit. Supported by the Academy of Finland.     

A numerical investigation of the one-dimensional Newtonian three-body problem

The one-dimensional Newtonian three-body problem is known to have stable (quasi-)periodic orbits when the masses are equal. The existence and size of the stable region is discussed here in the case where the three masses are arbitrary. We consider only the stability of the periodic (generalized) Schubart's (1956) orbit. If this orbit is linearly stable it is almost always surrounded by a region of stable quasi-periodic orbits and the size and shape of this stable region depends on the masses. The three-dimensional linear stability of the periodic orbits is also determined. Final results show that the region of stability has a complicated shape and some of the stable regions in the mass-plane are quite narrow. The non-linear three-dimensional stability is studied independently by extensive numerical integrations and the results are found to be in agreement with the linear stability analysis. The boundaries of stable region in the mass-plane are given in terms of polynomial approximations. The results are compared with a similar work by Héenon (1977).We thank the referee for pointing out this reference to us.