A minimal dynamical model for tidal synchronization and orbit circularization

We study tidal synchronization and orbit circularization in a minimal model that takes into account only the essential ingredients of tidal deformation and dissipation in the secondary body. In previous work we introduced the model (Escribano et al. in Phys. Rev. E, 78:036216, 2008); here we investigate in depth the complex dynamics that can arise from this simplest model of tidal synchronization and orbit circularization. We model an extended secondary body of mass m by two point masses of mass m/2 connected with a damped spring. This composite body moves in the gravitational field of a primary of mass M ≫ m located at the origin. In this simplest case oscillation and rotation of the secondary are assumed to take place in the plane of the Keplerian orbit. The gravitational interactions of both point masses with the primary are taken into account, but that between the point masses is neglected. We perform a Taylor expansion on the exact equations of motion to isolate and identify the different effects of tidal interactions. We compare both sets of equations and study the applicability of the approximations, in the presence of chaos. We introduce the resonance function as a resource to identify resonant states. The approximate equations of motion can account for both synchronization into the 1:1 spin-orbit resonance and the circularization of the orbit as the only true asymptotic attractors, together with the existence of relatively long-lived metastable orbits with the secondary in p:q (p and q being co-prime integers) synchronous rotation.     

Geochemical differentiation in the stratigraphy of a peat bed as an indicator of its evolution in the Holocene

The paper reports geochemical parameters of units in a peat bed in a raised bog in the southern Tyumen territory. Based on radiocarbon dates and the variability of the geochemical data, the following four evolutionary stages of the bed in the Holocene are distinguished: an ancient lake (5600–5750 years B.P.), low-land-bog peat (4550–5600 years B.P.), transitional-type peat (4200–4550 years B.P.), raised-bog peat. The major-component technique was applied to analyze relations between various parameters of the bed and evaluate the variations in the condition under which the bog evolved with time, including climatic conditions (in relative units). An anthropogenic signal of the accumulation of certain metals in bog systems is distinguished.     

Pollen representation,source area,and basin size: Toward a unified theory of pollen analysis

The concepts of pollen source area and of production and dispersal biases in pollen representation are quantified by means of a simple theoretical model. Source areas and relative pollen representation are shown to depend on basin size according to functions that describe the amount of pollen remaining airborne at increasing distances from single pollen sources. The form of these functions is determined by physical processes. Standard formulas for elevated sources do not apply, but the integrated form of Sutton's equation for particle dispersal from a ground-level source gives useful approximations applicable to pollen transport over a forest canopy. Simulations using this equation yielded source areas that increased realistically with basin size, showed substantial differences between source areas for pollen grains with different deposition velocities, and predicted that lighter pollen grains should become better represented with increasing basin size. All of these predictions are qualitatively consistent with present knowledge of the characteristics of pollen assemblages in different depositional environments. The model further allows parameters that can be estimated by statistical calibration methods to be predicted from underlying physical quantities. This extension suggests procedures for testing the theory with quantitative data on surface pollen and forest composition. Preliminary results showed reasonable agreement between estimated and predicted values of dispersal indices for the most abundant taxa in pollen spectra from the northern midwestern United States.     

The charge distribution on interstellar grains—The effect of induced charge

A calculation of the equilibrium charge acquired by interstellar grains is given, which takes account of polarization charges that are induced in a grain by incident ions and electrons.Both metal and dielectric grains are considered and photoionization of the latter grains by UV radiation is taken into account where necessary. It is found that the inclusion of the polarization charges in the calculation is only important in gas clouds where the mean charge on a grain is low (<1e); that is, for HI regions and dense molecular clouds. In such clouds, the effect of the polarization charges is to increase the amount of negative charge acquired by a grain. A discussion is given concerning the validity of the classical electrostatic theory employed in the paper for small grains of radius 10^–6 cm, and some astrophysical consequences of the modification of the grain charge by polarization effects are considered.     

Imaging Observations of Quasi-Periodic Pulsatory Nonthermal Emission in Two-Ribbon Solar Flares

Using RHESSI and some auxiliary observations we examine possible connections between the spatial and temporal structure of nonthermal hard X-ray (HXR) emission sources from the two-ribbon flares of 29 May 2003 and 19 January 2005. In each of these events quasi-periodic pulsations (QPP) with time period of 1 – 3 minutes are evident in both hard X rays and microwaves. The sources of nonthermal HXR emission are situated mainly at the footpoints of the flare arcade loops observed by TRACE and the SOHO/EIT instrument in the EUV range. At least one of the sources moves systematically during and after the QPP phase in each flare. The sources move predominantly parallel to the magnetic inversion line during the 29 May flare and along flare ribbons during the QPP phase of both flares. By contrast, the sources start to show movement perpendicular to the flare ribbons with velocity comparable to that along the ribbons’ movement after the QPP phase. The sources of each pulse are localized in distinct parts of the ribbon during the QPP phase. The measured velocity of the sources and the estimated energy release rate do not correlate well with the flux of the HXR emission calculated from these sources. The sources of microwaves and thermal HXRs are situated near the apex of the flare loop arcade and are not stationary either. Almost all of the QPP as well as some pulses of nonthermal HXR emission during the post-QPP phase reveal soft – hard – soft spectral behavior, indicating separate acts of electron acceleration and injection. In our opinion at least two different flare scenarios based on the Nakariakov et al. (2006, Astron. Astrophys. 452, 343) model and on the idea of current-carrying loop coalescence are suitable for interpreting the observations. However, it is currently not possible to choose between them owing to observational limitations.     

Tidal dwarfs in the M81 group: the second generation?

We present a quantitative star formation history derivation of the four suspected tidal dwarf galaxies in the M 81 group: Holmberg IX, BK3N,Arp-loop (A0952+69) and Garland using HST/WFPC2 images of these galaxies. We construct a library of synthetic Colour-Magnitude Diagrams(CMDs) based on theoretical isochrones and data-derived determinations of photometric errors. These synthetic CMDs were combined linearly andχ²-compared to observed photometry. All the galaxies show continuous star formation between about 20 and 200 Myr ago with star formation rates between 7.5⋅10^-3 M_⊙/yr and 7.67⋅10^-4 M_⊙/yr. The metallicity of the detected stars is spanning rather a wide range, being lower than solar abundance. We suppose, that all the galaxies were formed out of material from metal-poor outer part of the giant spiral galaxy M81after tidal interaction about 200 Myr ago. However, this suggestion requires significantly more deep color-magnitude diagrams to be sure with the scenario of the galaxy evolution. This revised version was published online in July 2006 with corrections to the Cover Date.     

Stability of motion in the Sitnikov 3-body problem

We study the stability of motion in the 3-body Sitnikov problem, with the two equal mass primaries (m ₁ = m ₂ = 0.5) rotating in the x, y plane and vary the mass of the third particle, 0 ≤ m ₃ < 10⁻³, placed initially on the z-axis. We begin by finding for the restricted problem (with m ₃ = 0) an apparently infinite sequence of stability intervals on the z-axis, whose width grows and tends to a fixed non-zero value, as we move away from z = 0. We then estimate the extent of “islands” of bounded motion in x, y, z space about these intervals and show that it also increases as |z| grows. Turning to the so-called extended Sitnikov problem, where the third particle moves only along the z-axis, we find that, as m ₃ increases, the domain of allowed motion grows significantly and chaotic regions in phase space appear through a series of saddle-node bifurcations. Finally, we concentrate on the general 3-body problem and demonstrate that, for very small masses, m ₃ ≈ 10⁻⁶, the “islands” of bounded motion about the z-axis stability intervals are larger than the ones for m ₃ = 0. Furthermore, as m ₃ increases, it is the regions of bounded motion closest to z = 0 that disappear first, while the ones further away “disperse” at larger m ₃ values, thus providing further evidence of an increasing stability of the motion away from the plane of the two primaries, as observed in the m ₃ = 0 case.