Deuterium fractionation in the presolar nebula: Kinetic limitations on surface catalysis

Models assuming low temperature equilibrium fractionation have previously been employed to explain the range of D/H values observed in the solar system and to make predictions of deuterium enhancement in the outer planets. While the reaction rates of the homogeneous partitioning reactions are prohibitively low at nebular temperatures, it has been suggested that catalysis on grains could shorten equilibrium times sufficiently. This idea is quantitatively tested here. We find that under highly idealized conditions—the full cosmic abundance of nickel available for catalysis in pure 5-μm grains—the equilibrium time constant becomes greater than the lifetime of the nebula at temperatures lower than 560°K. Even this firm lower limit is not cold enough to allow strong fractionation. Speculations are offered on alternative explanations for the distribution of hydrogen isotopes in the solar system.     

Equilibrium resurfacing of Venus: Results from new Monte Carlo modeling and implications for Venus surface histories

Venus’ impact crater population imposes two observational constraints that must be met by possible model surface histories: (1) near random spatial distribution of ～975 craters, and (2) few obviously modified impact craters. Catastrophic resurfacing obviously meets these constraints, but equilibrium resurfacing histories require a balance between crater distribution and modification to be viable. Equilibrium resurfacing scenarios with small incremental resurfacing areas meet constraint 1 but not 2, whereas those with large incremental resurfacing areas meet constraint 2 but not 1. Results of Monte Carlo modeling of equilibrium resurfacing (Strom et al., 1994) is widely cited as support for catastrophic resurfacing hypotheses and as evidence against hypotheses of equilibrium resurfacing. However, the Monte Carlo models did not consider intermediate-size incremental resurfacing areas, nor did they consider histories in which the era of impact crater formation outlasts an era of equilibrium resurfacing. We construct three suites of Monte Carlo experiments that examine incremental resurfacing areas not previously considered (5%, 1%, 0.7%, and 0.1%), and that vary the duration of resurfacing relative to impact crater formation time (1:1 [suite A], 5:6 [suite B], and 2:3 [suite C]). We test the model results against the two impact crater constraints.Several experiments met both constraints. The shorter the time period of equilibrium resurfacing, or the longer the time of crater formation following the cessation of equilibrium resurfacing, the larger the possible areas of incremental resurfacing that satisfy both constraints. Equilibrium resurfacing is statistically viable for suite A at 0.1%, suite B at 0.1%, and suite C for 1%, 0.7%, and 0.1% areas of incremental resurfacing.     

On the Chermnykh-Like Problems: II. The Equilibrium Points

Motivated by Papadakis (2005a, b), we study a Chermnykh-like problem, in which an additional gravitational potential from the belt is included. In addition to the usual five equilibrium points (three collinear and two triangular points), there are some new equilibrium points for this system. We studied the conditions for the existence of these new equilibrium points both analytically and numerically.     

Degenerate equilibrium states of collisionless stellar systems

We study spherically symmetrical equilibrium states of collisionless stellar systems confined to a spherical box. These equilibrium states correspond to the statistics introduced by Lynden-Bell in his theory of 'violent relaxation', and are described by a Fermi–Dirac distribution function. We compute the corresponding equilibrium diagram and show that a global entropy maximum exists for any accessible control parameter. This equilibrium state shows a pronounced separation between a degenerate core and a halo. We therefore check that degeneracy is able to stop the gravitational collapse (of a collisionless system), and we propose a simple model for the 'core–halo' structure. We also discuss the relevance of our study for real galaxies or other astrophysical systems such as massive neutrinos.     

Magmatic history and parental melt composition of olivine‐phyric shergottite LAR 06319: Importance of magmatic degassing and olivine antecrysts in Martian magmatism

Several olivine‐phyric shergottites contain enough olivine that they could conceivably represent the products of closed‐system crystallization of primary melts derived from partial melting of the Martian mantle. Larkman Nunatak (LAR) 06319 has been suggested to represent a close approach to a Martian primary liquid composition based on approximate equilibrium between its olivine and groundmass. To better understand the olivine–melt relationship and the evolution of this meteorite, we report the results of new petrographic and chemical analyses. We find that olivine megacryst cores are generally not in equilibrium with the groundmass, but rather have been homogenized by diffusion to Mg# 72. We have identified two unique grain types: an olivine glomerocryst and an olivine grain preserving a primary magmatic boundary that constrains the time scale of eruption to be on the order of hours. We also report the presence of trace oxide phases and phosphate compositions that suggest that the melt contained approximately 1.1% H₂O and lost volatiles during cooling, also associated with an increase in oxygen fugacity upon degassing. We additionally report in situ rare earth element measurements of the various mineral phases in LAR 06319. Based on these reported trace element abundances, we estimate the oxygen fugacity in the LAR 06319 parent melt early in its crystallization sequence (i.e., at the time of crystallization of the low‐Ca and high‐Ca pyroxenes), the rare earth element composition of the parent melt, and those of melts in equilibrium with later formed phases. We suggest that LAR 06319 represents the product of closed‐system crystallization within a shallow magma chamber, with additional olivine accumulated from a cumulate pile. We infer that the olivine megacrysts are antecrysts, derived from a single magma chamber, but not directly related to the host magma, and suggest that mixing of antecrysts within magma chambers may be a common process in Martian magmatic systems.     

The dynamical behaviour of aN-shell model for an expanding universe

We consider a homogeneous expanding universe consisting of dust which is represented byN concentric massive spherical shells. We assume an explosive perturbation of the innermost shell at some instant of time. The effect of shell crossing and exchange of energy is investigated by deriving the equations of motion and obtaining their stationary and quasi-stationary solutions. Existing equilibrium stages and the density distribution for theN-shell system are discussed. Gravodynamics is a primary source for an understanding of gravitational clustering.     

Numerical experiments on the evolution in coronal magnetic configurations including a filament in response to the change in the photosphere

We investigate equilibrium height of a flux rope, and its internal equilibrium in a realistic plasma environment by carrying out numerical simulations of the evolution of systems including a current-carrying flux rope. We find that the equilibrium height of a flux rope is approximately described by a power-law function of the relative strength of the background field. Our simulations indicate that the flux rope can escape more easily from a weaker background field. This further confirms that a catastrophe in the magnetic configuration of interest can be triggered by a decrease in strength of the background field. Our results show that it takes some time to reach internal equilibrium depending on the initial state of the flux rope. The plasma flow inside the flux rope due to the adjustment for the internal equilibrium of the flux rope remains small and does not last very long when the initial state of the flux rope commences from the stable branch of the theoretical equilibrium curve. This work also confirms the influence of the initial radius of the flux rope in its evolution; the results indicate that a flux rope with a larger initial radius erupts more easily. In addition, by using a realistic plasma environment and a much higher resolution in our simulations,we notice some different characteristics compared to previous studies in Forbes.     

Behavior of nearby synchronous rotations of a Poincaré–Hough satellite at low eccentricity

This paper presents a study of the Poincaré–Hough model of rotation of the synchronous natural satellites, in which these bodies are assumed to be composed of a rigid mantle and a triaxial cavity filled with inviscid fluid of constant uniform density and vorticity. In considering an Io-like body on a low eccentricity orbit, we describe the different possible behaviors of the system, depending on the size, polar flattening and shape of the core. We use for that the numerical tool. We propagate numerically the Hamilton equations of the system, before expressing the resulting variables under a quasi-periodic representation. This expression is obtained numerically by frequency analysis. This allows us to characterise the equilibria of the system, and to distinguish the causes of their time variations. We show that, even without orbital eccentricity, the system can have complex behaviors, in particular when the core is highly flattened. In such a case, the polar motion is forced by several degrees and longitudinal librations appear. This is due to splitting of the equilibrium position of the polar motion. We also get a shift of the obliquity when the polar flattening of the core is small.     

Stability of stellar structure in non-equilibrium thermodynamics II. C-N-O cycle

A star is an open system which exchanges energy and matter with its surroundings and is also a thermodynamic system far from the equilibrium state. Using Prigogine's stability criterion of excess entropy production in non-linear and non-equilibrium thermodynamics for such a system, we study the stability of stars located at the upper part of the main sequence, for which the CNO cycle is the main energy source. We assume that the star is in hydrostatic equilibrium, the temperature in the region of nuclear reaction is constant, and convection and diffusion are unimportant. We have obtained five conditions for stability, that is, the formulae (14). The first three conditions are satisfied for a star. But the last two conditions, that is, the formulae (15) and (16), contradict each other. Therefore, the thermodynamic system is unstable. We discuss the reasons for the contradiction, and show that convection, diffusion, temperature variation and the cycle reactions other than the CNO cycle must be considered.     

Restricted four-body problem. The case of a central configuration: Libration points and their stability

We consider the problem of the motion of a zero-mass body in the vicinity of a system of three gravitating bodies forming a central configuration.We study the case where two gravitating bodies of equal mass lie on the same straight line and rotate around the central body with the same angular velocity. Equations for calculating the equilibrium positions in this system have been derived. The stability of the equilibrium points for a system of three gravitating bodies is investigated. We show that, as in the case of libration points for two bodies, the collinear points are unstable; for the triangular points, there exists a ratio of the mass of the central body to the masses of the extreme bodies, 11.720349, at which stability is observed.     

On the Chermnykh-Like Problems: I. the Mass Parameter μ = 0.5

Following Papadakis (2005)'s numerical exploration of the Chermnykh's problem, we here study a Chermnykh-like problem motivated by the astrophysical applications. We find that both the equilibrium points and solution curves become quite different from the ones of the classical planar restricted three-body problem. In addition to the usual Lagrangian points, there are new equilibrium points in our system. We also calculate the Lyapunov Exponents for some example orbits. We conclude that it seems there are more chaotic orbits for the system when there is a belt to interact with.     

On the influence of cooling and heating processes on the Parker instability – II. Numerical simulations

We investigate the Parker instability (PI) influenced by thermal processes in a non-adiabatic, gravitationally stratified interstellar medium and discuss a model including the photoionization heating together with the supplemental heating mechanisms postulated by Reynolds, Haffner and Tufte. A cooling rate due to radiative losses is described by an approximation to the realistic cooling function of Dalgarno and McCray for ionized interstellar gas. An unperturbed initial state of the system simultaneously represents both a magnetohydrostatic and thermal equilibrium, and is thermally stable. We perform a set of 3D numerical magnetohydrodynamic simulations using the zeusmp code. We find that PI developing in the presence of non-adiabatic effects promotes a transition of gas in magnetic valleys to a thermally unstable regime. We find that the region of initially enhanced density due to PI starts to condense more as the result of thermal instability action. The density in this region rises above the classical isothermal limit of two times the equilibrium value at the mid-plane. The maximum density in an evolved system reaches 10–40 times the equilibrium value at the mid-plane, and the structures so formed attain oval shapes. These results lead to the conclusion that PI, operating in the presence of realistic cooling and heating processes, can trigger the formation of dense clouds, which may give rise to giant molecular complexes.     

Shock wave phenomena in collisions between a current loop and a plasmoid

We present the results of 3-D MHD simulations of collisions between an equilibrium current and a plasmoid. Three typical equilibrium configurations were analyzed. Our simulation results show that when a plasmoid approaches a current loop, an active region is created in front of the plasmoid bounded on the front side by a bow shock wave and on the back side by a reverse shock wave. The collision process modifies the current system and a strong electric field is also induced in the active region. An additional magnetic field generated by the induced current upsets the initial equilibrium condition. As a result, the whole loop is compressed and heated. We found that when the plasmoid approaches the loop, before reaching it the induced electric field amounts to its maximum value. The current loop is curved under the collision. The core of the plasmoid can not drive into the loop, it is sprung back by a magnetic counterpressure. This collision process between a plasmoid and a current loop may be responsible for the triggering of a solar flare observed by Yohkoh.     

Global Dynamics in Self-Consistent Models of Elliptical Galaxies

We compare two different N-body models simulating elliptical galaxies. Namely, the first model is a non-rotating triaxial N-body equilibrium model with smooth center, called SC model. The second model, called CM model, is derived from the SC by inserting a central mass in it, so that all possible differences between the two models are due to the effect of the central mass. The central mass is assumed to be mainly due to a massive central black hole of mass about 1% of the total mass of the galaxy. By using the fundamental frequency analysis, the two systems are thoroughly investigated as regards the types of orbits described either by test particles, or by the real particles of the systems at all the energy levels. A comparison between the orbits of test particles and the orbits of real particles at various energy levels is made on the rotation number plane. We find that extensive stable regions of phase space, detected by test particles remain empty, i.e. these regions are not occupied by real particles, while many real particles move in unstable regions of phase space describing chaotic orbits. We run self-consistently the two models for more than a Hubble time. During this run, in spite of the noise due to small variations of the potential, the SC model maintains (within a small uncertainly) the number of particles moving on orbits of each particular type. In contrast, the CM model is unstable, due to the large amount of mass in chaotic motion caused by the central mass. This system undergoes a secular evolution towards an equilibrium state. During this evolution it is gradually self-organized by converting chaotic orbits to ordered orbits mainly of the short axis tube type approaching an oblate spheroidal equilibrium. This is clearly demonstrated in terms of the fundamental frequencies of the orbits on the rotation number plane and the time evolution of the triaxiality index.     

Nonlinear evolution of Tayler unstable equilibrium states

We investigate the nonlinear evolution of Tayler unstable toroidal fields in a disk geometry, by numerical simulations. We consider non‐rotating and rigid rotating disks, with different radial field profiles. The initial configuration is in equilibrium, which is achieved by a pressure gradient or an external potential force. The nonlinear evolution of the system leads to a stable equilibrium with a current free toroidal field. Only for the fast rotating case we could preserve a ring type structure of the toroidal field. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A simplified model for a nonlinear tidal effect on accretion disks in CVs

This paper investigates the tidal effect on accretion disk in CVs and sets up a simplified model in which the secondary's gravitation is substituted by a mean tidal torque. We find that a linear tidal torque will not be able to maintain an equilibrium disk. By using the result of the radius of the equilibrium disk approximately equals to the tidal radius, which was obtained by using the two dimensional numerical simulation invoking nonlinear tidal effect, we give the modified tidal dissipation function for our simplified model which could be used to interpret the outburst of the dwarf nova with tidal effect. The paper also shows that the radius of an equilibrium disk with a torus is slightly small than the Lubow-Shu radius, and the tidal effect may also cause the cycle of quiescence-superoutburst in addition to the cycle of quiescence-outbursts-superoutburst.     

On magnetostatic equilibrium in a stratified atmosphere

This is a study of the relationship between a magnetic field and its embedding plasma in static equilibrium in a uniform gravity. The ideal gas law is assumed. A system invariant in a given direction is treated first. We show that an exact integral of the equation for force balance across field lines can be derived in a closed form. Using this integral, exact solutions can be generated freely by integrating directly for the distributions of pressure, density and temperature necessary to keep a given magnetic field in equilibrium. Particular solutions are presented for illustration with the solar atmosphere in mind. Extending the treatment to the general system depending on all three spatial coordinates, we arrive at the general form of a theorem of Parker that a magnetic field in static equilibrium must possess certain symmetries. We derive an equation involving the Euler potentials of the magnetic field stipulating these necessary symmetries. Only those magnetic fields satisfying this equation can be in static equilibrium and for these fields, the endowed symmetries make the construction of exact solutions an essentially two dimensional problem as exemplified by the special case of invariance in a given direction.     

地月系潮汐演化长期趋势的估计

根据角动量守恒原理,计算了地月系经潮汐演化到达平衡状态时的旋转周期和地月距离.并根据当前与平衡状态时地月系的总能量差,计算了到达平衡状态的时间.进而估计了地月距离变化和地球自转速率变化的长期趋势.     

Phase Mixing in Unperturbed and Perturbed Hamiltonian Systems

This paper summarises a numerical investigation of phase mixing in time-independent Hamiltonian systems that admit a coexistence of regular and chaotic phase space regions, allowing also for low amplitude perturbations idealised as periodic driving, friction, and/or white and coloured noise. The evolution of initially localised ensembles of orbits was probed through lower order moments and coarse-grained distribution functions. In the absence of time-dependent perturbations, regular ensembles disperse initially as a power law in time and only exhibit a coarse-grained approach towards an invariant equilibrium over comparatively long times. Chaotic ensembles generally diverge exponentially fast on a time scale related to a typical finite time Lyapunov exponent, but can exhibit complex behaviour if they are impacted by the effects of cantori or the Arnold web. Viewed over somewhat longer times, chaotic ensembles typical converge exponentially towards an invariant or near-invariant equilibrium. This, however, need not correspond to a true equilibrium, which may only be approached over very long time scales. Time-dependent perturbations can dramatically increase the efficiency of phase mixing, both by accelerating the approach towards a near-equilibrium and by facilitating diffusion through cantori or along the Arnold web so as to accelerate the approach towards a true equilibrium. The efficacy of such perturbations typically scales logarithmically in amplitude, but is comparatively insensitive to most other details, a conclusion which reinforces the interpretation that the perturbations act via a resonant coupling.