The solar system evolution

The concepts on the spatially-periodic condensation in the solar system have been considered in the light of the general theory of the evolution of the solar system. It has been shown that as protodisks arise and compress, the role of hydromagnetic effects weakens. After the stage of spatially-periodic condensation and accretion, the concentration of gas in protodisks decreases and the role of hydromagnetic effects increases again. Specific features of the formation of planets near the Sun and satellites near the planets can be explained if these peculiarities of the evolution are taken into account. The corresponding role of the above processes has been evaluated numerically.The accretion of gas molecules both by jet streams arising after spatially-periodic condensation and by planet embryos has also been considered. Characteristic times of these processes have been estimated.The results obtained show that the general concept on the solar system evolution (Alfvén and Arrhenius, 1976) is in good agreement with the mechanism of spatially-periodic condensation, which takes place during the formation of primary rings of the solar and satellite systems (Gladyshev, 1977).     

The stability of our solar system

Most investigations of the stability of the solar system have been concerned with the question as to whether the very long term effect of the gravitational attractions of the planets on each other will be to alter the nearly coplanar, nearly circular nature of the orbits in which they move. Analytical investigations in the traditions of Laplace, Lagrange, Poisson and Poincaré strongly indicate stability, though rely on asymptotic expansions with difficult analytical properties. The question is related to the existence of invariant tori, which have been proved to exist in certain motions. Numerical integration experiments have thrown considerable light on possible types of motions, especially in fictitious solar systems in which the planetary masses have been increased to enhance the perturbations, and in testing how critical are stability boundary estimates given by Hill surface type methods.     

Restricted problem stability and the solar system

Reference periodic orbits are determined accurately for the planets of the solar system, using a restricted problem model with the Sun and Jupiter as the two primaries. The prediction is verified that stability of the planetary orbits should imply stability of those reference orbits that are simple-periodic.     

The inner solar system cratering record and the evolution of impactor populations

We review previously published and newly obtained crater size-frequency distributions in the inner solar system. These data indicate that the Moon and the terrestrial planets have been bombarded by two populations of objects. Population 1,dominating at early times, had nearly the same size distribution as the present-day asteroid belt, and produced heavily cratered surfaces with a complex, multi-sloped crater size-frequency distribution. Population 2, dominating since about 3.8–3.7 Gyr,had the same size distribution as near-Earth objects(NEOs) and a much lower impact flux, and produced a crater size distribution characterized by a differential –3single-slope power law in the crater diameter range 0.02 km to 100 km. Taken together with the results from a large body of work on age-dating of lunar and meteorite samples and theoretical work in solar system dynamics, a plausible interpretation of these data is as follows. The NEO population is the source of Population 2 and it has been in near-steady state over the past ～ 3.7–3.8 Gyr; these objects are derived from the main asteroid belt by size-dependent non-gravitational effects that favor the ejection of smaller asteroids. However, Population 1 was composed of main belt asteroids ejected from their source region in a size-independent manner, possibly by means of gravitational resonance sweeping during orbit migration of giant planets;this caused the so-called Late Heavy Bombardment(LHB). The LHB began some time before ～3.9 Gyr, peaked and declined rapidly over the next ～ 100 to 300 Myr,and possibly more slowly from about 3.8–3.7 Gyr to ～2 Gyr. A third crater population(Population S) consisted of secondary impact craters that can dominate the cratering record at small diameters.     

Origin and evolution of the solar system,II

(7)Formation of celestial bodies. The basic concepts of the accretional process are discussed, and the inadequacy of the contractional model is pointed out. A comparison is made between the general pre-planetary state on the one hand and the present state in the asteroidal region on the other. A model for accretion of resonance-captured grains leading to the formation of resonance-captured planets and satellites is suggested.(8)Spin and accretion. The relation between the accretional process and the spin of planets is analyzed.(9)Accretion of planets and satellites. It is shown that jet streams are a necessary intermediate stage in the formation of celestial bodies. The time sequence of planet formation is analyzed, and it is shown that the newly accreted bodies have a characteristic internal heat structure; the cases of the Earth and the Moon are considered in detail. A region of high initial temperature is found at 0.4 of the present Earth radius, whereas the culminating temperature of the Moon is near its present surface. An accretional heat wave is found to proceed outwards, and may produce the observed differentiation features.     

Higher-order stability of the restricted problem and the solar system

A generalization is expressed of the Poisson theorem referring to the invariance of the planetary semi-major axes using the restricted problem model. In particular, it is shown that first and second approximation in terms of a change in the initial states of planets describing closed motions in the solar system remain invariant in modulus after any number of revolutions. But third-order terms contain secular parts and, thus, they undergo a secular change in their orbital motion. Such change would be apparent after ^-2 Jovian years, where is a constant and is the maximum initial deviation of each planet from its reference orbit.     

The Titius-Bode law and the possibility of recent large-scale evolution in the solar system

Although it is by no means clear that the Titius-Bode law of planetary distances is indeed a “law” (even though there are enticing indications), it is proposed that if one assumes that the law is a “law” and that the planets obey it, then this argues against recent large-scale evolution in the solar system. Put another way: one can believe in the Titius-Bode law or in recent large-scale evolution or in neither of them. But it appears difficult to believe in both of them.     

The stability of coplanar three-body systems with application to the solar system

The c²H condition for determining the Hill stability of coplanar three-body systems is analysed for the particular situation where the primary mass is much greater than the other two. It is found that in this event the criterion can be expressed in a closed form. This is applied to three-body subsets of the Solar System.     

Large scale chaos and marginal stability in the solar system

Large scale chaos is present everywhere in the solar system. It plays a major role in the sculpting of the asteroid belt and in the diffusion of comets from the outer region of the solar system. All the inner planets probably experienced large scale chaotic behavior for their obliquities during their history. The Earth obliquity is presently stable only because of the presence of the Moon, and the tilt of Mars undergoes large chaotic variations from 0° to about 60°. On billion years time scale, the orbits of the planets themselves present strong chaotic variations which can lead to the escape of Mercury or collision with Venus in less than 3.5 Gyr. The organization of the planets in the solar system thus seems to be strongly related to this chaotic evolution, reaching at all time a state of marginal stability, that is practical stability on a time-scale comparable to its age.This lecture was given at the XIth International Congress of Mathematical Physics, Paris, july 1994     

Galactic chemical evolution and the oxygen isotopic composition of the solar system

Abstract– We review current observational and theoretical constraints on the galactic chemical evolution (GCE) of oxygen isotopes to explore whether GCE plays a role in explaining the lower ¹⁷O/¹⁸O ratio of the Sun, relative to the present‐day interstellar medium, or the existence of distinct ¹⁶O‐rich and ¹⁶O‐poor reservoirs in the solar system. Although the production of both ¹⁷O and ¹⁸O are related to the metallicity of progenitor stars, ¹⁷O is most likely produced in stars that evolve on longer timescales than those that produce ¹⁸O. Therefore, the ¹⁷O/¹⁸O ratio need not have remained constant over time, contrary to preconceptions and the simplest models of GCE. An apparent linear, slope‐one correlation between δ¹⁷O and δ¹⁸O in the ISM need not necessarily reflect an O isotopic gradient, and any slope‐one galactocentric gradient need not correspond to evolution in time. Instead, increasing ¹⁷O/¹⁸O is consistent both with observational data from molecular clouds and with modeling of the compositions of presolar grains. Models in which the rate of star formation has decelerated over the past few Gyr or in which an enhanced period of star formation occurred shortly before solar birth (“starburst”) can explain the solar‐ISM O‐isotopic difference without requiring a local input of supernova ejecta into the protosolar cloud. “Cosmic chemical memory” models in which interstellar dust is on average older than interstellar gas predict that primordial solar system solids should be ¹⁶O‐rich, relative to the Sun, in conflict with observations. However, scenarios can be constructed in which the ¹⁶O‐rich contribution of very massive stars could lead to ¹⁶O‐poor solids and a ¹⁶O‐rich bulk Sun, if the solar system formed shortly after a starburst, independent of the popular scenario of photochemical self‐shielding of CO.     

Time travel and chemical evolution: a look at the outer solar system

Many space scientists think that the chemical conditions today on planets and moons of the outer solar system are similar to conditions on Earth soon after it formed. If so, we can learn much about the chemistry that led to life on this planet. We can also speculate about exotic habitats that might have given rise to other types of life. And if we are able to discern the chemical reactions now occurring in the outer solar system, we may be able to extrapolate these rules to other solar systems, and so define the habitable zones around other stars where the potential for life is high.     

On the thickness and evolution of the dust layer during the formation of the solar system

We discuss certain dynamical processes during the final stage of the sinking of the dust layer. We supposed that turbulance gave rise to a state of slow sinking (quasi-equilibrium) and evaluated the critical thickness at the onset of gravitational instability in the radial direction. We gave a precise numerical relation between 3 length-scales: $\text{〈|Z|〉c : h}{}_1\text{: λ}{}_{\mathrm{T}}\text{= 0.02107 : 0.1592 : 1}$, the first being the mean height of the dust particles at the onset of radial instability, the second being that value of the half-thickness and of the height at which the self-gravity of the dust layer is equal to the solar z-component, and the last being the longest wavelength at the onset of ring instability. We also calculated the time required for the formation of rings and found it to be far shorter than the sinking time.     

The stability and evolution of two-component isothermal clusters

The stability of two-component isothermal clusters surrounded by a rigid non-conducting spherical wall is examined by linear normal analyses and nonlinear simulations. The examinations are done for four types of models, classified by the differences concerning gravo-thermal stability and Spitzer's condition. Our results show that perturbations in gravo-thermally stable systems disappears with time and the systems tend to isothermal ones with equipartition, as is expected. On the other hand, in the gravo-thermally unstable systems, the presence of small amount of massive component which has higher central density accelerates the gravo-thermal collapse by heat flowing from the massive component to the less massive component and being transported outward efficiently. This effect of the interaction between two components on gravo-thermal collapse is shown clearly in the forms of the respective eigenfunctions.On leave from Department of Astronomy, Institut Teknologi, Bandung.     

Orbital stability of massive protoplanets in the terrestrial planet region of the solar system

A number of theories of the formation of the planets advocate that the terrestrial planets were originally of cosmic composition and that it is only subsequent evolution that has removed their volatile components. This paper shows that such protoplanets could have remained in the terrestrial planet region without significant changes occurring in their orbits for an acceptable time interval.     

The stability of electron beams in the flaring solar corona

The conditions required for the stability of a steady-state electron beam propagating in the solar corona are determined using the quasi-linear theory. The growth rate for electron plasma waves in a magnetized plasma is evaluated, with the electron distribution function being given by an analytic solution of the linearized Fokker-Planck equation. It is shown that, when the gyrofrequency is less than the plasma frequency, the instability has a narrow angular range, with the maximum growth rate occuring along the magnetic field. A stability boundary in parameter space is determined, indicating that electron beams must be highly collimated at injection to be Langmuir unstable at any point in space. The implications of the results for alternative models of hard X-ray bursts are discussed and it is argued that Langmuir instability will not occur on either the trap model or the thermal model. Such models would, therefore, be refuted by the detection of a large flux of plasma microwave radiation associated with hard X-ray emission.     

WIMPs and solar evolution code

The Saclay solar evolution code is used to check the effect of WIMPs on solar evolution. In this paper we study the effects of various types of Cosmion-matter interactions, give constraints on the crosssections compatible with the measured neutrino rate of 2 SNU on chlorine, and relate these constraints to ongoing dark matter detection experiments.Unité associée au CNRS UA 280, F-75251 Paris Cedex 05, France.On leave from LPC, Collège de France.     

The relationship between solar activity and coronal hole evolution

We examine the relationship between coronal hole evolution and solar active regions during the Skylab period. We find a tendency for holes to grow or remain stable when the activity nearby, seen as calcium plages and bright regions in X-rays, is predominantly large, long-lived regions. This is consistent with results of previous studies, using somewhat different methods. We also find that there is a significantly higher number of small, short-lived active regions, as indicated by X-ray bright points, in the vicinity of decaying holes than there is near other holes. We interpret this to mean that holes disappear at least in part because they become filled with many small scale, magnetically closed, X-ray emitting features. This interpretation, together with the previously reported observation that the number of X-ray bright points was much larger near solar minimum than it was during the Skylab period, provides a possible explanation for the disappearance of the large, near-equatorial coronal holes at the time of solar minimum.     

The role of protostellar jets in star formation and the evolution of the early solar system: Astrophysical and meteoritical perspectives

Abstract– The rock record from the early solar system indicates high‐temperature thermal processing sufficient to melt refractory oxides and silicates. The astrophysical context for the formation and evolution of our solar system, from a molecular cloud to a “clean” planetary system, is difficult to constrain tightly because of the large scales and lack of resolution of astronomical observations. Protostellar jets and winds, commonly associated with forming stars, are likely to play a role in heating and redistribution of the processed material in the solar system. We have recently proposed that disk‐winds can cause melting of small inclusions to distances out to several AU. Particularly energetic outbursts, such as the FU‐Orionis and EXor events, occur over relatively short time scales (approximately 100 and 1 yr, respectively), and are probably events related to formation of the refractory solids present in primitive meteorites.     

On the stability of the solar wind

The stability of the solar wind is studied in the case of spherical symmetry and constant temperature. It is shown that the stability problem must be formulated as a mixed initial and boundary-value problem in which are prescribed the perturbation values of velocity and density at an initial time and additionally the velocity perturbation at the base of the corona for all times. The solution is constructed by linear superposition of normal solutions, which contain the time only in an exponential factor. The stability problem becomes a singular eigenvalue problem for the amplitudes of the velocity and pressure perturbations, since additionally to the boundary condition at the base of the corona one must add the condition that the amplitudes behave regularly at the critical point. It is proved that only stable eigenvalues exist.