Time scale for the formation of the earth and planets and its role in their geochemical evolution

The initial mass of the solar nebula is discussed. Models of a massive nebula (two solar masses and more) encounter serious difficulties: an effective mechanism of transfer of the momentum from the central part of the nebula outward, capable of leading to formation of the sun and removal of half the mass of the nebula from the solar system has not been found. As a consequence of the instability of these models, their evolution can end with the formation, not a planetary system, but of a binary star. The possibility is demonstrated of obtaining acceptable growth rates for Uranus and Neptune by prolonging the thickening of preplanetary dust in the region of large masses. The important role of large bodies in the process of formation of the planets is noted. The impacts of such bodies, moving in heliocentric orbits, could have imparted considerable additional energy to the forming Moon, which, together with the energy given off by the joining of a small number of large protomoons, could have led to a high initial temperature of the moon

Dynamical evolution of planetesimals in protoplanetary disks

The current picture of terrestrial planet formation relies heavily on our understanding of the dynamical evolution of planetesimals -- asteroid-like bodies thought to be planetary building blocks. In this study we investigate the growth of eccentricities and inclinations of planetesimals in spatially homogeneous protoplanetary disks using methods of kinetic theory. We explore disks with a realistic mass spectrum of planetesimals evolving in time, similar to that obtained in self-consistent simulations of planetesimal coagulation. We calculate the behavior of planetesimal random velocities as a function of the planetesimal mass spectrum both analytically and numerically; results obtained by the two approaches agree quite well. Scaling of random velocity with mass can always be represented as a combination of power laws corresponding to different velocity regimes (shear- or dispersion-dominated) of planetesimal gravitational interactions. For different mass spectra we calculate analytically the exponents and time dependent normalizations of these power laws, as well as the positions of the transition regions between different regimes. It is shown that random energy equipartition between different planetesimals can only be achieved in disks with very steep mass distributions (differential surface number density of planetesimals falling off steeper than m^{-4}), or in the runaway tails. In systems with shallow mass spectra (shallower than m^{-3}) random velocities of small planetesimals turn out to be independent of their masses. We also discuss the damping effects of inelastic collisions between planetesimals and of gas drag, and their importance in modifying planetesimal random velocities.Comment: 20 pages, 17 figures, 1 table, submitted to A

Two evolutional paths of an axisymmetric gravitational instability in the dust layer of a protoplanetary disk

Nonlinear numerical simulations are performed to investigate the density evolution in the dust layer of a protoplanetary disk due to the gravitational instability and dust settling toward the midplane. We assume the region where the radial pressure gradient at equilibrium is negligible so that the shear-induced instability is avoided, and also restrict to an axisymmetric perturbation as a first step of nonlinear numerical simulations of the gravitational instability. We find that there are two different evolutional paths of the gravitational instability depending on the nondimensional gas friction time, which is defined as the product of the gas friction time and the Keplerian angular velocity. If the nondimensional gas friction time is equal to 0.01, the gravitational instability grows faster than dust settling. On the other hand, if the nondimensional gas friction time is equal to 0.1, dust aggregates settle sufficiently before the gravitational instability grows. In the latter case, an approximate analytical calculation reveals that dust settling is faster than the growth of the gravitational instability regardless of the dust density at the midplane. Thus, the dust layer becomes extremely thin and may reach a few tenth of the material density of the dust before the gravitational instability grows.Comment: 4 pages, 3 figure

Iron oxide nanoparticles fabricated by electric explosion of wire: Focus on magnetic nanofluids

Nanoparticles of iron oxides (MNPs) were prepared using the electric explosion of wire technique (EEW). The main focus was on the fabrication of de-aggregated spherical nanoparticles with a narrow size distribution. According to XRD the major crystalline phase was magnetite with an average diameter of MNPs, depending on the fraction. Further separation of air-dry EEW nanoparticles was performed in aqueous suspensions. In order to provide the stability of magnetite suspension in water, we found the optimum concentration of the electrostatic stabilizer (sodium citrate and optimum pH level) based on zeta-potential measurements. The stable suspensions still contained a substantial fraction of aggregates which were disintegrated by the excessive ultrasound treatment. The separation of the large particles out of the suspension was performed by centrifuging. The structural features, magnetic properties and microwave absorption of MNPs and their aqueous solutions confirm that we were able to obtain an ensemble in which the magnetic contributions come from the spherical MNPs. The particle size distribution in fractionated samples was narrow and they showed a similar behaviour to that expected of the superparamagnetic ensemble. Maximum obtained concentration was as high as 5 % of magnetic material (by weight). Designed assembly of de-aggregated nanoparticles is an example of on-purpose developed magnetic nanofluid. Copyright © 2012 Author(s)

Dust Size Growth and Settling in a Protoplanetary Disk

We have studied dust evolution in a quiescent or turbulent protoplanetary disk by numerically solving coagulation equation for settling dust particles, using the minimum mass solar nebular model. As a result, if we assume an ideally quiescent disk, the dust particles settle toward the disk midplane to form a gravitationally unstable layer within 2x10^3 - 4x10^4 yr at 1 - 30 AU, which is in good agreement with an analytic calculation by Nakagawa, Sekiya, & Hayashi (1986) although they did not take into account the particle size distribution explicitly. In an opposite extreme case of a globally turbulent disk, on the other hand, the dust particles fluctuate owing to turbulent motion of the gas and most particles become large enough to move inward very rapidly within 70 - 3x10^4 yr at 1 - 30 AU, depending on the strength of turbulence. Our result suggests that global turbulent motion should cease for the planetesimal formation in protoplanetary disks.Comment: 27 pages, 8 figures, accepted for publication in the Ap

An evolution equation as the WKB correction in long-time asymptotics of Schrodinger dynamics

We consider 3d Schrodinger operator with long-range potential that has short-range radial derivative. The long-time asymptotics of non-stationary problem is studied and existence of modified wave operators is proved. It turns out, the standard WKB correction should be replaced by the solution to certain evolution equation.Comment: This is a preprint of an article whose final and definitive form has been published in Comm. Partial Differential Equations, available online at http://www.informaworld.co

Planetary migration in evolving planetesimals discs

In the current paper, we further improved the model for the migration of planets introduced in Del Popolo et al. (2001) and extended to time-dependent planetesimal accretion disks in Del Popolo and Eksi (2002). In the current study, the assumption of Del Popolo and Eksi (2002), that the surface density in planetesimals is proportional to that of gas, is released. In order to obtain the evolution of planetesimal density, we use a method developed in Stepinski and Valageas (1997) which is able to simultaneously follow the evolution of gas and solid particles for up to 10^7 yrs. Then, the disk model is coupled to migration model introduced in Del Popolo et al. (2001) in order to obtain the migration rate of the planet in the planetesimal. We find that the properties of solids known to exist in protoplanetary systems, together with reasonable density profiles for the disk, lead to a characteristic radius in the range 0.03-0.2 AU for the final semi-major axis of the giant planet.Comment: IJMP A in prin