Formation of solar nebula and mass distribution in the planetary system

The formation of the solar nebula and the distribution of mass in its planetary system is studied. The underlying idea is that the protosun, fragmented out from an interstellar cloud as a result of cluster formation, gathered the planetary material and, hence, spin angular momentum by gravitational accretion during its orbital motion around the centre of the Galaxy. The study gives the initial angular momentum of the solar nebula nearly equal to the present value of the solar system.     

The distribution of mass in the planetary system and solar nebula

A model solar nebula is constructed by adding the solar complement of light elements to each planet, using recent models of planetary compositions. Uncertainties in this approach are estimated. The computed surface density varies approximately asr ^–3/2. Mercury, Mars and the asteroid belt are anomalously low in mass, but processes exist which would preferentially remove matter from these regions. Planetary masses and compositions are generally consistent with a monotonic density distribution in the primordial solar nebula.     

Orbital resonances in the solar nebula: Implications for planetary accretion

The influence of gas drag and gravitational perturbations by a planetary embryo on the orbit of a planetesimal in the solar nebula was examined. Non-Keplerian rotation of the gas causes secular decay of the orbit. If the planetesimal's orbit is exterior to the perturber's, resonant perturbations oppose this drag and can cause it to be trapped in a stable orbit at a commensurability of order j/(j + 1), where j is an integer. Numerical and analytical demonstrations show that resonant trapping occurs for wide ranges of perturbing mass, planetesimal size, and j. Induced eccentricities are large, causing overlap of orbits for bodies in different resonances with j > 2. Collisions between planetesimals in different resonances, or between resonant and nonresonant bodies, result in their disruption. Fragments smaller than a critical size can pass through resonances under the influence of drag and be accreted by the embryo. This effect speeds accretion and tends to prevent dynamical isolation of planetary embryos, making gas-rich scenarios for planetary formation more plausible.     

Temperature distribution in the solar nebula at successive stages of its evolution

We have constructed a model of the solar nebula that allows for the temperature and pressure distributions at various stages of its evolution to be calculated. The mass flux from the accretion envelope to the disk and from the disk to the Sun, the turbulent viscosity parameter α, the opacity of the disk material, and the initial angular momentum of the protosun are the input model parameters that are varied. We also take into account the changes in the luminosity and radius of the young Sun. The input model parameters are based mostly on data obtained from observations of young solar-type stars with disks. To correct the input parameters, we use the mass and chemical composition of Jupiter, as well as models of its internal structure and formation that allow constraints to be imposed on the temperature and surface density of the protoplanetary disk in Jupiter’s formation zone. Given the derived constraints on the input parameters, we have calculated models of the solar nebula at successive stages of its evolution: the formation inside the accretion envelope, the evolution around the young Sun going through the T Tauri stage, and the formation and compaction of a thin dust layer (subdisk) in the disk midplane. We have found the following evolutionary trend: an increase in the temperature of the disk at the stage of its formation, cooling at the T Tauri stage, and the subsequent internal heating of the dust subdisk by turbulence dissipation that causes a temperature rise in the formation zone of the terrestrial planets at the high subdisk density and the opacity in this zone. We have obtained the probable ranges of temperatures in the disk midplane, i.e., the temperatures of the protoplanetary material in the formation region of the terrestrial planets at the initial stage of their formation.     

Hydrodynamic instability of the solar nebula in the presence of a planetary core

When a planetary core composed of condensed matter is accumulated in the primitive solar nebula, the gas of the nebula becomes gravitationally concentrated as an envelope surrounding the planetary core. Models of such gaseous envelopes have been constructed subject to the assumption that the gas everywhere is on the same adiabat as that in the surrounding nebula. The gaseous envelope extends from the surface of the core to the distance at which the gravitational attraction of core plus envelope becomes equal to the gradient of the gravitational potential in the solar nebula; at this point the pressure and temperature of the gas in the envelope are required to attain the background values characteristics of the solar nebula. In general, as the mass of the condensed core increases, increasing amounts of gas became concentrated in the envelope, and these envelopes are stable against hydrodynamic instabilities. However, the core mass then goes through a maximum and starts to decrease. In most of the models tested, the envelopes were hydrodynamically unstable beyond the peak in the core mass. An unstable situation was always created if it was insisted that the core mass contain a larger amount of matter than given by these solutions. For an initial adiabat characterized by a temperature of 450°K and a pressure of 5 × 10^?6 atm, the maximum core mass at which instability occurs is approximately 115 earth masses; this value is rather insensitive to the position in the solar nebula or to the background pressure of the solar nebula. However, if the adiabat is lowered, then the core mass corresponding to instability is decreased. Since the core masses found by Podolak and Cameron for the giant planets are significantly less than the critical core mass corresponding to the initial solar nebula adiabat, we conclude that the giant planets obtained their large amounts of hydrogen and helium by a hydrodynamic collapse process in the solar nebula only after the nebula had been subjected to a considerable period of cooling.     

Spectrophotometry of the planetary nebula KjPn 8

Flux-calibrated low-resolution spectra covering the optical wavelength range from 3400 to 7500 Å have been obtained over the central region and the surroundings of the extraordinary planetary nebula (PN) KjPn 8 (PNG 112.5-00.1). The spectrum from the core is of low excitation with T _e(N  II ) = 8000 K and n _e(S  II ) = 550 cm⁻³. KjPn 8 is found to be a Type I PN according to the original classification scheme of Peimbert & Torres-Peimbert, with enriched He/H and N/O ratios with respect to mean values for PN. Increased O/H, Ne/H and Ar/H ratios over those of average PN reflect the possible metal-rich environment from which the progenitor star formed, and also are similar to those found in the extreme Type I PN He 2-111. The N/H ratio is found to be only moderately high compared to the average PN and consequently, the large O abundance pulls the N/O ratio towards the lower limit of the criterion for Type I planetary nebulae (PNe) in this case. In addition, the spectra of some knots and faint regions in the KjPn 8 surroundings are presented, which show only a few spectral lines. Low electron densities ranging from 100 to 300 cm⁻³ have been derived in these outer regions.     

Formation of planetary and satellite systems

A solar nebula-type theory recently published by the author can explain much more about our planetary system and the satellite systems than all other theories known to date. Here only a few additional and relatively simple aspects are pointed out, especially the formation of the Moon and of the Martian satellites.     

Contraction of the solar nebula

The concept of Roche limit is applied to the Laplacian theory of the origin of the solar system to study the contraction of a spherical gas cloud (solar nebula). In the process of contraction of the solar nebula, it is assumed that the phenomenon of supersonic turbulent convection described by Prentice (1978) is operative and brings about the halt at various stages of contraction. It is found that the radius of the contracting solar nebula follows Titius-Bode law R _p = Ra^p, where R is the radius of the present Sun and a = 1.442. We call a the Roche's constant. The consequences of the relation are also discussed. The aim, here, is an attempt to explain, on the basis of the concept of Roche limit, the distribution of planets in the solar system and try to understand the physics underlying it.     

Evolutionary status of WR-type planetary nebula nuclei

In this paper we review the evolutionary paths that lead to the different types of planetary nebulae nuclei, including hydrogen and helium-burning central stars. Starting from the empirical definition of WR central stars, based on stellar spectra, we examine the theoretical work produced to account for the observed configurations. Then we discuss the constraints provided by recent galactic and extragalactic observations, and finally state the possible developments in this field to achieve a better understanding of the subject.     

The optical spectrum of the planetary nebula NGC 6543

With the Hamilton echelle spectrograph at the Lick Observatory, emission-rich spectral lines of the planetary nebula NGC 6543 were secured in the wavelength range from 3550 to 10 100 Å. We chose two bright regions, ∼8 arcsec east and ∼13 arcsec north of the central star, the physical conditions and chemical abundances of which may differ as a result of the different physical characteristics involving the mass ejection of different epochs. By combining Hamilton echelle observations with archive UV data secured with the International Ultraviolet Explorer ( IUE ), we obtain improved diagnostics and chemical compositions for the two observed regions. The diagnostic diagram gives the average value of T _e=8000∼8300 K, and the electron number density near N _e∼5000 cm⁻³ for most ions, while some low-excitation lines indicate much higher temperatures, i.e. T _e∼10 000 K. With the construction of a photoionization model, we try to fit the observed spectra in a self-consistent way: thus, for most elements, we employ the same chemical abundances in the nebular shell; and we adopt an improved Sobolev approximation model atmosphere for the hydrogen-deficient Wolf–Rayet type central star. Within the observational errors, the chemical abundances do not seem to show any positional variation except for helium. The chemical abundances of NGC 6543 appear to be the same as in average planetary nebulae. The progenitor star may have been an object of one solar mass, most of the heavier elements of which were less plentiful than in the Sun.     

Spectroscopic study of the variable planetary nebula IC 4997

Based on our spectroscopic observations of the variable planetary nebula IC 4997 in 2003–2009, we have obtained the relative fluxes in optical emission lines. The interstellar extinction c = 0.35 has been found from the Balmer decrement by taking into account the effect of self-absorption in hydrogen lines in dense nebular regions. The variations in the Balmer decrement point to variability of the self-absorption and circumstellar extinction. We have investigated the variations in the relative intensities of some spectral lines and their ratios with time. The drop in the ratios F(λ4363)/F(Hγ) and F(λ363)/F(λ4959) that began back in 1990–1995 has continued, suggesting a decrease in the electron density and temperature in the central nebular region. The ratio F(λ6731)/F(λ6717) has remained constant. It gives an estimate for the electron density in the outer regions of IC 4997, N _e ∼ 10⁴ cm⁻³.     

Kamacite sulfurization in the solar nebula

Abstract— The kinetics and mechanisms of kamacite sulfurization were studied experimentally at temperatures and H₂S/H₂ ratios relevant to the solar nebula. Pieces of the Canyon Diablo meteorite were heated at 558 K, 613 K, and 643 K in 50 parts per million by volume (ppmv) H₂S-H₂ gas mixtures for up to one month. Optical microscopy and x-ray diffraction analyses show that the morphology and crystal orientation of the resulting sulfide layers vary with both time and temperature. Electron microprobe analyses reveal three distinct phases in the reaction products: monosulfide solid solution (mss), (Fe, Ni, Co)_1-xS, pentlandite (Fe, Ni, Co)_9-xS₈, and a P-rich phase. The bulk composition of the remnant metal was not significantly changed by sulfurization. Kamacite sulfurization at 558 K followed parabolic kinetics for the entire duration of the experiments. Sulfide layers that formed at 613 K grew linearly with time, while those that formed at 643 K initially grew linearly with time then switched to parabolic kinetics upon reaching a critical thickness. The experimental results suggest that a variety of thermodynamic, kinetic, and physical processes control the final composition and morphology of the sulfide layers. We combine morphological, x-ray diffraction, electron microprobe, and kinetic data to produce a comprehensive model of sulfide formation in the solar nebula. Then, we present a set of criteria to assist in the identification of solar nebula condensate sulfides in primitive meteorites.     

Dust in the solar system and in extra-solar planetary systems

Among the observed circumstellar dust envelopes a certain population, planetary debris disks, is ascribed to systems with optically thin dust disks and low gas content. These systems contain planetesimals and possibly planets and are believed to be systems that are most similar to our solar system in an early evolutionary stage. Planetary debris disks have been identified in large numbers by a brightness excess in the near-infrared, mid-infrared and/or submillimetre range of their stellar spectral energy distributions. In some cases, spatially resolved observations are possible and reveal complex spatial structures. Acting forces and physical processes are similar to those in the solar system dust cloud, but the observational approach is obviously quite different: overall spatial distributions for systems of different ages for the planetary debris disks, as opposed to detailed local information in the case of the solar system. Comparison with the processes of dust formation and evolution observed in the solar system therefore helps understand the planetary debris disks. In this paper, we review our present knowledge of observations, acting forces, and major physical interactions of the dust in the solar system and in similar extra-solar planetary systems.