Grains accretion processes in a protoplanetary nebula: Conducting and insulating materials

In a previous work the authors estimated cross-sections for constructive and destructive collisions (‘constructive’ and ‘destructive’ cross-sections) related to silica grains embedded in a protoplanetary nebula. The outstanding point of the problem has induced the authors to examine more closely the physical conditions in which the accretion processes occur, and their dependence on the materials, by which the particles are probably made. In this paper the interaction processes among conducting grains (iron, graphite) and among the insulating (silica) ones have been considered. The following results have been obtained: (1) insulating grains have smaller constructive crossections than conducting; and (2) conducting grains show very large cross-sections for masses up to about 10^?9 g.     

Grains accretion processes in a protoplanetary nebula: Effects of the presence of liquid drops

The temporal behaviour of the mass distribution function of iron solid and/or liquid grains is studied in the inner regions of the solar nebula during its gravitational collapse. At distances from the centre of the nebula equal to 0.2 AU, 0.5 AU and 0.7 AU a mass limit for the accretionary process equal, respectively, to 17.6 g, 5.2 g and 3×10^–3 g is obtained in a reasonable time interval. The importance of a drop phase during the growth of the particles and of the sedimentation of the grains during the disk phase is underlined.     

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.     

Accumulation processes in the primitive solar nebula

Particle accumulation processes are discussed for a variety of physical environments, ranging from the collapse phase of an interstellar cloud to the different parts of the models of the primitive solar nebula constructed by Cameron and Pine. Because of turbulence in the collapsing interstellar gas, it is concluded that interstellar grains accumulate into bodies with radii of a few tens of centimeters before the outer parts of the solar nebula are formed. These bodies can descend quite rapidly through the gas toward midplane of the nebula, and accumulation to planetary size can occur in a few thousand years. Substantial modifications of these processes take place in the outer convection zone of the solar nebula, but again it is concluded that bodies in that zone can grow to planetary size in a few thousand years.From the discussion of the interstellar collapse phase it is concluded that the angular momentum of the primitive solar nebula was predominantly of random turbulent origin, and that it is plausible that the primitive solar nebula should have possessed satellite nebulae in highly elliptical orbits. It is proposed that the comets were formed in these satellite nebulae.A number of other detailed conclusions are drawn from the analysis. It is shown to be plausible that an iron-rich planet should be formed in the inner part of the outer nebular convection zone. Discussions are given of the processes of planetary gas accretion, the formation of satellites, the T Tauri solar wind, and the dissipation of excess condensed material after the nebular gases have been removed by the T Tauri solar wind. It is shown that the present radial distances of the planets (but not Bode's Law) should be predicted reasonably well by a solar nebula model intermediate between the uniform and linear cases of Cameron and Pine.     

Study of magnetized accretion flow with cooling processes

We have studied shock in magnetized accretion flow/funnel flow in case of neutron star with bremsstrahlung cooling and cyclotron cooling. All accretion solutions terminate with a shock close to the neutron star surface, but at some regions of the parameter space, it also harbours a second shock away from the star surface. We have found that cyclotron cooling is necessary for correct accretion solutions which match the surface boundary conditions.     

The solar oxygen-isotopic composition: Predictions and implications for solar nebula processes

Abstract— The outer layers of the Sun are thought to preserve the average isotopic and chemical composition of the solar system. The solar O-isotopic composition is essentially unmeasured, though models based on variations in meteoritic materials yield several predictions. These predictions are reviewed and possible variations on these predictions are explored. In particular, the two-component mixing model of Clayton and Mayeda (1984) (slightly revised here) predicts solar compositions to lie along an extension of the calcium-aluminum-rich inclusion (CAI) ¹⁶O line between (δ¹⁸O, δ¹⁷O) = (16.4, 11.4)%0 and (12.3, 7.5)%0. Consideration of data from ordinary chondrites suggests that the range of predicted solar composition should extend to slightly lower δ¹⁸O values. The predicted solar composition is critically sensitive to the solid/gas ratio in the meteorite-forming region, which is often considered to be significantly enriched over solar composition. A factor of two solid/gas enrichment raises the predicted solar (δ¹⁸O, δ¹⁷O) values along an extension of the CAI ¹⁶O line to (33, 28)%0. The model is also sensitive to the nebular O gas phase. If conversion of most of the gaseous O from CO to H₂O occurred at relatively low temperatures and was incomplete at the time of CM aqueous alteration, the predicted nebular gas composition (and hence the solar composition) would be isotopically heavier along a slope 1/2 line. The likelihood of having a single solid nebular O component is discussed. A distribution of initial solid compositions along the CAI ¹⁶O line (rather than simply as an end-member) would not significantly change the predictions above in at least one scenario. Even considering these variations within the mixing model, the predicted range of solar compositions is distinct from that expected if the meteoritic variations are due to non-mass-dependent fractionation. Thus, a measurement of the solar O composition to a precision of several permil would clearly distinguish between these theories and should clarify a number of other important issues regarding solar system formation.     

Scattering of light in a spherical nebula

Leningrad State University. Translated fromAstrofizika, Vol. 35, No. 1, pp. 97–109, July–August, 1991.     

The effects of nebula surface density profile and giant‐planet eccentricities on planetary accretion in the inner solar system

Abstract— We describe results of 32 N‐body planetary accretion simulations that investigate the dependence of terrestrial‐planet formation on nebula surface density profile σ and evolution of the eccentricities of Jupiter and Saturn e_j,s. Two surface density profiles are examined: a decaying profile with σ ∝ 1/a, where a is orbital semi‐major axis, and a peaked profile in which σ increases for a < 2 AU and decreases for a > 2 AU. The peaked profiles are generated by models of coagulation in an initially hot nebula. Models with initial e_j,s = 0.05 (the current value) and 0.1 are considered. Simulations using the decaying profile with e_j,s = 0.1 produce systems most like the observed planets in terms of mass‐weighted mean a and the absence of a planet in the asteroid belt. Simulations with doubled σ produce planets roughly twice as massive as the nominal case. Most initial embryos are removed in each simulation via ejection from the solar system or collision with the Sun. The asteroid belt is almost entirely cleared on a timescale of 10–100 Ma that depends sensitively on e_j,s. Most initial mass with a < 2 AU survives, with the degree of mass loss increasing with a. Mass loss from the terrestrial region occurs on a timescale that is long compared to the mass loss time for the asteroid belt. Substantial radial mixing of material occurs in all simulations, but is greater in simulations with initital e_j,s = 0.05. The degree of mixing is equivalent to a feeding zone of half width 1.5 and 0.9 AU for an Earth mass planet at 1 AU for the cases e_j,s = 0.05 and 0.1, respectively. In simulations with e_j,s = 0.05, roughly one‐third and 5–10% of the mass contained in final terrestrial planets originated in the region a > 2.5 AU for the decaying and peaked profiles, respectively. In the case e_j,s = 0.1, the median mass accreted from a > 2.5 AU is zero for both profiles.     

An investigation of a peculiar nebula in monoceros

A faint nebula, between the Rosette and NGC 2264, appears to be a supernova remnant. This was photographed with long exposures through narrow filters centred on the bright nebular emission lines. Interferograms were also taken. These revealed extensive regions emitting broad lines, and showed that the nebula did not have the large expansion velocity that was expected.     

Formation of the regular satellites of giant planets in an extended gaseous nebula I: subnebula model and accretion of satellites

We model the subnebulae of Jupiter and Saturn wherein satellite accretion took place. We expect each giant planet subnebula to be composed of an optically thick (given gaseous opacity) inner region inside of the planet’s centrifugal radius (where the specific angular momentum of the collapsing giant planet gaseous envelope achieves centrifugal balance, located at rCJ ∼ 15R_J for Jupiter and rCS ∼ 22R_S for Saturn) and an optically thin, extended outer disk out to a fraction of the planet’s Roche-lobe (R_H), which we choose to be ∼R_H/5 (located at ∼150 R_J near the inner irregular satellites for Jupiter, and ∼200R_S near Phoebe for Saturn). This places Titan and Ganymede in the inner disk, Callisto and Iapetus in the outer disk, and Hyperion in the transition region. The inner disk is the leftover of the gas accreted by the protoplanet. The outer disk may result from the nebula gas flowing into the protoplanet during the time of giant planet gap-opening (or cessation of gas accretion). For the sake of specificity, we use a solar composition “minimum mass” model to constrain the gas densities of the inner and outer disks of Jupiter and Saturn (and also Uranus). Our model has Ganymede at a subnebula temperature of ∼250 K and Titan at ∼100 K. The outer disks of Jupiter and Saturn have constant temperatures of 130 and 90 K, respectively.Our model has Callisto forming in a time scale ∼10⁶ years, Iapetus in 10⁶-10⁷ years, Ganymede in 10³-10⁴ years, and Titan in 10⁴-10⁵ years. Callisto takes much longer to form than Ganymede because it draws materials from the extended, low density portion of the disk; its accretion time scale is set by the inward drift times of satellitesimals with sizes 300-500 km from distances ∼100R_J. This accretion history may be consistent with a partially differentiated Callisto with a ∼300-km clean ice outer shell overlying a mixed ice and rock-metal interior as suggested by Anderson et al. (2001), which may explain the Ganymede-Callisto dichotomy without resorting to fine-tuning poorly known model parameters. It is also possible that particulate matter coupled to the high specific angular momentum gas flowing through the gap after giant planet gap-opening, capture of heliocentric planetesimals by the extended gas disk, or ablation of planetesimals passing through the disk contributes to the solid content of the disk and lengthens the time scale for Callisto’s formation. Furthermore, this model has Hyperion forming just outside Saturn’s centrifugal radius, captured into resonance by proto-Titan in the presence of a strong gas density gradient as proposed by Lee and Peale (2000). While Titan may have taken significantly longer to form than Ganymede, it still formed fast enough that we would expect it to be fully differentiated. In this sense, it is more like Ganymede than like Callisto (Saturn’s analog of Callisto, we expect, is Iapetus). An alternative starved disk model whose satellite accretion time scale for all the regular satellites is set by the feeding of planetesimals or gas from the planet’s Roche-lobe after gap-opening is likely to imply a long accretion time scale for Titan with small quantities of NH₃ present, leading to a partially differentiated (Callisto-like) Titan. The Cassini mission may resolve this issue conclusively. We briefly discuss the retention of elements more volatile than H₂O as well as other issues that may help to test our model.     

Evolutionary processes in protoplanetary accretion disks: the propagation of axisymmetric shock waves

In this paper we investigate both the global and the local hydrodynamics of axisymmetric accretion disks around young stellar objects under the simultaneous action of viscosity, self-gravity and pressure forces. For simplicity, we take for the global model a polytropic equation of state, make the infinitely thin disk approximation and characterize the surface density and temperature profiles in the disk as power laws in the radial distance r from the protostar. We solve the problem of the general density profile of a Keplerian disk showing that self-gravity could not be an important factor for the fast formation of the rocky cores of giant gaseous planets in our solar system. Under the hypothesis that the unperturbed rotation curve of the disk is nearly Keplerian throughout the radial extent, we can estimate with our polytropic model a lower limit for the resulting masses M_d(r) of stable disks up to 100 AU. These masses are in the range of the so-called minimum mass solar nebular (_d/M_s ≈ 0.01–0.02).By adopting a simplified viscosity model, where the height-integrated turbulent dynamical viscosity ν is a function of the surface density σ like η ∝ σ^Γ, we derive in the local shearing sheet model linearized evolution equations for small density perturbations describing both a diffusion process and the propagation of acoustic density waves. We solve a special initial value problem and calculate the appropriate Green's function. The analytical solutions so obtained describe in the case Γ < 0 the successive formation of quasi-stationary ring-shaped density structures in a disk with a definite mode of maximum instability, whereas in the case Γ > Γ_c the density wave equation describes the propagation of an “overstable” ring-shaped acoustic density wavelet to the outer ranges of the accretion disk. Whereas the group velocity of the wave packet is subsonic, the phase velocities of individual wave crests in the wave packet are supersonic. The mode of maximum instability, the growth rate and the number of growing waves in the wavelet are controlled by Γ and α. Our present knowledge concerning turbulent viscosity in protoplanetary disks is not sufficient to decide whether or not the case Γ > Γ_c is realized.The suggested structuring processes in the linear theory should initiate in the non-linear regime the formation of narrow ring-shaped density shock waves moving through the protoplanetary disk. These non-linear waves could produce extremely spatially and temporally heterogeneous temperature regions in the disk. We speculate that ring-shaped density waves, excited by inner boundary conditions and which have dominated the disk's evolution at early times, are responsible both for the fast growth of dust to planetesimals and at least for the rapid accretion of the rocky cores of giant gaseous planets in the protoplanetary accretion disk (shock wave trigger hypothesis). We derive provisional scaling rules for planetary systems regarding the spacing of orbits as a function of the mass ratio of the protoplanetary disk to the protostar. However, further analytical work and linear as well as nonlinear numerical simulations of density waves excited by inner boundary conditions are needed to consolidate the results and speculations of our linear wave mechanics in the future.     

Study of a triple emission nebula in Orion

The Hii regions S254, 255 and 257 in the constellation of Orion are close together on the sky and appear like a triple object. Fabry-Pérot radial velocities of the Hii regions as well asUBV photo-electric magnitudes of their exciting stars are obtained. The data show that (1) all three nebulae are at a distance of 2.5 kpc; (2) an excess extinction is observed in S255 and S257 while S254 shows no excess extinction; (3) S255, identified as an IR and a molecular source, is the youngest object of the group. It is concluded that the three Hii regions are at different evolutionary stages.     

Evolution of grains in a turbulent solar nebula

In accretion disk models of the solar nebula, turbulence is driven by convective instability. This mechanism requires high opacity, which must be provided by solid grains. Evolution of the grain size distribution in a turbulent disk is computed numerically, using realistic collisional outcomes and strengths of grain aggregates, rather than an arbitrary “sticking efficiency.” The presence of turbulence greatly increases the rate of grain collisions; the coagulation rate is initially much greater than in a nonturbulent disk. Aggregates quickly reach sizes ～0.1–1 cm, but erosion and breakup in collisions prevent growth of larger bodies for plausible aggregate impact strengths. These aggregates are too small to settle to the plane of the disk, and planetesimal formation is impossible as long as the turbulence persists. However, the opacity of the disk is reduced by aggregate formation; some combinations of opacity law and surface density produce an optically thin disk, cutting off turbulent convection. The disk may experience alternating periods of turbulence and quiescence, as grains are depleted by coagulation and replenished by infall from the presolar cloud. Planetesimals can form only during the quiescent intervals; it is argued that such episodes were rare during the lifetime of the accretion disk.     

Appearance of a nebula near Y Ori

The results of photographic and photoelectric observations for the star Y Ori are presented. During these observations a red nebulosity appeared around the star Y Ori near the maximum of brightness. The optical sizes of the nebulosity are comparable with the OH sizes of long period variables and OH/IR stars. A real brightness increase on the decreasing branch of the light curve was detected in U spectral band.Published in Astrofizika, Vol. 38, No. 4, pp. 555–558, October–December, 1995.     

Formation of the galilean satellites in a gaseous nebula

A model for Galilean satellite formation was analyzed in which the satellites accrete in the presence of a dense, gaseous disk-shaped nebula and rapidly form optically thick, gravitationally bound primordial atmospheres. Upper-bound temperatures expected during accretion lead to partially differentiated structures for both Ganymede and Callisto, although with Ganymede much more differentiated than Callisto. When allowance is made for the aerodynamic breaking of infalling planetesimal fragments, lower surface temperatures result, and the amount of partial differentiation of Callisto is small, possibly approaching zero for a narrow size distribution of infalling planetesimals. The model is chosen to be consistent with the observed densities of the Galilean satellites and our current understanding of Jupiter formation. The retention of ices more volatile than H₂O is considered but not modeled in detail. A nominal nebula of ～0.1 Jupiter masses is constructed by consideration of likely surface density profiles and existing Jupiter collapse calculations. This nebula is optically thick (even if grain opacity is ignored) in both radial and vertical directions and has a temperature profile T ～ 3600 (R_J/R), where R_J is Jupiter's radius and R is the radial distance in the disk midplane. Satellites accrete very rapidly (dynamical time scales being 10²–10⁴ years) and their optically thick gaseous envelopes are unable to eliminate the heat of accretion by radiation. Water-saturated, convective, adiabatic envelopes form, through which planetesimals fall, break up, and partially disseminate their mass. The resulting satellite surface temperatures during accretion are calculated. Possible implications of these models for the subsequent evolution of Ganymede and Callisto are explored and it is suggested that the extensive differentiation undergone by Ganymede may provide the right environment for subsequent resurfacing, whereas the relative lack of extensive differentiation for Callisto may explain the inferred absence of endogenic tectonism.     

Planetary nebula with a neutral envelope?

IUE ultraviolet spectral recording for a low excitating planetary nebula NGC 6369 is obtained. The very strong doublet 2800 Mgii in emission as well as not less strong absorption line 2852 Mgi are discovered in the spectrum of this nebula. It is shown that the resonance line 2852 Mgi may originate only in a neutral envelope, around the nebula, consisting of neutral hydrogen, neutral magnesium, and dust particles (Hi+Mgi). The importance of this absorption line as a powerful indicator of the discovery of neutral envelopes around the planetary nebulae is outlined.The possibility of the existence of one more envelope—transition zone—immediately contacting with the bright that is ionized part of nebula (Hii+Mgii) is also shown. The transition zone consists of neutral hydrogen, ionized magnesium, and dust particles (Hi+Mgii), main parameters of this zone are also obtained (Table IV).The temperature of the central star of this nebula is obtained for the first time:T _*=48000 K. Continuous background in the interval 2600–3000 Å is identified with Balmer continuum with electron temperatureT _e =12500 K.     

Correlated accretion ages and ε54Cr of meteorite parent bodies and the evolution of the solar nebula

We look at the relationship between the value of ε⁵⁴Cr in bulk meteorites and the time (after calcium‐aluminum‐rich inclusion, CAI) when their parent bodies accreted. To obtain accretion ages of chondrite parent bodies, we estimated the maximum temperature reached in the insulated interior of each parent body, and estimated the initial ²⁶Al/²⁷Al for this temperature to be achieved. This initial ²⁶Al/²⁷Al corresponds to the time (after CAI formation) when cold accretion of the parent body would have occurred, assuming ²⁶Al/²⁷Al throughout the solar system began with the canonical value of 5.2 × 10^?5. In cases of iron meteorite parent bodies, achondrite parent bodies, and carbonaceous chondrite parent bodies, we use published isotopic ages of events (such as core formation, magma crystallization, and growth of secondary minerals) in each body's history to obtain the probable time of accretion. We find that ε⁵⁴Cr correlates with accretion age: the oldest accretion ages (1 ± 0.5 Ma) are for iron and certain other differentiated meteorites with ε⁵⁴Cr of ?0.75 ± 0.5, and the youngest ages (3.5 ± 0.5 Ma) are for hydrated carbonaceous chondrites with ε⁵⁴Cr values of 1.5 ± 0.5. Despite some outliers (notably Northwest Africa [NWA] 011 and Tafassasset), we feel that the correlation is significant and we suggest that it resulted from late, localized injection of dust with extremely high ε⁵⁴Cr.