Noble gases in angrites Northwest Africa 1296, 2999/4931, 4590, and 4801: Evolution history inferred from noble gas signatures

Noble gases in the five angrites Northwest Africa (NWA) 1296, 2999, 4590, 4801, and 4931 were analyzed with total melting and stepwise heating methods. The noble gases consist of in situ components: spallogenic, radiogenic, nucleogenic, and fission. Cosmic-ray exposure ages of the angrites (including literature data) spread uniformly from <0.2 to 56 Ma, and coarse-grained angrites have longer exposure ages than fine-grained angrites. It is implied that the parent bodies from which the two subgroups of angrites were ejected are different and have distinct orbital elements. The ²⁴⁴Pu-¹³⁶Xe relative ages of the angrites obtained by using ²⁴⁴Pu/¹⁵⁰Nd ratios are as old as that of Angra dos Reis, reflecting their early formation. On the other hand, another method to obtain ²⁴⁴Pu-¹³⁶Xe relative ages, using fission ¹³⁶Xe, spallogenic ¹²⁶Xe, and Ba/REE ratios, yields systematically older ²⁴⁴Pu-¹³⁶Xe ages than those obtained by using ²⁴⁴Pu/¹⁵⁰Nd ratios, which is explained by apparently high Ba/REE ratios caused by Ba contamination during terrestrial weathering. The ²⁴⁴Pu/²³⁸U ratio at 4.56 Ga of angrites is estimated as 0.0061 ± 0.0028, which is consistent with those for chondrules, chondrites, achondrites, and a terrestrial zircon. It is suggested that initial ²⁴⁴Pu/²³⁸U ratio has been spatially homogeneous at least in the inner part of the early solar system.     

Thermal modeling of shock melts in Martian meteorites: Implications for preserving Martian atmospheric signatures and crystallization of high‐pressure minerals from shock melts

The distribution of shock melts in four shergottites, having both vein and pocket geometry, has been defined and the conductive cooling time over the range 2500 °C to 900 °C calculated. Isolated 1 mm² pockets cool in 1.17 s and cooling times increase with pocket area. An isolated vein 1 × 7 mm in Northwest Africa (NWA) 4797 cools to 900 °C in 4.5 s. Interference between thermal haloes of closely spaced shock melts decreases the thermal gradient, extending cooling times by a factor of 1.4 to 100. This is long enough to allow differential diffusion of Ar and Xe from the melt. Small pockets (1 mm²) lose 2.2% Ar and 5.2% Xe during cooling, resulting in a small change in the Ar/Xe ratio of the dissolved gas over that originally trapped. With longer cooling times there is significant fractionation of Xe from Ar and the Ar/Xe ratio increases rapidly. The largest pockets show less variation of Ar/Xe and likely preserve the original trapped gas composition. Considering all of the model calculations, even the smallest isolated pockets have cooling times greater than the duration of the pressure pulse, i.e., >0.01 s. The crystallization products of these shock melts will be unrelated to the peak shock pressure experienced by the meteorite.     

Martian albedo feature variations with season: Data of 1971 and 1973

This paper is a qualitative and quantitative investigation of recent seasonal and secular albedo feature variations on Mars using the improved red-filter photography of the International Planetary Patrol Program obtained during the 1971 and 1973 apparitons. The boundaries of telescopic albedo features showing significant changes and uncommonly bright areas were measured with an image projection reader and plotted on Mars maps in order to compare changes with Mariner 9 variable feature data obtained in 1972. The Daedalia-Claritas darkening (90–130°W, 25°S) of 1973 was the most significant change observed on Mars since the Laocoontis-Alcyonius darkening of the 1950 decade. The 1973 apparition presented six excellent examples of normal seasonal changes.Photographic photometry of 21 albedo features located in three longitude regions was systematically done on 120 original red-filter negatives, about half representing the Martian southern spring season and the other half the southern summer season. These two sets of photographs differed about 90° in L_s but were nearly equal in viewing geometry. They were identical in image scale, emulsion, color response, and quality. The data, consisting of 3960 density measurements, were analyzed in terms of albedo ratios and their fluctuations. Several types of diagnostic graphs are presented.Seasonal differences of the mean brightness ratios for most of the features were found to be consistent with the contrast changes shown on photographic Mars maps. Seasonal variations of brightnesses with latitude and region were indicated, but not in the strict classical sense of a wave-of-darkening. Most albedo features were more variable during southern spring than they were in summer. Most light albedo features were more active than dark ones during both seasons. There was a general loss of relative contrast in southern summer. No systematic dependence on solar phase angle was detected within the range (38° > i > 16°) spanned by both sets of photographs.     

Noble gases and chemical composition of Shergotty mineral fractions,Chassigny, and Yamato 793605: The trapped argon-40/argon-36 ratio and ejection times of Martian meteorites

Abstract— We report the elemental and isotopic composition of the noble gases as well as the chemical abundances in pyroxene, maskelynite/mesostasis glass, and bulk material of Shergotty and of bulk samples from Chassigny and Yamato 793605. The ⁴⁰K-⁴⁰Ar isochron for the Shergotty minerals yields a gas retention age of 196 Ma, which is, within errors, in agreement with previously determined Rb-Sr internal isochron ages. Argon that was trapped at this time has a ⁴⁰Ar/³⁶Ar ratio of 1100. For Chassigny and Y-793605, we obtain trapped ⁴⁰Ar/³⁶Ar ratios of 1380 and 950, respectively. Using these results and literature data, we show that the three shergottites, Shergotty, Zagami, and QUE 94001; the lherzolites ALH 77005, LEW 88516, and Y-793605; as well as Chassigny and ALH 84001 contain a mixture of Martian mantle and atmospheric Ar; whereas, the trapped ⁴⁰Ar/³⁶Ar ratio of the nakhlites, Nakhla, Lafayette, and Governador Valadares cannot be determined with the present data. We show that Martian atmospheric trapped Ar in Martian meteorites is correlated with the shock pressure that they experienced. Hence, we conclude that the Martian atmospheric gases were introduced by shock into the meteoritic material. For the Shergotty minerals, we obtain ³He-, ²¹Ne-, and ³⁸Ar-based cosmic-ray exposure ages of 3.0 Ma, and for the lherzolite Y-793605, 4.0 Ma, which confirms our earlier conclusion that the lherzolites were ejected from Mars ～1 Ma before the shergottites. Chassigny yields the previously known ejection age of 11.6 Ma.     

Interior textures,chemical compositions,and noble gas signatures of Antarctic cosmic spherules: Possible sources of spherules with long exposure ages

Abstract– The interior texture and chemical and noble gas composition of 99 cosmic spherules collected from the meteorite ice field around the Yamato Mountains in Antarctica were investigated. Their textures were used to classify the spherules into six different types reflecting the degree of heating: 13 were cryptocrystalline, 40 were barred olivine, 3 were porphyritic A, 24 were porphyritic B, 9 were porphyritic C, and 10 were partially melted spherules. While a correlation exists between the type of spherule and its noble gas content, there is no significant correlation between its chemical composition and noble gas content. Fifteen of the spherules still had detectable amounts of extraterrestrial He, and the majority of them had ³He/⁴He ratios that were close to that of solar wind (SW). The Ne isotopic composition of 28 of the spherules clustered between implantation‐fractionated SW and air. Extraterrestrial Ar, confirmed to be present because it had a ⁴⁰Ar/³⁶Ar ratio lower than that of terrestrial atmosphere, was found in 35 of the spherules. An enigmatic spherule, labeled M240410, had an extremely high concentration of cosmogenic nuclides. Assuming 4π exposure to galactic and solar cosmic rays as a micrometeoroid and no exposure on the parent body, the cosmic‐ray exposure (CRE) age of 393 Myr could be computed using cosmogenic ²¹Ne. Under these model assumptions, the inferred age suggests that the particle might have been an Edgeworth‐Kuiper Belt object. Alternatively, if exposure near the surface of its parent body was dominant, the CRE age of 382 Myr can be estimated from the cosmogenic ³⁸Ar using the production rate of the 2π exposure geometry, and implies that the particle may have originated in the mature regolith of an asteroid.     

Supermassive black hole in an elliptical galaxy: Accretion of a hot gas with a low but finite angular momentum

The accretion of hot slowly rotating gas onto a supermassive black hole is considered. The important case where the velocities of turbulent pulsations at the Bondi radius r _B are low, compared to the speed of sound c _s, is studied. Turbulence is probably responsible for the appearance of random average rotation. Although the angular momentum at r _B is low, it gives rise to the centrifugal barrier at a depth r _c = l ² /GM _BH ? r _B, that hinders supersonic accretion. The numerical solution of the problem of hot gas accretion with finite angular momentum is found taking into account electron thermal conductivity and bremsstrahlung energy losses of two temperature plasma for density and temperature near Bondi radius similar to observed in M87 galaxy. The saturation of the Spitzer thermal conductivity was also taken into account. The parameters of the saturated electron thermal conductivity were chosen similar to the parameters used in the numerical simulations of interaction of the strong laser beam radiation with plasma targets. These parameters are confirmed in the experiments. It is shown that joint action of electron thermal conductivity and free-free radiation leads to the effective cooling of accreting plasma and formation of the subsonic settling of accreting gas above the zone of a centrifugal barrier. A toroidal condensation and a hollow funnel that separates the torus from the black hole emerge near the barrier. The barrier divides the flow into two regions: (1) the settling zone with slow subKeplerian rotation and (2) the zone with rapid supersonic nearly Keplerian rotation. Existence of the centrifugal barrier leads to significant decrease of the accretion rate ? in comparison with the critical Bondi solution for γ = 5/3 for the same values of density and temperature of the hot gas near Bondi radius. Shear instabilities in the torus and related friction cause the gas to spread slowly along spirals in the equatorial plane in two directions.As a result, outer (r > r _c) and inner (r < r _c) disks are formed. The gas enters the immediate neighborhood of the black hole or the zone of the internal ADAF flow along the accretion disk (r < r _c). Since the angular momentum is conserved, the outer disk removes outward an excess of angular momentum along with part of the matter falling into the torus. It is possible, that such outer Keplerian disk was observed by Hubble Space Telescope around the nucleus of the M87 galaxy in the optical emission lines. We discuss shortly the characteristic times during which the accretion of the gas with developed turbulence should lead to the changes in the orientation of the torus, accretion disk and, possibly, of the jet.     

Noble gases in chondrules and associated metal‐sulfide‐rich samples: Clues on chondrule formation and the behavior of noble gas carrier phases

Abstract— Chondrules are generally believed to have lost most or all of their trapped noble gases during their formation. We tested this assumption by measuring He, Ne, and Ar in chondrules of the carbonaceous chondrites Allende (CV3), Leoville (CV3), Renazzo (CR2), and the ordinary chondrites Semarkona (LL3.0), Bishunpur (LL3.1), and Krymka (LL3.1). Additionally, metalsulfide‐rich chondrule coatings were measured that probably formed from chondrule metal. Low primordial ²⁰Ne concentrations are present in some chondrules, while even most of them contain small amounts of primordial ³⁶Ar. Our preferred interpretation is that‐in contrast to CAIs‐the heating of the chondrule precursor during chondrule formation was not intense enough to expel primordial noble gases quantitatively. Those chondrules containing both primordial ²⁰Ne and ³⁶Ar show low presolar‐diamond‐like ³⁶Ar/²⁰Ne ratios. In contrast, the metal‐sulfide‐rich coatings generally show higher gas concentrations and Q‐like ³⁶Ar/²⁰Ne ratios. We propose that during metalsilicate fractionation in the course of chondrule formation, the Ar‐carrying phase Q became enriched in the metal‐sulfide‐rich chondrule coatings. In the silicate chondrule interior, only the most stable Ne‐carrying presolar diamonds survived the melting event leading to the low observed ³⁶Ar/²⁰Ne ratios. The chondrules studied here do not show evidence for substantial amounts of fractionated solar‐type noble gases from a strong solar wind irradiation of the chondrule precursor material as postulated by others for the chondrules of an enstatite chondrite.     

Chondrules: Precursors and interactions with the nebular gas

Abstract– Chondrule compositions suggest either ferroan precursors and evaporation, or magnesian precursors and condensation. Type I chondrule precursors include granoblastic olivine aggregates (planetary or nebular) and fine‐grained (dustball) precursors. In carbonaceous chondrites, type I chondrule precursors were S‐free, while type II chondrules have higher Fe/Mn than in ordinary chondrites. Many type II chondrules contain diverse forsteritic relicts, consistent with polymict dustball precursors. The relationship between finer and coarser grained type I chondrules in ordinary chondrites suggests more evaporation from more highly melted chondrules. Fe metal in type I, and Na and S in type II chondrules indicate high partial pressures in ambient gas, as they are rapidly evaporated at canonical conditions. The occurrence of metal, sulfide, or low‐Ca pyroxene on chondrule rims suggests (re)condensation. In Semarkona type II chondrules, Na‐rich olivine cores, Na‐poor melt inclusions, and Na‐rich mesostases suggest evaporation followed by recondensation. Type II chondrules have correlated FeO and MnO, consistent with condensation onto forsteritic precursors, but with different ratios in carbonaceous chondrites and ordinary chondrites, indicating different redox history. The high partial pressures of lithophile elements require large dense clouds, either clumps in the protoplanetary disk, impact plumes, or bow shocks around protoplanets. In ordinary chondrites, clusters of type I and type II chondrules indicate high number densities and their similar oxygen isotopic compositions suggest recycling together. In carbonaceous chondrites, the much less abundant type II chondrules were probably added late to batches of type I chondrules from different O isotopic reservoirs.     

Argon in the Martian atmosphere: Do the results of Mars 6 agree with the optical and radio occultation measurements?

Mars 6 discovered an inert gas (probably argon) in the Martian atmosphere. An analysis is carried out for the available spectroscopic observations, radio occultation results, and other data with the aim of determining the maximum argon content with which they are consistent. Possible seasonal variations of pressure are taken into account. It is shown that 25–30% of argon is consistent with all these data. The presence of argon slightly increases the mean pressure estimates; 25% argon increases pressures derived from radio occultation data by 0.5 mbar.     

Noble gas record and cosmic‐ray exposure history of the new CO3 chondrite Moss––Comparison with Lancé and other CO chondrite falls

Abstract– The Moss meteorite is the first CO chondrite fall after a time period of 70 yr and the least terrestrially contaminated member of its group. Its cosmic‐ray exposure (CRE) age (T₃ ～ 13.5 Ma; T₂₁ ～ 14.6 Ma) is distinct among CO chondrites and, within witnessed falls is the shortest after Lancé, which we have reanalyzed. Gas retention ages are approximately 3.95 × 10⁹ yr (U/Th‐He) and approximately 4.43 × 10⁹ yr (K/Ar), respectively. Trapped Ar, Kr, and Xe are present in Moss in abundances typical for CO chondrites, with “planetary” elemental and isotopic compositions. Presence of HL‐xenon from presolar diamonds is observed in the stepwise release analysis of Lancé. It may also be present in Moss, but it is difficult to ascertain in single‐step bulk analyses. It follows from our new data combined with a survey of the literature that the abundance of trapped gases in CO chondrites is not a good indicator of their petrological subtype.     

Formation of gas giant planets: core accretion models with fragmentation and planetary envelope

We have calculated formation of gas giant planets based on the standard core accretion model including effects of fragmentation and planetary envelope. The accretion process is found to proceed as follows. As a result of runaway growth of planetesimals with initial radii of ∼10 km, planetary embryos with a mass of ∼10²⁷ g (∼ Mars mass) are found to form in ∼10⁵ years at Jupiter's position (5.2 AU), assuming a large enough value of the surface density of solid material (25 g/cm²) in the accretion disk at that distance. Strong gravitational perturbations between the runaway planetary embryos and the remaining planetesimals cause the random velocities of the planetesimals to become large enough for collisions between small planetesimals to lead to their catastrophic disruption. This produces a large number of fragments. At the same time, the planetary embryos have envelopes, that reduce energies of fragments by gas drag and capture them. The large radius of the envelope increases the collision rate between them, resulting in rapid growth of the planetary embryos. By the combined effects of fragmentation and planetary envelope, the largest planetary embryo with 21M_⊕ forms at 5.2 AU in 3.8×10⁶ years. The planetary embryo is massive enough to start a rapid gas accretion and forms a gas giant planet.     

Simulations of spiral galaxies with an active potential: molecular cloud formation and gas dynamics

We describe simulations of the response of a gaseous disc to an active spiral potential. The potential is derived from an N -body calculation and leads to a multi-armed time-evolving pattern. The gas forms long spiral arms typical of grand-design galaxies, although the spiral pattern is asymmetric. The primary difference from a grand-design spiral galaxy, which has a consistent two-/four-armed pattern, is that instead of passing through the spiral arms, gas generally falls into a developing potential minimum and is released only when the local minimum dissolves. In this case, the densest gas is coincident with the spiral potential, rather than offset as in the grand-design spirals. We would therefore expect no offset between the spiral shock and star formation, and no obvious corotation radius. Spurs which occur in grand-design spirals when large clumps are sheared off leaving the spiral arms, are rare in the active, time-evolving spiral reported here. Instead, large branches are formed from spiral arms when the underlying spiral potential is dissolving due to the N -body dynamics. We find that the molecular cloud mass spectrum for the active potential is similar to that for clouds in grand-design calculations, depending primarily on the ambient pressure rather than the nature of the potential. The largest molecular clouds occur when spiral arms collide, rather than by agglomeration within a spiral arm.     

Evolution of galaxies: One-zone model with a birth-rate stellar function depending on gas density and temperature

In this paper closed one-zone models with a birth-rate stellar function depending on gas density and temperature are built up, in order to make a zeroth order approximation of thermo-chemical evolution of galaxies. To get a more realistic picture, the models are allowed first to expand with the universe and then to contract according to three successive time-scales, in order to simulate violent relaxation, rapid contraction, and slow contraction processes.Star formation occurs according to a birth-rate (m, t) _g ⁿ T ^r m ^p ( _g , gas density;T, gas temperature; andm, star mass), which reproduces the usual Schmidt-type law in the limitr0. Further we suppose that synthesized metals and helium are instantaneously mixed when returned to gas component at star death, and that relative metal abundances are time-independent: ( any element heavier than He, ). An energy fraction of each typical supernova event is assumed to heat interstellar medium, which is also though always to maintain a steady state.Under these hypotheses it becomes possible to use the interstellar cooling function of Dalgarno and McCray (1972), which is related to a special cosmic abundance of elements, to express analytically an interstellar cooling function related to any abundance. At this stage, numerical computations are performed up to about 12 Gy and the results analyzed in order to reproduce some morphological features observed in the galaxy, namely: (i) the extreme scarcity of stars with nearly zero metal content; (ii) the metal content and mass fraction of halo stars; (iii) the metal content and mass fraction of disk stars; and (iv) the ratio of the present-day birth-rate to the past birth-rate averaged over the age of the disk. It is found that a whole class of theoretical models exist, with slope of the mass spectrum between –2.5 and –2.6, which range from a Schmidt's law limitn=1.3 andr=0 to the opposite limitn=0 andr=–1.2, and are able to fit more or less at the same extent the observations mentioned above. On the analysis of further computations, it is also shown that an universal birth-rate stellar function is in contradiction with neither a dynamical hystory starting from the initial expansion of proto-galaxies, nor a morphological sequence where the amount of angular momentum is the only free parameter for any given mass, at least for what concerns spiral types. Finally, possible refinements for future work are briefly outlined.     

Models of α Centauri A and B with and without seismic constraints: time dependence of the mixing-length parameter

The α Centauri (α Cen) binary system is a well-known stellar system with very accurate observational constraints on the structure of its component stars. In addition to the classical non-seismic constraints, there are also seismic constraints for the interior models of α Cen A and B. These two types of constraint give very different values for the age of the system. While we obtain 8.9 Gyr for the age of the system from the non-seismic constraints, the seismic constraints imply that the age is about 5.6–5.9 Gyr. There may be observational or theoretical reasons for this discrepancy, which can be found by careful consideration of similar stars. The α Cen binary system, with its solar-type components, is also suitable for testing the stellar mass dependence of the mixing-length parameter for convection derived from the binaries of Hyades. The values of the mixing-length parameter for α Cen A and B are 2.10 and 1.90 for the non-seismic constraints. If we prioritize the seismic constraints, we obtain 1.64 and 1.91 for α Cen A and B, respectively. By taking into account these two contrasting cases for stellar mass dependence of the mixing-length parameter, we derive two expressions for its time dependence, which are also compatible with the mass dependence of the mixing-length parameter derived from the Hyades stars. For assessment, these expressions should be tested in other stellar systems and clusters.     

Laboratory impacts into dry and wet sandstone with and without an overlying water layer: Implications for scaling laws and projectile survivability

Abstract— Scaling laws describing crater dimensions are defined in terms of projectile velocity and mass, densities of the materials involved, strength of the target, and the local gravity. Here, the additional importance of target porosity and saturation, and an overlying water layer, are considered through 15 laboratory impacts of 1 mm diameter stainless steel projectiles at 5 km s^?1 into a) an initially uncharacterized sandstone (porosity ?17%) and b) Coconino Sandstone (porosity ?23%). The higher‐porosity dry sandstone allows a crater to form with a larger diameter but smaller depth than in the lower‐porosity dry sandstone. Furthermore, for both porosities, a greater volume of material is excavated from a wet target than a dry target (by 27–30%). Comparison of our results with Pi‐scaling (dimensionless ratios of key parameters characterizing cratering data over a range of scales) suggests that porosity is important for scaling laws given that the new data lie significantly beneath the current fit for ice and rock targets on a π_v versus π₃ plot (π_v gives cratering efficiency and π₃ the influence of target strength). An overlying water layer results in a reduction of crater dimensions, with larger craters produced in the saturated targets compared to unsaturated targets. A water depth of approximately 12 times the projectile diameter is required before craters are no longer observed in the targets. Previous experimental studies have shown that this ratio varies between 10 and 20 (Gault and Sonett 1982). In our experiments ?25% of the original projectile mass survives the impact.     

Jet–gas interactions in z∼ 2.5 radio galaxies: evolution of the ultraviolet line and continuum emission with radio morphology

We present an investigation into the nature of the jet–gas interactions in a sample of 10 radio galaxies at  2.3 < z < 2.9  using deep spectroscopy of the ultraviolet (UV) line and continuum emission obtained at Keck II and the Very Large Telescope. Kinematically perturbed gas, which we have shown to be within the radio structure in previous publications, is always blueshifted with respect to the kinematically quiescent gas, is usually spatially extended, and is usually detected on both sides of the nucleus. In the three objects from this sample for which we are able to measure line ratios for both the perturbed and quiescent gases, we suggest that the former has a lower ionization state than the latter.
We propose that the perturbed gas is part of a jet-induced outflow, with dust obscuring the outflowing gas that lies on the far side of the object. The spatial extent of the blueshifted perturbed gas, typically ∼35 kpc, implies that the dust is spatially extended at least on similar spatial scales.
We also find interesting interrelationships between UV line, UV continuum and radio continuum properties of this sample.     

Sublimation extraction coupled with gas chromatography-mass spectrometry: A new technique for future in situ analyses of purines and pyrimidines on Mars

We have developed a sublimation technique coupled with chemical derivatization and gas chromatography mass spectrometry (GC-MS) to detect nucleobases and other volatile organic compounds derived from bacteria in Mars analog materials. To demonstrate this technique, a sample of serpentine inoculated with Escherichia coli (E. coli) cells was heated to 500 °C for several seconds under Martian ambient pressure. The sublimate was collected on a cold finger, then derivatized and analyzed by GC-MS. We found that adenine, cytosine, thymine and uracil were the most abundant molecules detected in the sublimed E. coli extract by GC-MS. In addition, nucleobases were also detected in sublimed extracts of a deep-sea sediment sample, seawater, and soil collected from the Atacama Desert in Chile after heating the samples under the same conditions. Our results indicate that nucleobases can be easily isolated directly from natural samples using sublimation and then detected by GC-MS after chemical derivatization. The sublimation-based extraction technique is one approach that should be considered for use by future in situ instruments designed to detect organic compounds relevant to life in the Martian regolith.     

Orbital evolution and accretion of protoplanets tidally interacting with a gas disk: I. Effects of interaction with planetesimals and other protoplanets

We have performed N-body simulations on the stage of protoplanet formation from planetesimals, taking into account so-called “type-I migration,” and damping of orbital eccentricities and inclinations, as a result of tidal interaction with a gas disk without gap formation. One of the most serious problems in formation of terrestrial planets and jovian planet cores is that the migration time scale predicted by the linear theory is shorter than the disk lifetime (10⁶-10⁷ years). In this paper, we investigate retardation of type-I migration of a protoplanet due to a torque from a planetesimal disk in which a gap is opened up by the protoplanet, and torques from other protoplanets which are formed in inner and outer regions. In the first series of runs, we carried out N-body simulations of the planetesimal disk, which ranges from 0.9 to 1.1 AU, with a protoplanet seed in order to clarify how much retardation can be induced by the planetesimal disk and how long such retardation can last. We simulated six cases with different migration speeds. We found that in all of our simulations, a clear gap is not maintained for more than 10⁵ years in the planetesimal disk. For very fast migration, a gap cannot be created in the planetesimal disk. For migration slower than some critical speed, a gap does form. However, because of the growth of the surrounding planetesimals, gravitational perturbation of the planetesimals eventually becomes so strong that the planetesimals diffuse into the vicinity of the protoplanets, resulting in destruction of the gap. After the gap is destroyed, close encounters with the planetesimals rather accelerate the protoplanet migration. In this way, the migration cannot be retarded by the torque from the planetesimal disk, regardless of the migration speed. In the second series of runs, we simulated accretion of planetesimals in wide range of semimajor axis, 0.5 to 2-5 AU, starting with equal mass planetesimals without a protoplanet seed. Since formation of comparable-mass multiple protoplanets (“oligarchic growth”) is expected, the interactions with other protoplanets have a potential to alter the migration speed. However, inner protoplanets migrate before outer ones are formed, so that the migration and the accretion process of a runaway protoplanet are not affected by the other protoplanets placed inner and outer regions of its orbit. From the results of these two series of simulations, we conclude that the existence of planetesimals and multiple protoplanets do not affect type-I migration and therefore the migration shall proceed as the linear theory has suggested.     

Orbital evolution and accretion of protoplanets tidally interacting with a gas disk: II. Solid surface density evolution with type-I migration

This paper investigates the surface density evolution of a planetesimal disk due to the effect of type-I migration by carrying out N-body simulation and through analytical method, focusing on terrestrial planet formation. The coagulation and the growth of the planetesimals take place in the abundant gas disk except for a final stage. A protoplanet excites density waves in the gas disk, which causes the torque on the protoplanet. The torque imbalance makes the protoplanet suffer radial migration, which is known as type-I migration. Type-I migration time scale derived by the linear theory may be too short for the terrestrial planets to survive, which is one of the major problems in the planet formation scenario. Although the linear theory assumes a protoplanet being in a gas disk alone, Kominami et al. [Kominami, J., Tanaka, H., Ida, S., 2005. Icarus 167, 231-243] showed that the effect of the interaction with the planetesimal disk and the neighboring protoplanets on type-I migration is negligible. The migration becomes pronounced before the planet's mass reaches the isolation mass, and decreases the solid component in the disk. Runaway protoplanets form again in the planetesimal disk with decreased surface density. In this paper, we present the analytical formulas that describe the evolution of the solid surface density of the disk as a function of gas-to-dust ratio, gas depletion time scale and semimajor axis, which agree well with our results of N-body simulations. In general, significant depletion of solid material is likely to take place in inner regions of disks. This might be responsible for the fact that there is no planet inside Mercury's orbit in our Solar System. Our most important result is that the final surface density of solid components (Σd) and mass of surviving planets depend on gas surface density (Σg) and its depletion time scale (τdep) but not on initial Σd; they decrease with increase in Σg and τdep. For a fixed gas-to-dust ratio and τdep, larger initial Σd results in smaller final Σd and smaller surviving planets, because of larger Σg. To retain a specific amount of Σd, the efficient disk condition is not an initially large Σd but the initial Σd as small as the specified final one and a smaller gas-to-dust ratio. To retain Σd comparable to that of the minimum mass solar nebula (MMSN), a disk must have the same Σd and a gas-to-dust ratio that is smaller than that of MMSN by a factor of 1.3×(τdep/1 Myr) at ∼1 AU. (Equivalently, type-I migration speed is slower than that predicted by the linear theory by the same factor.) The surviving planets are Mars-sized ones in this case; in order to form Earth-sized planets, their eccentricities must be pumped up to start orbit crossing and coagulation among them. At ∼5 AU, Σd of MMSN is retained under the same condition, but to form a core massive enough to start runaway gas accretion, a gas-to-dust ratio must be smaller than that of MMSN by a factor of 3×τdep/1 Myr.