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.     

A gas-poor planetesimal capture model for the formation of giant planet satellite systems

Assuming that an unknown mechanism (e.g., gas turbulence) removes most of the subnebula gas disk in a timescale shorter than that for satellite formation, we develop a model for the formation of regular (and possibly at least some of the irregular) satellites around giant planets in a gas-poor environment. In this model, which follows along the lines of the work of Safronov et al. [1986. Satellites. Univ. of Arizona Press, Tucson, pp. 89-116], heliocentric planetesimals collide within the planet's Hill sphere and generate a circumplanetary disk of prograde and retrograde satellitesimals extending as far out as ∼RH/2. At first, the net angular momentum of this proto-satellite swarm is small, and collisions among satellitesimals leads to loss of mass from the outer disk, and delivers mass to the inner disk (where regular satellites form) in a timescale ?¹⁰⁵ years. This mass loss may be offset by continued collisional capture of sufficiently small <1 km interlopers resulting from the disruption of planetesimals in the feeding zone of the giant planet. As the planet's feeding zone is cleared in a timescale ?¹⁰⁵ years, enough angular momentum may be delivered to the proto-satellite swarm to account for the angular momentum of the regular satellites of Jupiter and Saturn. This feeding timescale is also roughly consistent with the independent constraint that the Galilean satellites formed in a timescale of ¹⁰⁵-¹⁰⁶ years, which may be long enough to accommodate Callisto's partially differentiated state [Anderson et al., 1998. Science 280, 1573; Anderson et al., 2001. Icarus 153, 157-161]. In turn, this formation timescale can be used to provide plausible constraints on the surface density of solids in the satellitesimal disk (excluding satellite embryos for satellitesimals of size ∼1 km), which yields a total disk mass smaller than the mass of the regular satellites, and means that the satellites must form in several ∼10 collisional cycles. However, much more work will need to be conducted concerning the collisional evolution both of the circumplanetary satellitesimals and of the heliocentric planetesimals following giant planet formation before one can assess the significance of this agreement. Furthermore, for enough mass to be delivered to form the regular satellites in the required timescale one may need to rely on (unproven) mechanisms to replenish the feeding zone of the giant planet. We compare this model to the solids-enhanced minimum mass (SEMM) model of Mosqueira and Estrada [2003a. Icarus 163, 198-231; 2003b. Icarus 163, 232-255], and discuss its main consequences for Cassini observations of the saturnian satellite system.     

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.     

Distance law and formation of satellite systems

In the solar system satellite systems of Jupiter, Saturn and Uranus are typical ones. The distribution of the semi-major axis of satellite orbits in each system may be expressed by an empirical formula corresponding to the Titius-Bode law. We found that it can be written as a_n = B′ · Bⁿ, where B′ and B are constants. Values of B′ and B depend on formation conditions of each system. Satellites should be formed in the gas-satellitesimal disk around a planet and by aggregation of satellitesimals. The gas is the major component in the disk and its damping effect must play an important role in the process of aggregation of satellitesimals. It may be proved that radial small perturbation in the disk can cause the gravitational instability and the formation of gaseous rings with increased density, where satellitesimals can easy aggregat into satellites.     

An accretion disk,a bipolar outflow,and an envelope—A structure that accompanies the formation of a protostar

We analyze the superfine structure of the supermaser H₂O emission region in Orion KL over the period 1979–1999. The angular resolution reached 0.1 mas, which corresponds to 0.045 AU at a distance to Orion KL of 450 pc. We determined the velocity of the local standard of rest, V_LSR = 7.65 km s^?1. The formation of a protostar is accompanied by a structure that consists of an accretion disk, a bipolar outflow, and a surrounding envelope. The disk is at the stage of separation into protoplanetary rings. The disk plane is warped like the brim of a hat. The disk is 27 AU in diameter and ～0.3 AU in thickness. The rings contain ice granules. Radiation and stellar wind sublimate and blow away the water molecules to form halos around the rings, maser rings. The radiation from the rings is concentrated in the azimuthal plane, and its directivity reaches 10^?3. The relative velocities of the rings located in the central part of the disk 15 AU in diameter correspond to rigid-body rotation, V_rot = ΩR. The rotation period is T ≈ 170 yr. The injector is surrounded by a toroidal structure 1.2 AU in diameter. The diameter of the injected flow does not exceed 0.05 AU. A highly collimated bipolar outflow with a diameter of ～0.1 AU is observed at a distance as large as 3 AU. Precession of the injector axis with a period of ～10 yr forms a spiral flow structure. The flow velocity is ～10 km s^?1. The kinetic energy of the accreting matter and the disk is assumed to be transferred to the bipolar outflow, causing the rotation velocity distribution of the rings to deviate from the Keplerian velocity. The surrounding envelope amplifies the emission from the structure at a velocity of 7.65 km s^?1 in a band of ～0.5 km s^?1 by more than two orders of magnitude, which determines the supermaser emission.     

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.     

N-Body simulations of growth from 1 km planetesimals at 0.4 AU

We present N-body simulations of planetary accretion beginning with 1 km radius planetesimals in orbit about a 1 M_⊙ star at 0.4 AU. The initial disk of planetesimals contains too many bodies for any current N-body code to integrate; therefore, we model a sample patch of the disk. Although this greatly reduces the number of bodies, we still track in excess of 10⁵ particles. We consider three initial velocity distributions and monitor the growth of the planetesimals. The masses of some particles increase by more than a factor of 100. Additionally, the escape speed of the largest particle grows considerably faster than the velocity dispersion of the particles, suggesting impending runaway growth, although no particle grows large enough to detach itself from the power law size-frequency distribution. These results are in general agreement with previous statistical and analytical results. We compute rotation rates by assuming conservation of angular momentum around the center of mass at impact and that merged planetesimals relax to spherical shapes. At the end of our simulations, the majority of bodies that have undergone at least one merger are rotating faster than the breakup frequency. This implies that the assumption of completely inelastic collisions (perfect accretion), which is made in most simulations of planetary growth at sizes 1 km and above, is inappropriate. Our simulations reveal that, subsequent to the number of particles in the patch having been decreased by mergers to half its initial value, the presence of larger bodies in neighboring regions of the disk may limit the validity of simulations employing the patch approximation.     

Numerical experiments on the stability of preplanetary disks

Gravitational stability of gaseous protostellar disks is relevant to theories of planetary formation. Stable gas disks favor formation of planetesimals by the accumulation of solid material; unstable disks allow the possibility of direct condensation of gaseous protoplanets. We present the results of numerical experiments designed to test the stability of thin disks against large-scale, self-gravitational disruption. The disks are represented by a distribution of about 6 × 10⁴ point masses on a two-dimensional (r, φ) grid. The motions of the particles in the self-consistent gravity field are calculated, and the evolving density distributions are examined for instabilities. Two parameters that have major influences on stability are varied: the initial temperature of the disk (represented by an imposed velocity dispersion), and the mass of the protostar relative to that of the disk. It is found that a disk as massive as 1M_⊙, surrounding a 1M_⊙ protostar, can be stable against long-wavelength gravitational disruption if its temperature is about 300°K or greater. Stability of a cooler disk requires that it be less massive, but even at 100°K a stable disk can have an appreciable fraction ($\text{～}\text{1}\text{3}$) of a solar mass.     

Formation of the regular satellites of giant planets in an extended gaseous nebula II: satellite migration and survival

For a satellite to survive in the disk the time scale of satellite migration must be longer than the time scale for gas dissipation. For large satellites (∼1000 km) migration is dominated by the gas tidal torque. We consider the possibility that the redistribution of gas in the disk due to the tidal torque of a satellite with mass larger than the inviscid critical mass causes the satellite to stall and open a gap (W.R. Ward, 1997, Icarus 26, 261-281). We adapt the inviscid critical mass criterion to include gas drag, and m-dependent nonlocal deposition of angular momentum. We find that such a model holds promise of explaining the survival of satellites in the subnebula, the mass versus distance relationship apparent in the saturnian and uranian satellite systems, the concentration of mass in Titan, and the observation that the satellites of Jupiter get rockier closer to the planet whereas those of Saturn become increasingly icy. It is also possible that either weak turbulence (close to the planet) or gap-opening satellite tidal torque removes gas on a similar time scale (10⁴-10⁵ years) as the orbital decay time of midsized (200-700 km) regular satellites forming in the inner disk (inside the centrifugal radius (I. Mosqueira and P.R. Estrada, 2003, Icarus, this issue)). We argue that Saturn’s satellite system bridges the gap between those of Jupiter and Uranus by combining the formation of a Galilean-sized satellite in a gas optically thick subnebula with a strong temperature gradient, and the formation of smaller satellites, closer to the planet, in a disk with gas optical depth ?1, and a weak temperature gradient.Using an optically thick inner disk (given gaseous opacity), and an extended, quiescent, optically thin outer disk, we show that there are regions of the disk of small net tidal torque (even zero) where satellites (Iapetus-sized or larger) may stall far from the planet. For our model these outer regions of small net tidal torque correspond roughly to the locations of Callisto and Iapetus. Though the precise location depends on the (unknown) size of the transition region between the inner and outer disks, the result that Saturn’s is found much farther out (at ∼3rcS, where rcS is Saturn’s centrifugal radius) than Jupiter’s (at ∼ 2rcJ, where rcJ is Jupiter’s centrifugal radius) is mostly due to Saturn’s less massive outer disk and larger Hill radius. However, despite the large separation between Ganymede and Callisto and Titan and Iapetus, the long formation and migration time scales for Callisto and Iapetus (I. Mosqueira and P.R. Estrada, 2003, Icarus, this issue) makes it possible (depending on the details of the damping of acoustic waves) that the tidal torque of Ganymede and Titan clears the gas disk out to their location, thus stranding Callisto and Iapetus far from the planet. Either way, our model provides an explanation for the presence of regular satellites outside the centrifugal radii of Jupiter and Saturn, and the absence of such a satellite for Uranus.     

Formation of the saturnian system: A modern Laplacian theory

A theory for the formation of Saturn and its family of satellites, which is based on ideas of supersonic turbulent convection applied to the original Laplacian hypothesis, is presented. It is shown that if the primitive rotating cloud which gravitationally contracted to form Saturn possessed the same level of turbulent kinetic energy as the clouds which formed Jupiter and the Sun, given by % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSqaaSqaai% aaigdaaeaacaaIYaaaaOGaaiikaiabeg8aYnaaBaaajea4baGaamiD% aaWcbeaakiaadAhadaqhaaqcKfaGaeaadaWgaaqcKjaGaeaacaWG0b% aabeaaaSqaaiaaikdaaaGccaGGPaGaeyypa0ZaaSqaaSqaaiaaigda% aeaacaaIYaaaaOGaeqOSdiMaeqyWdiNaam4raiaad2eacaGGOaGaam% OCaiaacMcacaGGVaGaamOCaaaa!4D3D!\[\tfrac{1}{2}(\rho _t v_{_t }^2 ) = \tfrac{1}{2}\beta \rho GM(r)/r\] where =0.1065 ± 0.0015, then it would shed a concentric system of orbiting gas rings each of about the same mass: namely, 1.0 × 10^–3 M _S. The orbital radii R _n (n = 0, 1, 2, ...) of these gas rings form a geometric sequence similar to the observed distances of the regular satellites. It is proposed that the satellites condensed from the gas rings one at a time, commencing with Iapetus which originally occupied a circular orbit at radius 11.4 R _S. As the temperatures of the gas rings T _n increase with decreasing orbital size according as T _n 1/R _n , a uniform gradient should be evident amongst the satellite compositions: Mimas is expected to be the rockiest and Iapetus the least rocky satellite. The densities predicted by the model coincide with the Voyager-determined values. Iapetus contains some 8% by weight solid CH₄. Titan is believed to be a captured satellite. It was probably responsible for driving Iapetus to its present distant orbit. Accretional time-scales and the post-accretional evolution of the satellites are briefly discussed.     

Deciphering the origin of the regular satellites of gaseous giants - Iapetus: The Rosetta ice-moon

Ever since their discovery the regular satellites of Jupiter and Saturn have held out the promise of providing an independent set of observations with which to test theories of planet formation. Yet elucidating their origins has proven elusive. Here we show that Iapetus can serve to discriminate between satellite formation models. Its accretion history can be understood in terms of a two-component gaseous subnebula, with a relatively dense inner region, and an extended tail out to the location of the irregular satellites, as in the SEMM model of Mosqueira and Estrada (2003a,b) (Mosqueira, I., Estrada, P.R. [2003a]. Icarus 163, 198-231; Mosqueira, I., Estrada, P.R. [2003b]. Icarus 163, 232-255). Following giant planet formation, planetesimals in the feeding zone of Jupiter and Saturn become dynamically excited, and undergo a collisional cascade. Ablation and capture of planetesimal fragments crossing the gaseous circumplanetary disks delivers enough collisional rubble to account for the mass budgets of the regular satellites of Jupiter and Saturn. This process can result in rock/ice fractionation as long as the make up of the population of disk crossers is non-homogeneous, thus offering a natural explanation for the marked compositional differences between outer solar nebula objects and those that accreted in the subnebulae of the giant planets. For a given size, icy objects are easier to capture and to ablate, likely resulting in an overall enrichment of ice in the subnebula. Furthermore, capture and ablation of rocky fragments become inefficient far from the planet for two reasons: the gas surface density of the subnebula is taken to drop outside the centrifugal radius, and the velocity of interlopers decreases with distance from the planet. Thus, rocky objects crossing the outer disks of Jupiter and Saturn never reach a temperature high enough to ablate either due to melting or vaporization, and capture is also greatly diminished there. In contrast, icy objects crossing the outer disks of each planet ablate due to the melting and vaporization of water-ice. Consequently, our model leads to an enhancement of the ice content of Iapetus, and to a lesser degree those of Titan, Callisto and Ganymede, and accounts for the (non-stochastic) compositions of these large, low-porosity outer regular satellites of Jupiter and Saturn. For this to work, the primordial population of planetesimals in the Jupiter-Saturn region must be partially differentiated, so that the ensuing collisional cascade produces an icy population of ?1 m size fragments to be ablated during subnebula crossing. We argue this is likely because the first generation of solar nebula ∼10 km planetesimals in the Jupiter-Saturn region incorporated significant quantities of ²⁶Al. This is the first study successfully to provide a direct connection between nebula planetesimals and subnebulae mixtures with quantifiable and observable consequences for the bulk properties of the regular satellites of Jupiter and Saturn, and the only explanation presently available for Iapetus’ low density and ice-rich composition.     

An efficient, low-velocity, resonant mechanism for capture of satellites by a protoplanet

Numerical simulations of the gravitational scattering of planetesimals by a protoplanet reveal that a significant fraction of scattered planetesimals can become trapped as so-called quasi-satellites in heliocentric 1:1 co-orbital resonance with the protoplanet. While trapped, these resonant planetesimals can have deep low-velocity encounters with the protoplanet that result in temporary or permanent capture onto highly eccentric prograde or retrograde circumplanetary orbits. The simulations include solar nebula gas drag and use planetesimals with diameters ranging from ∼1 to ∼1000 km. Initial protoplanet eccentricities range from ep=0 to 0.15 and protoplanet masses range from 300 Earth-masses (M_⊕) down to 0.1M_⊕. This mass range effectively covers the final masses of all planets currently thought to be in possession of captured satellites—Jupiter, Saturn, Neptune, Uranus, and Mars. For protoplanets on moderately eccentric orbits (ep?0.1) most simulations show from 5-20% of all scattered planetesimals becoming temporarily trapped in the quasi-satellite co-orbital resonance. Typically, 20-30% of the temporarily trapped quasi-satellites of all sizes came within half the Hill radius of the protoplanet while trapped in the resonance. The efficiency of the resonance trapping combined with the subsequent low-velocity circumplanetary capture suggests that this trapped-to-captured transition may be important not only for the origin of captured satellites but also for continued growth of protoplanets.     

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.     

Kinematics and parameters of the gas in the vicinity of TW Hya

The following conclusions about the kinematics and parameters of the gas in the vicinity of TW Hya have been drawn from an analysis of optical and ultraviolet line profiles and intensities. The accreting matter rises in the magnetosphere to a distance z>R_* above the disk plane and falls to the star near its equator almost perpendicular to its plane. The matter outflows from a disk region with an outer radius of ≤0.5 AU. The [OI], [SII], and H2 lines originate in the disk atmosphere outside the outflow region, where the turbulent gas velocity is close to the local speed of sound. In the formation region of the forbidden lines, T?8500 K and N_e?5×10⁶ cm^?3, and the hydrogen is almost neutral: x_e<0.03. The absorption features observed in the blue wings of some of the ultraviolet lines originate in the part of the wind that moves almost perpendicular to the disk plane, i.e., in the jet of TW Hya. The V _z gas velocity component in the jet decreases with increasing distance from the jet axis from 200 to 30 km s^?1. The matter outflowing from the inner disk boundary, moves perpendicular to the disk plane in the formation region of blue absorption line components, at a distance of ～0.5 AU from the axis of symmetry of the disk. This region of the wind is collimated into the jet at a distance of <3 AU from the disk plane. The gas temperature in the formation region of absorption components is ?2×10⁴ K, and the gas density is <3×10⁶ cm^?3. This region of the jet is on the order of several AU away from the disk plane, while free recombination in the jet begins even farther from the disk. The mass-loss rate for TW Hya is \(\dot M_w < 7 \times 10^{ - 10} M_ \odot yr^{ - 1}\), which is a factor of 3lower than the mean accretion rate. The relative abundance of silicon and aluminum in the jet gas is at least an order of magnitude lower than its standard value.     

The formation of ring galaxies

The conditions under which a head-on collision between a disk galaxy and a spherical galaxy can lead to ring formation are investigated, using the impulsive approximation. The spherical galaxy is modeled as a polytrope of indexn=4 and radiusR _S and the disk galaxy as an exponential disk whose surface density is given by \(\sigma (r) = \sigma _c e^{ - 4r/R_D } \) , where σ _c is the central density andR _D is the radius of the disk. The formation and properties of the rings are closely related to the fractional change in binding energy of the disk galaxy, given by ΔU/?U?=γ _D β _D , where (GM _S ² R _D )/(V ² M _D R _S ² ),M _S andM _D being the masses of the spherical and disk galaxies, respectively, and β _D ≡β _D (n, σ, ?,i) is a function of the models of the two galaxies, the ratio of the radii of the two galaxies ?=R _S /R _D , and the angle of inclinationi, of the disk to the direction of relative motion of the two galaxies. Calculations are made for the caseR _S =R _D . Since practically the entire mass of the spherical galaxy, for the chosen model, lies within 1/3 of its radius, the radius of the spherical galaxy is effectively \(\tfrac{1}{3}\) that of the disk galaxy. It is found that as a result of the collision, the innermost and the outer parts of the disk galaxy are not much affected, but the intermediate region expands and gets evacuated, leading to the crowding of stars in a preferential region forming a ring structure. The rings are best formed for a normal, on-axis collision. For this case, rings form when ΔU/|U| lies between \(\tfrac{1}{2}\) and 2, while they are very sharp and bright when ΔU/|U| lies between \(\tfrac{1}{2}\) and 1. Within this range, as ΔU/|U| increases, the rings become sharper and their positions shift outwards with respect to the centre of the disk galaxy. The relationship $$\gamma _D = 0.0016 + 0.045s_{{\text{max}}}^2 ,$$ wheres _max is the radial distance of the density maximum of the ring from the centre of the disk galaxy (measured in terms of the radius of the disk galaxy as unit) enables us to finds _max from γ _D and vice versa, and interpret some prominent ring galaxies. The effect of introducing a bulge to the disk is to distribute the tidal disruptive effects more evenly and, hence, reduce the sharpness of the ring.     

Planetary growth with collisional fragmentation and gas drag

As planetary embryos grow, gravitational stirring of planetesimals by embryos strongly enhances random velocities of planetesimals and makes collisions between planetesimals destructive. The resulting fragments are ground down by successive collisions. Eventually the smallest fragments are removed by the inward drift due to gas drag. Therefore, the collisional disruption depletes the planetesimal disk and inhibits embryo growth. We provide analytical formulae for the final masses of planetary embryos, taking into account planetesimal depletion due to collisional disruption. Furthermore, we perform the statistical simulations for embryo growth (which excellently reproduce results of direct N-body simulations if disruption is neglected). These analytical formulae are consistent with the outcome of our statistical simulations. Our results indicate that the final embryo mass at several AU in the minimum-mass solar nebula can reach about ∼0.1 Earth mass within 10⁷ years. This brings another difficulty in formation of gas giant planets, which requires cores with ∼10 Earth masses for gas accretion. However, if the nebular disk is 10 times more massive than the minimum-mass solar nebula and the initial planetesimal size is larger than 100 km, as suggested by some models of planetesimal formation, the final embryo mass reaches about 10 Earth masses at 3-4 AU. The enhancement of embryos’ collisional cross sections by their atmosphere could further increase their final mass to form gas giant planets at 5-10 AU in the Solar System.     

Models of the protosatellite disk of Saturn: Conditions for Titan’s formation

Models of the protosatellite accretion disk of Saturn are developed that satisfy cosmochemical constraints on the volatile abundances in the atmospheres of Saturn and Titan with due regard for the data obtained with the Cassini orbiter and the Huygens probe, which landed on Titan in January 2005. All basic sources of heating of the disk and protosatellite bodies are taken into account in the models, namely, dissipation of turbulence in the disk, accretion of gaseous and solid material onto the disk from the feeding zone of Saturn in the solar nebula, and heating by the radiation of young Saturn and thermal radiation of the surrounding region of the solar nebula. Two-dimensional (axisymmetric) temperature, pressure, and density distributions are calculated for the protosatellite disk. The distributions satisfy the cosmochemical constraints on the disk temperature, according to which the temperature at the stage of the satellite formation ranged from 60–65 K to 90–100 K at pressures from 10^?7 to ?10^?4 bar in the zone of Titan’s formation (according to estimates, r = 20–35R _Sat). Variations of the basic input parameters (the accretion rate onto the protosatellite disk of Saturn from the feeding zone of the planet ?; the parameter α characterizing turbulent viscosity of the disk; and the mass concentration ratio in the solid/gas system) satisfying the aforementioned temperature constraint are found. The spectrum of models satisfying the cosmochemical constraints covers a considerable range of consistent parameters. A model with a rather small flux of ? = 10^?8 M _Sat/ yr and a tenfold depletion of Saturn’s disk in gas due to gas scattering from the solar nebula is at one side of this range. A model with a much higher flux of ? = 10^?6 M _Sat/yr and a hundredfold decrease in opacity of the disk matter owing to decreased concentration of dust particles and/or their agglomeration into large aggregates and sweeping up by planetesimals is at the other side of the range.     

Star formation efficiency in low-density regions in galactic disks

The radial dependences of the star formation efficiency??_SFE = ??_SFR/??_gas (per unit disk surface area) in normal surface brightness spiral galaxies and low surface brightness (LSB) galaxies are compared with the radial variations of the gas and stellar disk surface and volume densities. The volume density of the components in the disk midplane is found through a self-consistent solution of the disk equilibrium equations by taking into account the dark halo. The disk thickness variation with radius R is calculated within the model of a galaxy with a marginally stable disk by taking into account the increase of the stability parameter Q _T,c along the radius. We show that the star formation efficiency depends weakly (for LSB galaxies, does not depend at all) on the gas density but correlates well with the disk surface and volume density, with the normal and LSB galaxies forming a single sequence. The dependence vanishes only at extremely low disk densities (?? _disk ? (1?3) M _?? pc^?2, ?? _stars ?? (1?3) × 10^?24 g cm^?3), where star formation probably ceases to be related to disk properties. Estimations of the gas volume density allow us to check the expected form of the ??_SFR-?? _disk relationship that follows from the model by Ostriker et al., which relates the star formation rate to the pressure of the diffuse gas medium. For most of the galaxies considered, there is satisfactory agreement with the model, except for the densest (of the order of several hundred M _?? pc^?2) and least dense (several M?? pc^?2 or less) disk regions.     

Gravitational instability of interstellar magnetic clouds

The gravitational instability of a nonrotating isothermal gaseous disk permeated by a uniform frozen-in magnetic field is investigated using a fourth-order perturbation technique. From the results it is found that the disk is stable whenn/B ₀ < (4/3³ G)^–1/2, wheren andB are the column density of the disk and unperturbed magnetic field, respectively, andG is the gravitational constant. The disk is gravitationally unstable only whenn/B ₀ > (4/3³ G)^–1/2.