Runaway Accretion Research Articles

Paleodynamics: Solar System Formation and the Early Environment of the Sun

Our present paradigm of the formation of stars and planetary systems suggests that the early Solar System may have existed in much denser environments than the galactic disk, e.g., the cores of giant molecular clouds and open stellar clusters. Some constraints on a hypothetical primordial environment can be inferred from the present dynamical state of the Sun and planets. Tremaine (1991, Icarus 89, 85-92) has proposed that the large obliquities of the outer planets may have arisen from twisting of the ecliptic plane during the initial collapse of the protosolar cloud. I find that the current solar obliquity could only have been produced in the very dense environment of the initial collapse of the protoplanetary cloud: Mean post collapse densities would have a neglible effect on Solar System dynamics. The inclinations of the orbits of Uranus and Neptune, sensitive to perturbations on time scales of less than 1 myr, place a constraint on the number density of stars in the solar neighborhood. I place a 3σ limit on the product of the stellar density and residence time of 3 × 104 M ⊙ pc -3 Myr, still consistent with the average densities and lifetimes of observed open clusters. I examine the possible effect of the tidal field on planet formation. Tidal torquing can suppress runaway accretion of a massive body by maintaining a high velocity dispersion. I derive a limiting semimajor axis of ∼ 50 AU, but find that the sensitivity to parameters does not permit the observed extent of the planetary system to be used to infer limits on the tidal field during the epoch of planet formation. Stronger tides and a higher stellar density on a time scale of 10 8 year will affect comet cloud formation. I conclude that a transient comet cloud of a few M ⊕ could have formed at a few thousand atomic-units but this would have been rapidly destroyed by stellar encounters over 10 8 year. Uranus- and Neptune-crossing planetesimals could have been scattered into a belt about 200 AU from the Sun. Although the dynamical lifetimes of these objects are comparable to the Solar System, a time-scale comparison suggests that little mass could have reached such a cloud before the end of the cluster epoch.

Accretion in the Roche Zone: Coexistence of Rings and Ringmoons

Traditional accretion simulations predict rapid accumulation of ring debris into single satellites, while most theories of ring formation dismiss any accretion within the classical Roche limit. The former contradicts the continued presence of planetary rings, while the latter fails to adequately account for the many small satellites observed within ring systems. The coexistence of rings and small satellites thus challenges the premise of a strict boundary between accreting and nonaccreting regions. We have developed an accretion model designed to better examine accumulation processes in the dynamically transitional regime of outer planetary rings. We utilize "three-body" capture criteria, motivated by the work of Ohtsuki (1993 Icarus 106, 228-246), to account for the effects of strong tidal forces on accretion. Our findings indicate that tidally modified accretion occurs in a relatively broad range of orbital radii surrounding the classical Roche limit. Tidally modified accretion has a very unique character: for a given particle density, only bodies which differ greatly in mass can remain gravitationally bound, as like-sized bodies overflow their mutual Hill sphere. We find that this constraint greatly limits the degree of accretional growth and prevents runaway accretion near the Roche limit. Numerical simulations show that through the course of tidally modified accretion, a fragmentation-produced debris distribution evolves into a bimodal population, with one element consisting of a swarm of small, high-velocity bodies and the other composed of a small number of large "moonlets" on fairly circular orbits. The latter are precluded from accreting with one another due to the tidal influences of the planet. Tidally modified accretion thus offers a natural explanation for the formation of systems of coexisting rings and ringmoons from disrupted parent bodies.

Photoevaporation of the Solar Nebula and the Formation of the Giant Planets

We review the prevailing theories for the formation of the jovian planets and comment that they do not provide a natural explanation for the oft-noted subdivision into two separate classes: the gas-rich giants, Jupiter and Saturn, and the gas-poor giants, Uranus and Neptune. To account for the observed differences in envelope mass relative to core mass, the conventional discriminants would seem to require special timing for the phases: assemblage of the protoplanetary cores, runaway accretion of gas, and the dispersal of nebular gases. We propose a discriminant that relies on photoevaporation by Lyman continuum photons of the outer parts of the disk as the primary hydrogen (and helium) loss mechanism. We show that Saturn's orbit constitutes the natural transitional radius between gas retainage and loss in this sort of picture and that the evaporative wind in the Uranus and Neptune regions would have been large enough to get rid of the hydrogen and helium gas before these planets assembled a critical core mass for runaway gas accretion, if the primitive Sun had an enhanced extreme ultraviolet luminosity for a duration comparable to those estimated for classical T Tauri stars.

Timescales for planetary accretion and the structure of the protoplanetary disk

This paper outlines a unified scenario for Solar System formation consistent with astrophysical constraints. Jupiter's core could have grown by runaway accretion of planetesimals to a mass sufficient to initiate rapid accretion of gas in times of order of 5 x 10 5−10 6 years, provided the surface density of solids in its accretion zone was at least 5–10 times greater than that required by minimum mass models of the protoplanetary disk. After Jupiter had accreted large amounts of nebular gas, it could have gravitationally scattered the planetesimals remaining nearby into orbits which led to escape from the Solar System. Most of the planetesimals in the Mars-asteroids accretion zone could have been perturbed into Jupiter-crossing orbits by resonances with Jupiter and/or interactions with bodies scattered inwards from Jupiter's accretion zone; such Jupiter-crossing orbits would have subsequently led to ejection from the Solar System. However, removal of excess mass from sunward of 1 AU would have been much more difficult. The inner planets and the asteroids can be accounted for in this picture if the surface density of the solar nebula was relatively uniform (decreasing no more rapidly than r − 1 2 ) out to Jupiter's orbit. The total mass of the protoplanetary disk could have been less than one-tenth of a solar mass provided the surface density dropped off more steeply than r −1 beyond the orbit of Saturn. The outer regions of the nebula would still have contained enough solid matter to explain the growth of Uranus and Neptune in 5 x 10 6−10 8 years, together with the coincident ejection of comets to the Oort cloud. The formation of such a protoplanetary disk requires significant transport of mass and angular momentum, and is consistent with viscous accretion disk models of the solar nebula.

Planetesimal dissolution in the envelopes of the forming, giant planets

We have assessed the ability of planetesimals to penetrate through the envelopes of growing giant planets that form by a “core-instability” mechanism. According to this mechanism, a core grows by the accretion of solid bodies in the solar nebula and the growing core becomes progressively more effective in gravitationally concentrating gas from the surrounding solar nebula in an envelope until a “runaway” accretion of gas occurs. In performing this assessment, we have considered the ability of gas drag to slow down a planetesimal; the effectiveness of gas dynamical pressure in fracturing and ultimately finely fragmenting it; the ability of its strength and self-gravity to resist such fracturing; and the degree to which it is evaporated due to heating by the surrounding envelope, including shock heating that develops during the supersonic portion of its trajectory. We also consider what happens if the planetesimal is able to reach the core at free-fall velocity and the ability of the envelope to convectively mix dissolved materials to different radial distances. These calculations were performed for various epochs in the growth of a giant planet with the model envelopes derived by Bodenheimer and Pollack (1986,67, 391–408). As might have been anticipated, our results vary significantly with the size of the planetesimal, its composition, and the stage of growth of the giant planet and hence the mass of its envelope. Over much of the growth phase of the core, prior to its reaching its critical mass for runaway gas accretion, icy planetesimals less than about 1 m in size dissolve in the outer region of the envelope, ones larger than about 1 m and smaller than about 1 km dissolve in the middle region of the envelope, ones larger than 1 km either reach the core interface or dissolve in the deeper regions of the envelope. Similarly rocky planetesimals smaller than about a kilometer dissolve in the middle portion of the envelope, while larger ones can penetrate more deeply. Furthermore, the convection zones of the envelopes during this stage are confined to localized regions and hence dissolved materials experience little radial mixing then. Thus, if much of the accreted mass is contained in planetesimals larger than about a kilometer, the critical core mass for runaway accretion is not expected to change significantly when planetesimal dissolution is taken into account. After accretion is terminated and the planet contracts toward its present size, the convection zone grows until it encompasses the entire envelope. Therefore, dissolved material should eventually become well mixed through the envelope. We proposed that the envelopes of the giant planets should contain significant enhancements above solar proportions in the abundances of virtually all elements relative to that of hydrogen, with the magnitude of the enhancement increasing approximately linearly with the ratio of the high Z mass to the (H, He) mass for the bulk of the planet. This prediction is in accord both qualitatively and quantitatively with the systematic increase in the atmospheric C/H ratio from Jupiter to Saturn to Uranus and Neptune and semiquantitatively with the results of recent interior models of the giant planets. It is not clear whether it is consistent with the abundances of H2O and NH3 in the atmospheres of some of the outer planets. Finally, the complete reduction of some dissolved materials, especially C containing compounds, is expected to consume some of the H2 in the envelopes. Consequently, the He/H2 ratios in the atmospheres of Uranus and Neptune may be slightly enhanced over the solar ratio. We estimate that the He/H2 ratios for Uranus' and Neptune's atmospheres should be about 6 and 15% larger, respectively, than the solar ratio.

Novae and Accretion Disc Evolution

AbstractAt outburst the classical nova generates an extended optically-thick wind driven by radiation pressure in the continuum. At maximum light the optical luminosity is close to the Eddington-limit. The subsequent decline illustrates the interaction between radiation and matter in a wind which gradually thins as the mass loss rate falls at an approximately constant Eddington-limit luminosity. As the wind thins so the effective photosphere shrinks back into the underlying binary, and an increasing fraction of the radiation is emitted at ultraviolet wavelengths. Model atmosphere computations show how the increasing flux of ultraviolet photons is associated with the shell becoming more and more ionized through radiative ionization. Attempts to study the internal structure of the wind confirm that the luminosity must be close to the Eddington limit and must be expelled from close to the white dwarf surface. It is generally agreed that the outbursts are caused by runaway nuclear burning of accreted material at the white dwarf surface, but it is possible that some events of the classical nova type may be caused by runaway accretion at a super-critical rate.In dwarf novae very different behaviour is evident. The outbursts are located within the accretion disc and are generated either by mass-transfer bursts due to dynamical instability of the Roche-lobe filling star, or by an instability within the disc itself. In either case the eruption behaviour is due to an enhanced accretion flux through the accretion disc. One important aspect of the radiation hydrodynamics is the luminosity generated by impact of the mass-transfer stream with the accretion disc and penetration by the stream within the disc. Attempts at examining this penetration region are described and results compared with observed behaviour of disc evolution through the course of an outburst. The possibility that disc instabilities will not propogate in realistic discs which deviate from axial symmetry is considered.

The range of validity of the two-body approximation in models of terrestrial planet accumulation: II. Gravitational cross sections and runaway accretion

The validity of the two-body approximation in calculating encounters between planetesimals has been evaluated as a function of the ratio of unperturbed planetesimal velocity (with respect to a circular orbit) to mutual escape velocity when their surfaces are in contact ( V/V e ). Impact rates as a function of V/V e are calculated to within ∼20% by numerical integration of the equations of motion. It is found that when V/V e > 0.4, the two-body approximation is a good one. At low velocities ( V/V e < 0.1) two-body “collision-course” trajectories fail to lead to impacts. On the other hand, at these low velocities many impacts result from encounter trajectories with unperturbed separation distances far beyond the two-body gravitational radius. These two effects tend to cancel, and the resulting impact rates remain within a factor of ∼3 of the two-body value in spite of these major differences in the nature of the impact trajectories. Therefore, on the average, the two-body approximation is useful well below the value of V/V e for which it fails to describe individual encounters, and the required corrections are not large. As a consequence of this “anomalous gravitational focusing” planetesimals will continue to interact even when their orbits are noncrossing. This reduces the difficulty with premature isolation of planetesimal embryos during accumulation. Quantitatively, when 0.06 ≲ V/V e ≲ 0.2, the impact rate varies approximately with the fifth power of the radius of the larger body, and is about a factor of 3 above that predicted using the conventional two-body gravitational cross-section formula. At lower values of V/V e , the impact rate increases less rapidly. Finally, at the lowest values of V/V e (<.02), the impact rate increases only in proportion to the geometric cross section, as a consequence of the swarm being essentially two dimensional for large unperturbed encounter distances. The gravitational enhancement in effective cross section is thereby limited to a value of about 3000. This leads to an optimal size for growth of planetesimals from a swarm of given eccentricity, and places a limit on the extent of runaway accretion.

Accretion powers the brightest stars

The brightest known stars in external galaxies are the Hubble–Sandage variables. These are normally assumed to be hot, massive, single stars evolving either towards or off the main-sequence. An alternative model is developed here involving binary mass transfer and accretion on to main-sequence stars. In this case the Hubble–Sandage variables are a third, and presumably final, class of binary in which accretion generates the bulk of the radiation observed. The other two classes are binaries containing an accreting white dwarf (cataclysmic variables)1,2 and an accreting neutron star or black hole (binary X-ray sources)3,4. Accretion disk models developed in these two cases can be scaled directly to treat the main-sequence case. One of the most complex objects in our own Galaxy is the η Carina nebula, rivalling in this respect the Orion Nebula and the Crab. I suggest below that η Can itself is an accreting main sequence star whose explosive outburst in the nineteenth century was caused by runaway mass accretion.

Relative velocities of planetesimals and the early accumulation of planets

Safronov's statement that relative velocities of planetesimals are on the order of the escape velocity of the largest body of the population is shown to be correct only when a major part of the total mass resides in several large bodies. In the first stage of accumulation, runaway accretion produces large bodies separated by mass form the remaining population. At this stage, relative velocities of planetesimals are much smaller than those adopted earlier. This requires a modification of Schmidt's scheme of accumulation of the Earth and other terrestrial planets from material in their feeding zones. This also leads to removal of the author's arguments (Levin 1972c) in favor of a protoplanetary nebula with an extended, massive periphery.