## 1. IntroductionRecently, with the identification of a solar-like star showing evidence for planets circling around it (Mayor & Queloz 1995), our interest in understanding the formation of a planetary system on its largest scale has intensified and widened beyond the long-standing question of the origin of the solar system. It is therefore timely to attempt, on theoretical grounds and from an evolutionary point of view, a prediction of the large-scale properties of a planetary system around a solar-like star. Of particular interest is the spatial distribution of material making up a planetary system, as this is about the only information the present observations, based on the Doppler technique, can provide. To start addressing this problem we are developing a model that would keep track of circumstellar material as it evolves from the form of a protoplanetary disk to the form of a planetary system. In the first paper of the series (Stepinski & Valageas 1996; hereafter referred to as Paper I) we laid down the foundations of our model and developed a numerical method to study the effects of aerodynamic forces acting on solid particles entrained in a gaseous disk. We refer the reader to that paper for elucidation of the essential concepts underlying our approach. In the current paper we take our model one step further by taking into consideration the processes of coagulation, sedimentation, and evaporation/condensation of solid particles. These processes, acting in addition to gas-solid coupling caused by aerodynamic forces, shape the radial distribution of solid material around the star, until such time when solids augment to planetesimal sizes and further evolution of solid material is dominated by mutual gravitational interaction between planetesimals. Thus, our model, in its present form, given some initial distribution of gaseous and solid matter, computes the evolution of these two components, and can predict the radial distribution of solid mass locked into the planetesimal swarm. Arguably, such a distribution should well approximate the radial apportionment of condensed components of the planets spread over the radial extent of the mature planetary system. This is because the process of accumulation of planetesimals into planets or planetary cores is thought to happen with minimum radial displacement. The location of solid mass in the present-day solar system presents an inevitable test for our model, and the bulk of our calculations were carried out to determine what kind of initial conditions, if any, lead to the development of a planetesimal swarm consistent with the solid matter in the solar system. Indeed, we have found initial conditions leading to a configuration of solid matter in rough agreement with the large-scale architecture of the solar system. However, we have also found that the outcome is sensitive to initial conditions, as well as, in some cases, to the values of the free parameters characterizing our model. This opens the theoretical possibility of planetary system diversity. Additional diversity may result from the different quantities of gas that various planetary systems may subsequently add to some of their solid protoplanets. Note that, although we argue that our present model may predict the mass distribution of a condensed material in a nascent planetary system, it cannot predict the distribution of a whole planetary mass consisting of solid and volatile materials. Nevertheless, as solid protoplanets or cores constitute the backbone of a planetary system onto which volatile envelopes are subsequently added, modeling its structure is of a primary interest. The major novelty of our work is its emphasis on the global,
comprehensive treatment of the problem. This follows from our interest
in attempting to establish the link between initial conditions that
characterize a protoplanetary disk at the onset of star-disk
formation, and the large-scale character of an ultimate planetary
system. To achieve this goal we have to include all relevant physical
processes. This, in turn, presented us technically and, to certain
degree, conceptually with an intricate problem, which required major
simplification in order to become tractable. Therefore, our handling
of several processes, most notably coagulation, is less advanced than
can be found in some published work (for a review see Weidenschilling
& Cuzzi 1993) dedicated exclusively to the issue of coagulation
and not addressing the evolution of solids globally. In order to make
progress, we have assumed that the size distribution of particles at
any given radial location of a disk is narrowly peaked about a mean
value particular for this location and time instant. Such an
approximation was first proposed by Morfill (1985). This allows us to
keep track of the increase of the mean particle size alone, and frees
us from daunting calculations required for computing the shift in the
entire particle size distribution function. This approximation is
important for the viability of our calculations. It also captures the
essence of the coagulation process accurately enough, at least for our
purpose, which is to keep track of solid's mass whereabouts regardless
of how it is apportioned between particles of different sizes. Two
other major simplifications characterize our current model. First, we
concentrate on ice, the most abundant component of solid material, and
disregard other compositional constituents such as "rock" and "metal."
Hence, at present, we expect to model only the development of icy
planetesimals, or outer zones of planetary systems. In the context of
the solar system, we expect to model distribution of mass presently
located in solid cores of giant planets. Second, unlike in the
calculations by Cuzzi et al. (1993), which were devoted to the
investigation of growth and sedimentation of solid particles at the
Our basic method of simultaneously keeping track of the evolution of gaseous and solid components of protoplanetary disks is described in Sect. 2. Separately, in Sect. 3, we describe our treatment of coagulation and evaporation processes, and offer a very brief depiction of our numerical technique. The next two sections are devoted to the presentation of results. In Sect. 4 the results for an initially high-mass, high-concentration disk are given, and in Sect. 5 an initially low-mass, low-concentration disk is examined for various values of dimensionless viscosiameter . Finally, in Sect. 6, we present discussion and conclusions. © European Southern Observatory (ESO) 1997 Online publication: July 3, 1998 |