A decade ago, theoreticians modeling the formation of planets had only a sample of nine objects with which to compare their computed results. Today we have over 150 planets and 13 extrasolar planet systems (Marcy et al. 2005) that challenge the formation models and the previously developed scenarios. These planets are believed to be gas giants, and with new detection techniques, the number of planets and the range in planet masses will be expanded. Discoveries of Neptune-like planets (e.g., Butler et al. 2004) and transit planets (e.g., Richardson et al. 2004) have been announced. These planets are diverse in their characteristics (Bodenheimer & Lin 2002), and planet scientists are working to learn and explain their formation mechanism.

There are two major models for the formation of gas giant planets: (1) the core accretion-gas capture model (which will be referred to as the CAGC or the core accretion model), and (2) the gas instability model (sometimes referred to as the GGPP model). The core accretion model (Safronov 1969; Perri & Cameron 1974; Mizuno et al. 1978; Mizuno 1980; Bodenheimer & Pollack 1986; Pollack et al. 1996; Bodenheimer et al. 2000) proposes that giant planets form in two stages: the formation of a massive solid core by coagulation of planetesimals in the solar nebula, followed by the gravitational capture by the core of a massive envelope from the solar nebula gas. The gas instability model is a single-stage model in which the solar nebula becomes gravitationally unstable and rapidly collapses to form a gravitationally bound subcondensation known as a giant gaseous protoplanet (Kuiper 1951; Cameron 1978; DeCampli & Cameron 1979; Boss 1998, 2000; Mayer et al. 2002, 2004; Pickett et al. 2003; Rice & Armitage 2003; Rice et al. 2003; Boss 2003).

The core accretion model is generally accepted as the more likely scenario of the two formation theories. In the past few years, computer simulations based on the CAGC model have been quite successful in explaining many features of the gas giant planets in the Solar System (Pollack et al. 1996; hereafter referred to as Paper 1) and in situ formation of companions to 51 Peg, p CrB, and 47 UMa (Bodenheimer et al. 2000). In the past, the core accretion model had difficulties making planets in a short time and with small core masses; the smaller the core mass, the longer the formation time. However, recent calculations (Hubickyj et al. 2005; hereafter referred to as HBL05) demonstrate that models of Jupiter can be computed well within the observational limits and those set by interior models of Jupiter based on observations.

The evolution of a gas giant planet in the core accretion model is described in Boden-heimer et al. (2000) and is viewed to occur in the following sequence:

(1) Dust particles in the solar nebula form planetesimals that accrete, resulting in a solid core surrounded by a low-mass gaseous envelope. Solid runaway accretion occurs, during which the gas accretion rate is much slower than that of solids. As the solid material in the feeding zone is depleted, the solid accretion rate is reduced. The gas accretion steadily increases, and eventually becomes greater than the solid accretion rate.

(2) The protoplanet continues to grow as the gas accretes at a relatively constant rate. The mass of the solid core also increases, but at a slower rate. Eventually, the core and envelope masses become equal (called the crossover mass, Mcross).

(3) Runaway gas accretion occurs and the protoplanet grows at rapidly accelerating rate. The evolution of stages (1)-(3) is referred to as the nebular stage, because the outer boundary of the protoplanetary envelope is in contact with the solar nebula, and the density and temperature at this interface are given nebular values.

(4) The gas accretion rate reaches a limiting value defined by the rate at which the nebula can transport gas to the vicinity of the planet. After this point, the equilibrium region of the protoplanet contracts inside the effective accretion radius (defined in Bo-denheimer et al. 2000), and gas accretes hydrodynamically onto this equilibrium region. This part of the evolution is considered to be the transition stage.

(5) Accretion is stopped by either the opening of a gap in the disk as a consequence of the tidal effect of the planet, or by dissipation of the nebula. Once accretion stops, the planet enters the isolation stage.

(6) The planet contracts and cools to the present state at constant mass.

This chapter describes the scenario for the formation of the gas giant planets. Observational constraints on the model are summarized in Section 2. A short overview of the development of the CAGC model is described in Section 3, and a description of the computer simulation of the CAGC model is in Section 4. Recent results of the computer simulations are reported in Section 5, and conclusions and summaries are presented in Section 6.

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