Nonaxisymmetry in the Solar Nebula: Disk Evolution or Giant Gaseous Protoplanet Formation?

Radiative hydrodynamical calculations of the thermal structure of an axisymmetric (2D) protoplanetary disk with a mass of N 0.14Mo predict that the outer disk may be cool enough to become gravitationally unstable. The dynamical evolution of a 0.14Mo disk has been computed with a 3D hydrodynamics code in order to learn the outcome of gravitational instability in an intermediate-mass disk orbiting a solar-mass star. Growth of nonaxisymmetry occurs within a few rotation periods of the outer disk (Po),. and the nonaxisymmetry is large enough to result in disk evolution through gravitational torques within N l o 5 yrs. After about 10 Po, the dominant m = 2 (bar) mode begins to saturate at an amplitude greater than 1 by this time, two Jupiter-mass clumps of gas have formed around 8 AU and continue to gain mass. The hot inner disk remains nearly axisymmetric throughout this interval. The model suggests a best of both worlds scenario may be tenable: formation of terrestrial planets through collisional accumulation in the hot inner nebula, and rapid formation of giant gaseous protoplanets in the cool outer nebula through gravitational instability of the disk. INTRODUCTION. Forming the gas giant planets within the expected lifetime of the solar nebula (N lo5 to lo7 yrs [I]) is a longstanding problem for planetary formation by collisional accumulation. Possible solutions include a phase of runaway accretion in a nebula with a suitably high surface density in the outer planet region [2]. The alternative is rapid formation of giant gaseous protoplanets (GGPP) through gravitational inst ability of the gasous portion of the nebula [3]. The latter idea has not been pursued, in part because ice and rock are believed to be soluble in Jovian planet envelopes [4], thereby preventing formation of the rock/ice cores of the gas giant planets in a planet formed by gravitational instability [5]. However, km-sized or larger planetesimals should be able to reach the core of a GGPP [6], so this objection could be removed if Jupiter received its excess solids by ingesting planetesimals rather than dust grains. The possibility of a mixed scenario [7] with collisional accumulation of the terrestrial planets and gravitational instability of the gas disk forming the gas giant planets then becomes more attractive. The mixed scenario is also suggested by thermal profiles calculated for protoplanetary disks with a 2D radiative hydrodynamics code [8,9] surface densities in intermediatemass (0.14Mo) disks can be high enough in the cool outer disk to exceed Toomre's Q stability criterion [lo], implying gravitational instability. Gravitational instability could lead to GGPP formation, or at least to rapid disk evolution through gravitational torques [I 1,121, perhaps helping to solve the equally longstanding problem of disk evolution. METHODS. The temperature distribution from the 2D radiative transfer calculation was assumed to be appropriate throughout the 3D calculation. This approximation is necessary to allow the 3D calculation to be followed for N loPo. The inner disk rotation period Pi is 1 year, and 10Po z 200 yrs. The active computational volume (N, = 51, No = 23 in 7r/2 2 8 > 0, N+ = 64) extends from 1 AU to 10 AU, with boundary conditions at 10 AU chosen to absorb outward-moving velocity perturbations and to maintain constant density. The initial disk density is seeded with a ~ 0 . ~ 2 4 perturbation (amplitude a,=;! = 0.01) and with random noise (m = 1,2, ... 16 with a N 0.001). RESULTS. The m = 2 mode grows monotollically and dominates the disk throughout the evolution (see Figures). By loPo, the outer disk has formed two well-defined spiral arms with rapidly increasing density maxima the outer disk appears to be forilling two GGPP with masses of at least a Jupiter mass and average temperatures 50 I<. Gravitational torques associated with the nonaxisymmetry are large enough to transport all the disk's angular inomenturn in N lo5 yrs. The disk's surface density is beginning to pile-up at the inner edge ( N 7 AU) of the unstable region as a result of the torques.