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P. R. Estrada (NASA Ames), I. Mosqueira (NASA Ames/SETI Institute)
We expect that the largest objects forming in the solar nebula and giant-planet subnebulae truncated the gas disks in which they were formed, thus preventing gas outside their orbits from accreting onto the primary (Mosqueira and Estrada 2002a,b). The criterion for gap opening depends on two uncertain parameters; namely, the turbulent viscosity of the gas, and the damping length of the waves launched by the secondary in the neighborhood of resonant locations in the disk. In light of the difficulty of maintaining gas turbulence in disks with a positive radial gradient in specific angular momentum in the absence of a source of ``stirring'' (Ryu and Goodman 1992; Balbus et al. 1996), we adopt an inviscid disk. Regarding the second issue, there has been recent progress in characterizing the damping length of acoustic waves under several disk conditions. In a 2-D isothermal disk, wave steepening is likely to result in wave dissipation in a lengthscale of order ~rL, where rL is the radial location of a Lindblad resonance and this distance has a weak dependence on the mass of the secondary (Goodman and Rafikov 2001). In an optically thick, vertically thermally stratified, disk the radial lengthscale for ``wave-channeling'' and wave dissipation is~rL/m, where m is the azimuthal wavenumber (Lubow and Ogilvie 1998; Bate et al. 2002). In a 3-D vertically isothermal gas disk, a significant fraction of the angular momentum flux may be transported by waves with non-zero vertical group velocity and possible radial damping lengths of the order ~H, where H is the nebula scale-height (Bate et al. 2002; Mosqueira and Houben, this conference).
The above can be used to compute the inertial mass (Ward and Hourigan 1989) and constrain the surface density of the disk at the time of gap opening. Here we do so for Jupiter in the solar disk (M2/M1 = 9.5 x 10-4), Ganymede in the jovian disk (M2/M1 = 7.8 x 10-5), Titan in the saturnian disk (M2/M1 = 2.4 x 10-4), and Titania in the uranian disk (M2/M1 = 4.1 x 10-5), where M2/M1 is the mass ratio of the secondary to the primary. Provided that these objects are just large enough to open a gap at their present locations, we find that while the disks that led to the formation of the satellites of the giant planets are roughly in agreement with a ``minimum mass'' model, the solar nebula must be significantly enhanced relative to ``minimum mass''.
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Bulletin of the American Astronomical Society, 34, #3< br> © 2002. The American Astronomical Soceity.