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[28.10] Excitation and Damping of Acoustic Waves in Three-Dimensional Accretion Disks

I. Mosqueira (NASA Ames/SETI Institute), H. Houben (NASA Ames/Bay Area Environmental Research Institute)

The damping of acoustic waves plays a key role in determining the criterion for gap opening (see Estrada and Mosqueira, this conference). Because of the potential significance of gap-opening in regulating the rate of accretion and of radial migration, it is important to investigate all sources of wave damping in an accretion disk. Here we mainly discuss damping mechanisms arising from 3-D effects in disks with aspect ratio H/r ~0.1.

A 2-D treatment is valid when the response of the disk is locally isothermal with adiabatic index \gamma = 1 and the vertical forcing is ignored. In that case, tidal forcing will generate a 2-D wave which is likely to damp due to wave steepening in a lengthscale of order ~r_L (with weak dependence on the mass of the pertuber), where r_L is the radial location of the Lindblad resonance where the acoustic wave is launched (Goodman and Rafikov 2001; Rafikov 2002). On the other hand, vertically thermally stratified disks, as may be the case for active disks with high-optical depth, generate 3-D waves which damp due to non-linear dissipation in a lengthscale of order ~r_L/m, where m is the azimuthal wavenumber (Lubow and Ogilvie 1998). In this case, most of the angular momentum flux is carried by the f-mode; however, tidal forcing also excites other modes. Finally, in a vertically isothermal (but not radially) disk with \gamma = 5/3 horizontal tidal forcing excites buoyancy g waves that receive ~20 per cent of the energy flux for a m = 0 mode (Bate et al. 2002). These g-waves have non-zero vertical group velocity, and are excited primarily away from the midplane, where non-linear dissipation is more readily attained. The radial damping length for these waves is likely to be ~H and only weakly dependent on the mass of the perturber. We generalize the problem to include the effects of vertical tidal forcing in a vertically isothermal atmosphere with \gamma > 1, and calculate the vertical flux of angular momentum of acoustic waves with m < r/H. The effects of allowing m ~r/H will be discussed.

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Bulletin of the American Astronomical Society, 34, #3< br> © 2002. The American Astronomical Soceity.