**31st Annual Meeting of the DPS, October 1999**

*Session 36. Planet Formation: Solar Nebula*

Contributed Oral Parallel Session, Wednesday, October 13, 1999, 10:30am-12:00noon, Sala Kursaal
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## [36.03] Spiral Bending Waves Launched at a Vertical Secular Resonance

*J.M. Hahn (LPI), W.R. Ward (SWRI)*

The excitation of spiral bending waves at a vertical secular
resonance is described. These nodal bending waves are
launched at sites where the secondary's nodal regression
rate matches the disk's rate, and they propagate in both
particle and gas disks. In planet--forming environments
where the local disk mass is often in excess of the
secondary's mass, it is the disk--gravity that determines
the precession rates of the secondary as well as the disk
material. If there is no gap in the disk, the resonance will
lie quite close to the secondary's orbit a_{s}, and the
bending waves will have a wavelength
\lambda~sqrt{ha_{s}} where h is the disk scale height.

The excitation of nodal bending waves will damp out the
secondary's inclination and ultimately shut off subsequent
wave generation. An Earth--mass protoplanet embedded in a
minimum--mass planetesimal disk will have its inclination
damped out in less than ~00 orbits provided there is
no gap in the disk and its Toomre stability parameter obeys
Q<100. The protoplanet's eccentricity is also damped at a
comparable rate due to the excitation of spiral density
waves at its apsidal secular resonance.

However disk stirring by the secondary or gap formation
tends to weaken the wave interaction by slowing the
secondary's nodal regression rate and pushing the resonance
radially away. Consequently, a Jovian--mass protoplanet
orbiting in a minimum--mass nebula gas disk will lose its
inclination in ~00 orbits if it resides in a gap.

The consequences of these inclination and
eccentricity--damping mechanisms for planet--formation will
also be discussed.

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