Potential Vorticity Evolution in the Co-orbital Region of Embedded Protoplanets Page: 61 of 175
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Planet
rp di
Star ri Gas Blob
Figure 5.1: Diagram of the disk with a planet used for torque calculations.
where QP is the angular velocity of the planet (D'Angelo et al., 2002; Ward, 1997).
5.2 Phase Transition
Our simulation results are generally in agreement with previous simulations for
the planet on a fixed circular orbit (see Masset, 2002). The generic structures, pro-
duced in the disk by the tidal interactions between the planet and its surrounding
flows, are the same. Since the planet mass is relatively small, only density dips are
generated with no gaps (at least during the few hundred orbits simulated here).
One of the key finding is shown in Fig. 5.2 which displays the total torque on
the planet from the disk. It has two very distinct phases:
(1) Phase I: the total torque is negative and smooth, modulated by a period that
is similar to the libration period near the L4 and L5 points (Tub ~ 4/27p ~ 40P
where P is one orbit at r = 1).44
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Koller, J. Potential Vorticity Evolution in the Co-orbital Region of Embedded Protoplanets, thesis or dissertation, September 1, 2004; Los Alamos, New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc779530/m1/61/: accessed April 20, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.