This initially axisymmetric configuration is dynamically unstable toward the
development of a so-called bar-mode instability; actually, the unstable
eigenfunction has a slight two-armed spiral character. Here is the movie
that shows the nonlinear development of this instability:
[This Quicktime movie is 5.907 MBytes in size.]
This evolution is viewed from the inertial frame of reference. After "ejecting" a small portion of its mass into a "circumstellar" disk/ring, the model settles down into a nearly steady-state, rotating bar-like configuration that, for all intents and purposes is a compressible analog of a Riemann ellipsoid. (This is the theme of the CT00 paper, mentioned above.)
In order to illustrate how close this configuration was to a steady-state
system, Cazes shifted the simulation into a frame of reference that was
rotating with the pattern speed of the bar, then extended the evolution
for several more pattern rotation periods. Here is the movie
showing this segment of the evolution from a frame that is rotating with
the bar's overall pattern speed:
[This Quicktime movie is 7.169 MBytes in size.]
For additional properties of this system, both at the start and at the end of this movie, see Table 2 of CT00.
Cazes then "cooled" this steady-state model in a manner that is described
in Chapter 5 of his dissertation. (This portion of the simulation has
not been submitted for formal publication.) Here is a movie illustrating
the last phase of this cooling evolution:
[This Quicktime movie is 8.514 MBytes in size.]
A more detailed discussion of this "cooling" evolution is presented on the following URL: http://www.phys.lsu.edu/astro/movie_captions/fission.html. A few additional movie sequences that illustrate the internal flow of this system can also be found linked to this URL.
This initially axisymmetric configuration is dynamically unstable toward the
development of a so-called bar-mode instability. You'll note, however,
that in this case the unstable eigenfunction has much less of a spiral
character than "Model A," shown above. Here is the movie
that shows the nonlinear development of this instability as viewed
from the inertial reference frame:
[This Quicktime movie is 10.8 MBytes in size.]
This model also settles down into a nearly steady-state, rotating bar-like configuration that, for all intents and purposes is a compressible analog of a Riemann ellipsoid. It evolves to this configuration with much less fan-fare, however; very little mass or angular momentum is shed in the equatorial plane. This indicates to us that the initially selected distibution of angular momentum in this model (uniform vortensity) is fairly well suited to a barlike configuration.
In order to illustrate how close this configuration was to a steady-state
system, Cazes shifted the simulation into a frame of reference that was
rotating with the pattern speed of the bar, then extended the evolution
for several more pattern rotation periods. Here is the movie
showing this segment of the evolution:
[This Quicktime movie is 14.1 MBytes in size.]
For additional properties of this system, both at the start and at the end of this movie, see Table 3 of CT00.
This initially axisymmetric configuration is dynamically unstable toward the
development of a so-called bar-mode instability. Here is the movie
that shows the nonlinear development of this instability, as viewed from
the inertial reference frame:
[This Quicktime movie is 17.4 MBytes in size.]
This model's evolution is similar to Cazes' Model B evolution. Its differences can be attributed to two things: (a) This model has a higher initial value of T/|W|, so it has more of a spiral eigenfunction and its nonlinear deformation is a bit more severe. (b) This model filled a larger fraction of the grid (radially) initially, so when it expanded, it hit the edge of the grid and some of the mass/angular momentum was lost off of the grid.
Shangli "cooled" this model in the same manner as John Cazes had cooled
his "model A" earlier. But he cooled it a bit more slowly than the
earlier model. Here is a movie illustrating this entire "cooling"
evolution as viewed from a frame rotating with the initial pattern
frequency of the bar:
[This Quicktime movie is 12.946 MBytes in size.]
Note, as of 28 July 2002, we have not finished evolving this system. It looks like the "binary" amplitude is still slowly growing and, as expected, the pattern frequency is continuing to get higher as the system contracts.
This initially axisymmetric configuration is dynamically unstable toward the
development of a so-called bar-mode instability. Here is the movie
that shows the nonlinear development of this instability, as viewed from
the inertial reference frame:
[This Quicktime movie is 10.264 MBytes in size.]
Note that as of 28 July 2002, we are still running this evolution. It looks like the system is near its steady-state configuration and is therefore is almost ready to "cool."