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| Magnetohydrodynamics
by
Dr. Tony Allen |
| Simulation
of Magnetic Collapse |
We (Anthony
Allen collaborating with Frank Shu and Z. Li) have been
working on the collapse of magnetized singular isothermal
toroids. Recent improvements in the numerical codes have
made it possible to simulate collapse both with and without
rotation. Currently, Allen is investigating the possibility
of combining wind with collapse, which seems natural given
the results of the aforementioned works. In addition, Allen
is also simulating the pre-collapse phase of molecular clouds
leading to the pivotal state, which leads to gravitational
collapse. Another project in progress is the study of the
collapse of Toomre-Hayashi Toroids, which are self-similar
toroids first studied in the context of galactic dynamics.
The fragmentation of these toroids will make a useful starting
point into 3D simulations.
A refinement
to Allen and Shu (2000) involves allowing magnetic field,
which initially provides exact force balance with gravity,
to leak out of the cloud by ambipolar diffusion or to begin
with a magnetically (slightly) under-supported cloud, to
keep mass on the computational grid. The resulting tendency
toward collapse would be balanced by the expansive push
of the protostellar bipolar outflows. Self gravity and a
better treatment of outflows were implemented and tested
in the October of 2002. The code is now running on French
computers.
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These
are moment 0, 1, and 2 plots for MHD collapse calculations
of magnetized, rotating, singular isothermal toroids. Stars
are believed to have formed from the collapse of molecular
clouds. These clouds are observed to be cold, with weak
magnetic fields, and small initial rotation. Realistic models
of these clouds have been proposed by Frank Shu (Tsing-Hua
U.) and Zhi-yun Li (UVa). These models have been used as
initial states for magnetohydrodynamic collapse calculations
to study the physics of the early stages of star formation.
The moment-0 plot shows the false-color column density an
observer might see if viewing the cloud from a side perpendicular
to the axis of rotation. A high density, magnetically supported
pseudodisk is present in the mid-plane, but is hard to see
with this false-color scheme. The moment-1 plot shows the
velocity profile of the collapsing cloud. Far from the center,
the pre-collapse, rotational effects are visible. Closer
to the center, one can see slower, magnetically braked material
as well as a angular-momentum-carrying outflow. The outflow
is driven by the same magneto-centrifugal mechanism believed
to be responsible for jets, although it is at much lower
velocity than typical jets. This braking mechanism allows
for efficient transport of angular momentum from a forming
protostar to the outer cloud and is a possible explanation
of the angular momentum removal problem in star formation;
with magnetic braking, central accretion proceeds at a constant
rate allowing growth to stellar mass-scales. The moment-2
plot hows velocity dispersion in the region.
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Topics of Magnetohydrodynamics:
Simulation
of Magnetic Collapse
Zeus
2D Simulations of Wide-angle winds
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