Issue |
A&A
Volume 432, Number 3, March IV 2005
|
|
---|---|---|
Page(s) | 757 - 769 | |
Section | Astrophysical processes | |
DOI | https://doi.org/10.1051/0004-6361:20041948 | |
Published online | 07 March 2005 |
Global numerical simulations of differentially rotating disks with free eccentricity
Astronomy Unit, Queen Mary, University of London, Mile End Rd, London E1 4NS, UK e-mail: jcbp@maths.qmw.ac.uk
Received:
3
September
2004
Accepted:
10
December
2004
We study the nonlinear evolution of
global modes with low
pattern speeds in a differentially
rotating non magnetic disk, by means of two and three dimensional
numerical simulations. The modes make disk streamlines eccentric
with maximum eccentricity in the range
We found that long lived
patterns corresponding to eccentricities ~0.1
lasted for the duration
of the simulations of ~64 orbits at the disk outer boundary.
They had slow retrograde precession with period ~10
orbits at the outer boundary, in
good agreement with that found from
linear normal mode analysis.
As expected from linear stability analysis,
which leads one to expect a parametric instability associated
with the non circular streamlines,
we also found that three dimensional
simulations showed the growth of a local
instability to producing vertical
motions on a local scale that eventually results in small amplitude
turbulence with root mean square vertical velocity typically
∼
cs being the sound speed.
This turbulence together with much more
effective shocks produced by the interaction
of the eccentric disk with the inner boundary were responsible for damping
the disk eccentricity. Our first estimate of
the damping time associated with turbulence
for eccentricities ~0.1,
corresponded to that associated with a turbulent
viscosity acting to circularize
the eccentric streamlines with “α” parameter ~ 10-3.
For parameters appropriate
to protostellar disks at 5 AU this corresponds to
a decay time ∼
Thus although the indication is that disks with eccentric streamlines
are long lived, there is associated turbulence
even in the non magnetic case leading to
estimated decay times that may be significant
when the possibility of the growth of
orbital eccentricity for extrasolar planets is considered
through disk planet interaction on sufficiently long timescales.
Key words: accretion, accretion disks / instabilities / hydrodynamics / celestial mechanics / planets and satellites: formation
© ESO, 2005
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