sorry, that's what happens when one cuts and pastes from TeX files..
ARAA = Annual Reviews of Astronomy and Astrophysics
MNRAS = Monthly Notices of the Royal Astronomical Society
>How do you characterise the stability of the simulation - is it just
>measuring the standard deviation of the hamiltonian from its initial
>value ?
>
hmm. okay, welcome to dr hos' disk stability lecture I.
Self-gravitating rotating disks are very cranky beasts, full of
instabilities (the basic reference for just about everything here
can be found by looking up "Sellwood" in Astronomy & Astrophysics
abstracts -- he has done extensive work in this field. But a great
starting point would be "Instabilities in Stellar Discs" in
Numerical Simulations in Astrophysics ed J Franco, Cambridge U Press).
One of the strongest instability is the formation of a bar (m=2)
mode in the disk. This instability can be supressed with a sufficient
amount of material in a kinematically hot ("hot"=kinematically supported
by random motions, rather than rotational motion) component, ie a
massive dark halo (see Binney & Tremaine's "Galactic Dynamics" section
6.3 for a discussion of this "Ostriker-Peebles criterion"). However,
EVEN IF you satisfy the O-P criterion through a dark halo, in N-body
calculations, bar modes will grow -- albeit slowly -- due to the
amplification of discreteness noise in the halo particle distribution
(see the Sellwood 89 MNRAS article I referred to above). To defeat
this (ie to ensure the power in the m=2 mode stays small), you need to
reduce the discreteness noise in the halo potential ("root-N noise")
by increasing N. Therefore, to keep a disk from becoming bar unstable
over many rotational periods, you need MANY MANY particles (10^6).
Another problem -- unrelated to the bar mode -- makes it difficult to
model disk galaxies for a long period of time. Again, disks are kinematically
cold, meaning the velocity dispersion (random motions) in the disk are
much smaller than the rotational motion. sigma/v_rot ~ .1 - .2 or so.
Two body relaxation in Nbody models tends to randomize the velocity
distrribution of the particles, increasing sigma/v_rot -- the disk
is "heating" due to purely numerical effects. This is bad -- many of the
neat dynamical effects in disk galaxies are due to the kinematically cold
nature of the disk, and if your model disk is heating up artificially,
you wont be able to accurately model these things. For example, the
decay time of a satellite galaxy into a disk depends on the coupling
between the sat and the disk. The efficiency of this coupling depends on
how cold the disk is (and the orbit of the sat, too). Therefore, to get
the decay times right, you want disk that wont artificially heat. To reduce
the two-body relaxation effects, again you must increase N.
So in a not-so-brief summary, when I mentioned stability, I was referring
two 2 things -- not wanting an m=2 mode to form, and not wanting sigma/v
to rise. Big N is what you need, if you are going to do this self-consistently.
Of course, you can get around SOME of these problems using rigid (analytic)
halos, restricted three body routines, expansion techniques, etc. But
that's a shortcut that wont work for modeling galaxy interactions and
mergers, where you NEED a fully self-consistent model.
>>If you want to keep disk galaxies cool over more than a few Gyr,
>>**doing self-consistent (ie no rigid halos, three body models, etc) work**
>>then you need > 5x10^5 particles.
>
>>5e5 particles on a treecode takes ~ 20 Cray C90 hours to run a 1 Gyr
>>encounter (approx 8 halfmass rotation periods).
>
>What's a treecode?
A treecode is an Nbody code which sorts the particles into nested
hierarchical structures (hence the "tree" label) and evaluates the
force between each particle and either other particles or hierarchical
groups of particles, depending on accuracy criteria. It has the advantage
of the CPU time scaling as NlogN rather than N^2 as direct nbody routines
do. Check out the Sellwood ARAA reference, or Barnes & Hut 1986 Nature
324 446, or Hernquist 1987 Astrophysical Journal Supplement 64 715.
Now I need to go stick my head into the IRAF wringer. Hope this helps.
Chris
>
>Ross.
>--
> My opinions are wrong? - Well then please send me the correct
> neural net weightings.