==================================================================Models of
Starbursts in Merging Galaxies Chris Mihos & Lars Hernquist, UC
Santa Cruz
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MODELING
TECHNIQUES
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The modeling technique which goes into these models can largely be divided
into three areas: gravitational dynamics, ISM hydrodynamics, and star
formation. Gravitational forces are calculated using an N-body treecode.
In such a code, the galaxy is represented by N particles, and the
gravitational force on each particle is simply the sum of the force from
all the other particles. The phrase "treecode" referes to the fact that the
N particles are sorted into a hierarchical "tree" structure in which forces
from groups of particles at large distances may be approximated using their
center of mass and quadropole moments (see Barnes & Hut 1986, Nature, 324,
446; Hernquist 1987, Astrophysical Journal Supplement, 64, 715). Treecodes
currently represent the best method for Nbody modeling of interacting
galaxies in that they place no constraints on the symmetry or resolution of
the model (unlike field expansion techniques or particle-mesh algorithms)
while offering a favorable O(NlogN) scaling of CPU time (unlike the costly
O(N^2) scaling of direct-sum methods). The interstellar medium will be
treated as a smooth fluid obeying the Navier-Stokes equations for a
compressible gas. The evolution of the ISM gas is modeled using Smoothed
Particle Hydrodynamics, in a manner fully compatible with the
tree-structure used to evolve the collisionless components of the galaxies
(Hernquist & Katz 1989,Astrophysical Journal Supplement, 70, 419). In SPH,
the density field of the gas is represented by particles, each of which
carries along with it information describing the local thermodynamic and
hydrodynamic properties of the fluid. These properties are updated using
the hydrodynamic conservation laws, including an artificial viscosity to
capture shocks and sources of entropy generation to account for heating and
cooling of the gas. An interpolation procedure allows the properties of the
fluid, and their derivatives, to be estimated at any point in space from
neighboring particles. Thus, SPH is analogous to a grid-based code in
which the nodes in the mesh uniformly sample the mass and move freely with
the fluid. Finally, star formation is characterized by a Lagrangian form
of the Schmidt law, wherein the star formation rate in a particle is
proportional to the square root of the local gas density, yielding a
Schmidt lawof index n=1.5 (Mihos & Hernquist 1994, Astrophysical Journal,
in press). Each time star formation rates are recalculated, the
corresponding mass of gas is turned into stars, slowly converting the SPH
particles from gas to collisionless material. Star formation also adds
kinetic energy locally to the surrounding ISM, mimicking the energetic
effects of massive young stars and supernovae.