numerical issues in sph simulations of disk galaxy formation tobias kaufmann, lucio mayer, ben...
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Numerical issues in SPH simulations of disk galaxy
formationTobias Kaufmann, Lucio Mayer, Ben Moore, Joachim StadelTobias Kaufmann, Lucio Mayer, Ben Moore, Joachim Stadel
University of ZürichUniversity of ZürichInstitute for Theoretical PhysicsInstitute for Theoretical Physics
How to build a disk galaxy?Because of limited resolution in cosmological simulations we try to form a disk galaxy in an isolated NFW halo with an embedded gaseous halo in a lambda CDM universe.
The parameters like baryon fraction, mass, spin parameter ... are motivated by cosmological simulations and observations.Use of a standard cooling function (Compton and radiative cooling).
M33
How to build a disk galaxy?
Dark matter halo with gas
Because of limited resolution in cosmological simulations we try to form a disk galaxy in an isolated NFW halo with an embedded gaseous halo in a lambda CDM universe.
The parameters like baryon fraction, mass, spin parameter ... are motivated by cosmological simulations and observations.Use of a standard cooling function (Compton and radiative cooling).
How to build a disk galaxy?Milky Way type model
NFW dark matter halo, Mvirial ~9e11Msolar, baryon fraction ~ 9%concentration c = 8, spin parameter lambda ~ 0.045
LR 30,000 dm particles, 30,000 gas particlesIR 100k dm, 100k gas HR 1M dm, 500k gas
M33 type model
NFW Dark matter halo, Mvirial ~5e11Msolar, baryon fraction ~ 6%concentration c = 6.2, spin parameter lambda ~ 0.1
Resolution up to 1.1M dark, 500k gas particlesMass resolution better than 1e5 Msolar
Time evolution is done with GASOLINE, a parallel TreeSPH code on the zBox supercomputer.
How to build a disk galaxy?
Numerical aspects pointed out:
•Mass and angular momentum evolution versus resolution
•Torques: Gas physics versus gravity torques
•Softening effects on the morphology of the disk
•Influence of the Maxwellian velocity distribution of the dark matter
•Different starformation recipies
•Increasing resolution by using shell models
Discussed mostly using the Milky way model.
Mass and angular momentum convergence
green LR
black IR
red HR
For convergence in mass, IR is sufficient, but not in angular momentum.
Accretion of gas particles (initially from a sphere of 80kpc) on to the cold disk is plotted.
Cold vs. hot phase: resolution dependence
Evolution of the specific angular momentum of gas particles (initially from a shell from 70kpc to 80kpc).
All particles:black IR blue HRHot particles:magenta IR red HR
Hydro-torques: resolution dependenceTorques acting on the cold disk particles: left panel LR, right panel HR
green - total hydro torquered - hydro torques from hotmagenta - hydro torques from cold particles.
Torques: gravity dominatesTorques acting on the cold disk particles: left panel LR, right panel HR
green - hydro torquered - total torqueblue - gravitational torque
Torques: gravity dominates
Okamoto et al 2003 found bigger torques between hot and cold phase (due to limited resolution?)
Disk surface densities
Solid lines: softening = 0.5 kpc
Dashed lines: softening = 2 kpc
Both softening, resolution, dynamics (bar formation) play a role in altering the final mass distribution
The presence of a bar increases the scale-length of the surface density in the outer part of the disk.
The presence of a bar increases the scale-length of the surface density in the outer part of the disk.
Shape of the surface density of the resulting disk:
Disk surface densities
How physical is this bar?Maxwellian velocity distribution in the dark matter
vs. calculating the velocities from the distribution function(Kazantzidis et al 2004)
How physical is this bar?
Including different recipies of starformation
Katz 1992 (stars spawn from cold, Jeans unstable gas particles in regions of convergence flows)
increased efficiency
pure temperature criterion
Specific angular momentum of disk particles:Black: IR gas runRed solid: baryons SFHE
How physical is this bar?
T=1
T=2
T=3
T=5
Better resolution: Shell models
To resolve the inner part of the halo we need a
mass resolution < 10e5 Solar masses.
Idea: using shells with different mass particles:
Shell 1: 1e5 Msolar N=1M r = 20 kpc
Shell 2 : 1e6 Msolar N=0.5M r = 100 kpc
Shell 3: 7e6 Msolar N=100k
Better resolution: Shell modelsOkay for gravity.
But: SPH had some problems in our configuration with
different mass particles.
Better resolution: Shell models
Smoothing over particles of the same mass will solve the problem?
M33 model: gravitationally stable?Shell model for dark matter with 1.1M dark/500k gas:Mass resolution better than 1e5 Msolar, softening 250pc.
M33 model: gravitationally stable?Shell model for dark matter with 1.1M dark/500k gas:Mass resolution better than 1e5 Msolar, softening 250pc.
SPH simulation of M33: projected gas density of the cold gas after 3 Gyr, box length 40 kpc
Very close to exponential surface brightness profile
M33 model: gravitationally stable?Shell model for dark matter with 1.1M dark/500k gas:Mass resolution better than 1e5 Msolar, softening 250pc.
Conclusions:● It was not possible to build a disk galaxy without a bar
using Milky Way like parameters (baryon fraction, mass ...)
and small softening.● Using 6% baryons (M33) and higher spin ends up in a
disk galaxy (with nucleus) also with small softening.● Resolution does matter:
with 100k of gas particles one is close to convergence in
angular momentum and mass accretion.
Small softening is needed to resolve the inner structure
(use shell models to lower the computational time).● Gravity seems to be more important than gas physics.