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.