1. Numerical issues in SPH simulations of disk galaxy formation Tobias Kaufmann, Lucio Mayer, Ben Moore, Joachim Stadel University of Zürich Institute for Theoretical Physics

2. 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

3. 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).

4. 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 particles IR 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 particles Mass resolution better than 1e5 Msolar Time evolution is done with GASOLINE, a parallel TreeSPH code on the zBox supercomputer.

5. 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.

6. Mass and angular momentum convergence green LR blackIR redHR 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.

7. 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 IRblue HR Hot particles: magenta IRred HR

8. Hydro-torques: resolution dependence Torques acting on the cold disk particles: left panel LR, right panel HR green - total hydro torque red - hydro torques from hot magenta - hydro torques from cold particles.

9. Torques: gravity dominates Torques acting on the cold disk particles: left panel LR, right panel HR green - hydro torque red - total torque blue - gravitational torque

10. Torques: gravity dominates Okamoto et al 2003 found bigger torques between hot and cold phase (due to limited resolution?)

11. 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.

12. Shape of the surface density of the resulting disk: Disk surface densities

13. How physical is this bar? Maxwellian velocity distribution in the dark matter vs. calculating the velocities from the distribution function (Kazantzidis et al 2004)

14. 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 run Red solid: baryons SFHE

15. How physical is this bar? T=1 T=2 T=3 T=5

16. 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 MsolarN=1M r = 20 kpc Shell 2: 1e6 MsolarN=0.5Mr = 100 kpc Shell 3: 7e6 MsolarN=100k

17. Better resolution: Shell models Okay for gravity. But: SPH had some problems in our configuration with different mass particles.

18. Better resolution: Shell models Smoothing over particles of the same mass will solve the problem?

19. M33 model: gravitationally stable? Shell model for dark matter with 1.1M dark/500k gas: Mass resolution better than 1e5 Msolar, softening 250pc.

20. 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

21. M33 model: gravitationally stable? Shell model for dark matter with 1.1M dark/500k gas: Mass resolution better than 1e5 Msolar, softening 250pc.

22. 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.