One of the most commonly used numerical methods in simulating the formation of galaxies in the universe isN-body/SPH. The collisionless gravitational components like dark matter and stars are accurately modeled by theN-body part of the method (Hernquist & Quinn, 1989), while the hydro-dynamic components are treated by the SPH part of the code, where the fluid equations are solved ensuring Galilean invariance and the conservation of mass, momentum, angular momentum, energy and entropy by modeling the fluid as a Lagrangian mass-discretized particle fluid. This treatment of the fluid has several computational benefits, however, it has some downsides which strongly influence the outcome of simulations of galaxy formation in a cosmological context: Due to its particle treat-ment of the fluid, SPH fails to successfully mix different fluid phases as it cannot treat the contact discontinuities properly, which introduces a completely numerical artificial surface tension between fluid phases and thus instabilities like Kelvin-Helmholtz and Rayleigh-Taylor which normally lead to the mixing of the gas phases are suppressed (e.g., Agertz et al., 2007; Junk et al., 2010). In addition, this suppression of phase mixing leads to a transport of gas with low-entropy to the centers of galactic halos, which is not found in Eulerian codes. Another big issue of standard SPH is caused by its in-ability to treat subsonic turbulence, which leads to problems in the treatments of shocks and turbulent cosmic plasmas.
However, gas physics is highly important for the formation of galaxies, especially regarding the populations of spirals and irregulars, but also for spheroidals and the group and cluster environments.
In particular, the correct treatment of shocks, introduced by stars, AGNs and merger events, is crucial regarding the physics of (in-situ) star formation properties and the hot halo interactions (or cooling from the halo), as known from observations. Thus, to successfully perform cosmological simulations with baryons withN-Body-SPH, these problems need to be solved.
In our new improved SPH scheme we implement artificially conduction of internal energy (e.g., Price, 2008) to enable better treatment of the mixing between fluid phases, artificial viscosity (e.g., Dolag et al., 2005) where the particle velocity distributions are regulated in case of a shock event, the Wendland Kernel (Dehnen & Aly, 2012), and use a timestep limiter for strong shocks. Artificial vis-cosity and conduction are included in a time-dependent scheme, as well as a flow limiter for shearing flows.
In Fig. A.8 we show the impact of those new modifications on the properties of a “galaxy” formed from a cooling gas cloud inside a rotating dark matter halo of Milky Way like mass, including only a simple model for cooling, star formation and supernova feedback by Springel & Hernquist (2003).
In this test case, we ignore the influence of a cosmological context (i.e., the mass accretion history through merger events and accretion of gas from the surroundings). Similar to a cosmological con-text, stars are formed only from the gas and are not present at the beginning of the simulation. The simulation was performed once without our modifications and once including those modifications.
The resulting galaxy in both cases exhibits a bulge-like structure in the center surrounded by a gas disk, that also contains stars, however, the individual properties of those test galaxies are significantly different: The bulge formed in the new scheme is significantly smaller, the resulting disk is much more symmetrical and extended, and shows more pronounced spiral arms than in the old scheme. This is caused by the combined effect of the artificial viscosity and conduction, which solve the problem of
k The results of this work have been submitted to MNRAS asAn improved SPH scheme for cosmological simulationsby A. M. Beck, G. Murante, A. Arth,R.-S. Remus, A. F. Teklu, J. M. F. Donnert, S. Planelles, M. C. Beck, P. F¨orster, M.
Imgrund, K. Dolag, S. Borgani, ArXiv 1502.07358
A.8. DISK PROPERTIES IN THE NEW MODIFIED SPH 181
Figure A.8:Galaxy properties test for the new SPH scheme presented by Beck et al. (2015) (Fig. 17 therein).
Upper panels: Vertical (left) and radial (middle) density profiles as well as the vertical velocity dispersion (right) profiles of the stellar component at different timesteps (after3.5 Gyr(dashed lines),7 Gyr(dotted lines) and10 Gyr(solid lines)) for standard (blue) SPH and the new scheme (red). Lower panels: Same as upper panels but for the cold gas component (TGas<1×105K).
the numerical surface tension due to the mixing inability, which usually lead to the conversion of cold clumps in the gas disks, which lead to enhanced star formation causing the unphysically fast growth of the bulge. Fig. A.8 shows a more quantitative analysis of the effects of the improved SPH scheme:
The density in vertical and radial direction as well as the vertical velocity dispersion are shown for the stellar (upper panels) and gaseous (lower panel) components for both schemes at different timesteps of the simulation. The galaxy simulated with the new scheme has a thinner an much more radially extended stellar disk, and a more extended gas disk, which is significantly colder than the gas disk formed in the simulation with the old scheme, as seen in vertical velocity dispersion (lower left panel).
We conclude that our new SPH scheme including reduced artificial viscosity and conduction is significantly improving the treatment of gas physics in simulations of galaxies using SPH. Thus, it is an advanced treatment of the interactions between different fluid phases, resulting in a more realistic presentation of shocks and turbulence and the mixing of gas phases, which are crucial for star formation properties. This will, in the future, enhance our understanding of galaxy formation especially with regard to disk-dominated galaxies.
Appendix B
Magneticum Box4 uhr Galaxies
Figure B.1:The most massive galaxy cluster in Magneticum Box4 uhr at z=0.38
This image shows the most massive cluster within Box4 uhr, with its total mass of Mtot ≈2.3×1014Mstill a dwarf compared to the most massive clusters seen in the universe, which are roughly an order of magnitude more massive. Nevertheless, as in real clusters, our cluster has an extremely massive BCG in the center, surrounded by several smaller spheroidal and disk galaxies (stars in yellow (young) to red (old), gas in blue). However, those “small” spheroidal galaxies still have stellar masses comparable to the Milky Way, and as such are not at all “dwarfs”. Distance to the BCG from the observer’s point of view is 500 kpc.
Figure B.2:Galaxies in Magneticum at z=2.33
Disk galaxies
Spheroidal galaxies
Merging galaxies
A selection of galaxies from Magneticum Box4 uhr at a redshift of z=2.33, shown at the correct relative sizes.
Spheroidals are much more compact and concentrated than the disk galaxies, and the disk galaxies shown here have pronounced spiral patterns. Most galaxies at this redshift, however, are currently undergoing wet mergers, most of them with small substructures that support the formation of the spiral patterns (upper central panel), and some even have spectacular interactions showing tidal arms, but since they are so gas rich their final state will most likely still be a disk galaxy, different than at present day where such encounters involve only a small fraction of gas and the collisionless stars dominate the outcome of the merger event.
GALAXIES IN MAGNETICUM BOX4 UHR 185
Figure B.3:Galaxies in Magneticum at z=0.38
Disk galaxies
Spheroidal galaxies
S0 galaxies
A selection of galaxies from Magneticum Box4 uhr at a redshift of z=0.38, also shown at the correct relative sizes. The disks tend to have more massive bulges than at z=2.33, and their relative number has decreased.
The spheroidals are also much more massive than at z= 2.33, and their stellar components are much older (thus the red hue that indicates the age of the stars). While we basically did not find any S0-like galaxies (flattened spheroidals) at z=2.33, at z=0.38they are now present, some of them still having gas similar to the Sombrero galaxy (lower left panel).