Populating a cluster of galaxies - I. Results at z=0

TL;DR

The study combines high-resolution N-body simulations with semi-analytic galaxy formation on dark matter merging trees to populate a Coma-like cluster in a ΛCDM universe. It introduces SUBFIND to resolve subhaloes within haloes, enabling a subhalo-based treatment of central and satellite galaxies and their mergers, and calibrates parameters against the I-band Tully-Fisher relation and Milky-Way gas mass. The subhalo approach yields cluster-scale observables—Tully-Fisher and Faber-Jackson relations, a well-shaped cluster luminosity function, morphology-density trends, and color distributions—that align with observations, while highlighting the role of substructure in driving luminosity segregation and merger histories. This framework demonstrates that explicit tracking of subhaloes improves convergence and realism of galaxy populations in clusters, offering a powerful avenue for modeling hierarchical galaxy formation in dense environments.

Abstract

We simulate the assembly of a massive rich cluster and the formation of its constituent galaxies in a flat, low-density universe. Our most accurate model follows the collapse, the star-formation history and the orbital motion of all galaxies more luminous than the Fornax dwarf spheroidal, while dark halo structure is tracked consistently throughout the cluster for all galaxies more luminous than the SMC. Within its virial radius this model contains about 2.0e7 dark matter particles and almost 5000 distinct dynamically resolved galaxies. Simulations of this same cluster at a variety of resolutions allow us to check explicitly for numerical convergence both of the dark matter structures produced by our new parallel N-body and substructure identification codes, and of the galaxy populations produced by the phenomenological models we use to follow cooling, star formation, feedback and stellar aging. This baryonic modelling is tuned so that our simulations reproduce the observed properties of isolated spirals outside clusters. Without further parameter adjustment our simulations then produce a luminosity function, a mass-to-light ratio, luminosity, number and velocity dispersion profiles, and a morphology-radius relation which are similar to those observed in real clusters. In particular, since our simulations follow galaxy merging explicitly, we can demonstrate that it accounts quantitatively for the observed cluster population of bulges and elliptical galaxies.

Figures (16)

• Figure 1: The projected mass density fields in slices of thickness 10$\,h^{-1}{\rm Mpc}$ around the cluster center in the original GIF simulation (left), and in the S3 resimulation (right). The left image is $141\,h^{-1}{\rm Mpc}$ on a side, and the white square marks the region ($85\,h^{-1}{\rm Mpc}$ on a side) that is displayed in the image of the resimulation on the right. In the right panel, you may notice small traces of the spherical grid used to represent the density field in the boundary region. Note that these residuals of the grid structure are just seen because of projection effects that arise in the visualization technique.
• Figure 2: The dark matter distribution of the S4 cluster at $z=0$. The image shows all the mass in a box of sidelength $4\,h^{-1}{\rm Mpc}$ around the cluster center. To render the substructure visible, particles have been weighted by their local density (computed by adaptive kernel estimation), and a logarithmic color scale has been applied. Note that the small bright dots that are visible in the cluster should not be mistaken as noise -- they are in fact self-bound subhaloes and correspond to surviving cores of haloes that have fallen into the cluster at some earlier time.
• Figure 3: Example for a subhalo identification with SUBFIND. The top left panel shows a small FOF-group (44800 particles), identified at $z=0$ in the vicinity of the S2 cluster. SUBFIND identifies 56 subhaloes within this group, the largest one forms the background halo and is shown on the top right, while the other 55 subhaloes are plotted on a common panel on the lower left. In this example, the total mass in all the "true" subhaloes 2-56 is about 8% of the group mass. Particles not bound to any of the subhaloes form "fuzz", and are displayed on the lower right. These particles primarily lie close to the outer edge of the group. Spatial coordinates are given in $\,h^{-1}{\rm kpc}$.
• Figure 4: Substructure in the S2 cluster at $z=0$. The top left panel shows a color-coded projection of the FOF-group that contains the cluster. To highlight the substructure, particles have been given a weight proportional to the local dark matter density. In the top right panel we show the largest subhalo identified by SUBFIND, i.e. the background halo. The lower right shows the 495 other subhaloes identified in the object. Finally, on the lower right, we plot circles at the positions of each identified subhalo, with radius proportional to the third root of the particle number in the subhalo. Note that we actually found subhaloes within subhaloes in this example.
• Figure 5: Subhalo mass functions in the four clusters S1, S2, S3 and S4 at redshift $z=0$. In the top panel, we plot the cumulative number $N(m)$ of subhaloes with masses larger than $m$. The short vertical lines mark the ends of the graphs for the simulations S1 (lowest resolution), S2, and S3 (second highest resolution). The agreement between the four simulations is quite good. This good agreement is also present in the differential mass function ${\rm d} N/{\rm d} m$, which we show in the lower panel.