The Rockstar Phase-Space Temporal Halo Finder and the Velocity Offsets of Cluster Cores

Abstract: We present a new algorithm for identifying dark matter halos, substructure, and tidal features. The approach is based on adaptive hierarchical refinement of friends-of-friends groups in six phase-space dimensions and one time dimension, which allows for robust (grid-independent, shape-independent, and noise-resilient) tracking of substructure; as such, it is named Rockstar (Robust Overdensity Calculation using K-Space Topologically Adaptive Refinement). Our method is massively parallel (up to 10^5 CPUs) and runs on the largest current simulations (>10^10 particles) with high efficiency (10 CPU hours and 60 gigabytes of memory required per billion particles analyzed). A previous paper (Knebe et al 2011) has shown Rockstar to have class-leading recovery of halo properties; we expand on these comparisons with more tests and higher-resolution simulations. We show a significant improvement in substructure recovery as compared to several other halo finders and discuss the theoretical and practical limits of simulations in this regard. Finally, we present results which demonstrate conclusively that dark matter halo cores are not at rest relative to the halo bulk or satellite average velocities and have coherent velocity offsets across a wide range of halo masses and redshifts. For massive clusters, these offsets can be up to 350 km/s at z=0 and even higher at high redshifts. Our implementation is publicly available at http://code.google.com/p/rockstar .

• The paper introduces the Rockstar halo finder, a novel algorithm that uses adaptive hierarchical friends-of-friends refinement in six phase-space dimensions plus time.
• It achieves high computational efficiency by processing one billion particles in just 10 CPU hours while enhancing substructure recovery in cosmological simulations.
• The analysis reveals coherent velocity offsets in dark matter halo cores of up to 350 km/s in massive clusters, offering new insights into cluster dynamics.

Insights into the Rockstar Phase-Space Temporal Halo Finder

The paper by Behroozi, Wechsler, and Wu introduces the rockstar halo finder, a novel algorithm designed to overcome the limitations posed by previous halo finding approaches through an emphasis on phase-space and temporal analysis. The essence of this research lies in the advanced and adaptable methodology utilized for identifying dark matter halos, substructure, and tidal features in cosmological simulations. The rockstar finder advances the domain by leveraging adaptive hierarchical refinement of friends-of-friends (FOF) groups across six phase-space dimensions and one time dimension, resulting in a robust and noise-resilient methodology for the identification and analysis of halos.

The algorithm employs a sophisticated technique for creating a hierarchy of FOF subgroups in phase space, allowing for a grid-independent and shape-independent tracking of substructure. This is achieved by iteratively reducing the linking length in six-dimensional phase-space, setting it to capture a constant fraction of particles at successive levels of refinement. This ensures a high sensitivity to substructure, which is imperative for accurate halo characterization, especially in the case of major mergers and subhalos near the dense centers of larger halos.

Significant emphasis is placed on the computational efficiency of the rockstar algorithm, as it operates on massively parallel systems with impressive scalability, analyzing systems with over $10^{10}$ particles with minimal processing time. The high efficiency of this algorithm is noteworthy, requiring merely 10 CPU hours and 60 gigabytes of memory for analysis of one billion particles, marking a significant improvement over several other halo finders.

A strong point of this research is the empirical enhancement in substructure recovery compared to other halo finders, achieved through comprehensive tests with synthetic and high-resolution cosmological simulations. This is critical for advancing our understanding of the nonlinear growth of structure in the Lambda Cold Dark Matter (ΛCDM) cosmological model. Rockstar substantially improves the recovery of a multitude of halo properties such as positions, velocities, masses, and velocity dispersions, probing satellite masses down to the centers of host halos with high fidelity.

Furthermore, this paper contributes a significant finding about velocity offsets within dark matter halo cores. It conclusively demonstrates that dark matter halo cores possess coherent velocity offsets relative to the halo bulk or substructure average velocities. These offsets are profound in more massive clusters, exhibiting offsets of up to 350 km s$^{-1}$ at redshift $z=0$ and increasing at higher redshifts.

The availability of the rockstar halo finder as a publicly accessible tool provides a valuable resource for the community, enabling further exploration and validation of cosmic structure formation theories. By improving the consistency and accuracy of halo catalogs over timesteps, the rockstar algorithm significantly contributes to the precision modeling required for interpreting forthcoming data from major astronomical surveys.

In conclusion, the innovative advancements in the rockstar halo finder offer substantial theoretical implications for dark matter studies and practical enhancements for computational astrophysics. As simulations scale up in complexity and detail, methods that adeptly balance computational demand with accuracy, like rockstar, will be instrumental in pushing the boundaries of current cosmological research, potentially probing deeper into the underlying physics that govern cosmic evolution. The implications for future developments in AI and numerical simulations are significant, fostering a landscape where model uncertainties can progressively be minimized.