CWTHF: Subhalo Identification with Continuous Wavelet Transform

TL;DR

This paper extends the continuous wavelet transform halo finder (CWTHF) to identify subhalos within cosmological simulations by adding an unbinding-based substructure procedure and a recursive, cross-scale peak extraction that builds a hierarchical halo catalog. The approach preserves the original $\mathcal{O}(N)$ time complexity and leverages 4D wavelet maxima (3D space + scale) to locate substructures, with a fast maximum-exclusion step to prevent duplicates. Validation against IllustrisTNG datasets (TNG50-2 and TNG100-1) shows CWTHF recovers major substructures with a high degree of stability relative to SUBFIND, though it identifies fewer small satellites due to a limited scale range and background contamination; zoom-in tests demonstrate that expanding the scale range can recover more subhalos, confirming the method’s potential with adequate parameter choices. The work provides a fast, wavelet-based subhalo finder, highlights parameter dependencies on SHMF/SHPS, discusses limitations related to background contamination, and points to future optimizations (e.g., improved unbinding, domain decomposition) and publicly available code for community use.

Abstract

With advances in cosmology and computer science, cosmological simulations now resolve structures in increasingly fine detail. As key tracers of hierarchical structure formation, subhalos are among the most important objects within these simulations. In our previous work, we established that the continuous wavelet transform (CWT) can effectively extract clustering information and serve as a robust halo finder. Here, we extend the CWT framework to subhalo identification by adapting the CWTHF (Continuous Wavelet Transform Halo Finder) code. This extension extends the unbinding procedure, which enables the reliable identification of gravitationally bound substructures. The algorithm identifies density peaks within known halos or subhalos and segments the surrounding volume accordingly. Once a new subhalo is registered, its position is recorded to prevent duplicate detection. We validate our approach using the TNG50-2 and TNG100-1 simulations, as well as a single Friends-of-Friends (FOF) halo, by comparing the resulting CWT catalog against the reference SUBFIND catalog. Because the method inherits the original computational framework, our subhalo finder maintains a favorable linear time complexity of $\mathcal{O}(N)$.

Figures (12)

• Figure 1: Visualization of the subhalo-identification pipeline. Linked circles of the same color across adjacent panels mark the same physical region, while circles of the same color within a single panel represent subhalos detected at that specific scale. Once a subhalo is confirmed, its center is recorded, and any subsequent maximum found within its exclusion zone is discarded. For example, the central red structure in Step 2 and the central orange structure in Step 3 were removed due to their proximity to a previously validated subhalo.
• Figure 2: Scatter plot of a typical disrupted central subhalo. When maxima are not removed during identification, the non-orthogonality of the GDW generates a secondary peak at the same spatial location but on a smaller scale (higher $k_w$). This leads to the over-segmentation of the central subhalo from within, resulting in a hollow shell structure rather than a solid core.
• Figure 3: Scatterplot of the largest CWT halo (top panel) and its corresponding FOF halo (bottom panel) with their color encoding the local density. Each row, from left to right, shows the full halo, the central subhalo, and all remaining subhalos, respectively. The cube edge length is $2\,{h^{-1} {\rm Mpc}}$. Notably, the CWT halo is more compact, excluding the outermost regions of the FOF halo. The significantly more concentrated distribution in the subhalo panels, together with the small high-density patches visible within the central subhalo, indicates a systematic trend: in full-snapshot analysis, CWTHF captures all major substructures but tends to leave the smallest subhalos merged with the central subhalo.
• Figure 4: The rank (top) and the mass (bottom) of the six largest subhalos in the CWT catalogs, alongside their counterparts in the SUBFIND catalogs. The difference between the two finders is so minute that each corresponding pair of curves lies in close proximity.
• Figure 5: The SHMFs of SUBFIND and CWT subhalos (top) and their relative differences within each run (bottom). The red and blue lines represent the TNG50-2 and the TNG100-1, respectively. The dashed and solid lines indicate the SUBFIND and CWTHF methods, respectively.