CWTHF: Subhalo Identification with Continuous Wavelet Transform

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 $\mathcal{O}(N)$.

💡 Research Summary

This paper presents a significant extension of the CWTHF (Continuous Wavelet Transform Halo Finder) code, adapting its core framework for the identification of subhalos within cosmological N-body simulations. Subhalos, gravitationally bound substructures residing inside larger host halos, are crucial tracers of hierarchical structure formation and probes for various astrophysical phenomena, from dark matter physics to galaxy evolution.

The authors build upon their previous work, which established the Continuous Wavelet Transform (CWT) as an effective tool for defining and detecting dark matter halos. The CWT acts as a “mathematical microscope,” analyzing the density field across multiple scales. The subhalo identification pipeline operates iteratively over a sequence of scale factors, progressing from large to small scales. At each scale, particles are assigned to a grid, the CWT is computed, and local maxima in this 4D space (3 spatial dimensions + 1 scale dimension) are identified. A key innovation is the implementation of a filtering mechanism to prevent duplicate detections. Due to the non-orthogonality of the chosen wavelet, a single physical structure can produce multiple local maxima across different scales. To address this, the algorithm records the center of every confirmed halo or subhalo onto a Boolean mask grid. Any new maximum found within a predefined exclusion zone (a 3x3x3 grid cell neighborhood) of a previously identified structure is discarded. This efficient, O(N) operation ensures that only the first (largest-scale) detection at a given location is preserved.

After peak filtering, the CWT grid region surrounding each remaining maximum is segmented. Particles within a segmented region are grouped as a candidate substructure. These candidates undergo checks for a valid cross-scale maximum signature and a minimum density threshold (4 times the background density). Finally, a gravitational self-binding check is performed. Once a subhalo is confirmed, its parent host halo is determined, and its position is logged to the exclusion mask for subsequent iterations. An additional final self-binding check is applied to host halos after all their subhalos have been extracted, ensuring the host remains bound.

The method is validated using data from the IllustrisTNG simulations (TNG50-2 and TNG100-1 boxes) and a single Friends-of-Friends (FOF) halo. The resulting subhalo catalogs are compared against those generated by the widely-used SUBFIND algorithm, demonstrating the capability of CWTHF to reliably identify substructures. Remarkably, despite the added complexity of subhalo finding, the algorithm maintains the favorable linear time complexity, O(N), of the original halo finder. Furthermore, code optimizations during the integration of the subhalo module reportedly reduced the total runtime of CWTHF by 20%.

In conclusion, the study successfully extends the wavelet-based CWTHF framework to subhalo identification. It provides a robust, efficient, and scale-aware tool for dissecting the hierarchical structure of the universe in cosmological simulations, capable of processing both full simulation volumes and individual halos while maintaining computational efficiency.