Symfind: Addressing the Fragility of Subhalo Finders and Revealing the Durability of Subhalos

Technical Summary: Symfind: Addressing the Fragility of Subhalo Finders and Revealing the Durability of Subhalos

Problem Statement
A significant uncertainty in the $\Lambda$CDM cosmological model concerns the behavior and durability of subhalos, the dark matter structures that host satellite galaxies. Current theoretical predictions for satellite populations are hampered by the difficulty of accurately simulating subhalo evolution and reliably identifying them within simulation outputs. Existing halo finders, particularly the widely used Rockstar combined with consistent-trees (RCT), appear to suffer from "false convergence." While RCT results may appear stable as simulation resolution increases, they systematically lose track of subhalos at higher masses than physically expected, leading to premature disruption. This artificially limits the ability to predict satellite abundances and radial distributions, often necessitating post-hoc "orphan" modeling (tracking galaxies after their host subhalos are lost) to match observations. The paper argues that this fragility propagates into systematic errors in cosmological probes relying on small-scale clustering statistics.

Methodology: Symfind
The authors introduce Symfind, a new subhalo finder based on a "particle-tracking" framework. Unlike "single-epoch" finders that identify subhalos in individual snapshots and link them via merger trees, Symfind tracks the specific particles associated with a subhalo from before it falls into a host halo. The algorithm proceeds through the following steps:

1. Input Correction: It re-analyzes input merger trees (generated by Rockstar) to correct for errors such as spurious phase-space overdensities, mass spikes during disruption, and unphysical mass switching during major mergers.
2. Particle Tracking: For each subhalo, it identifies all particles that ever passed within the subhalo's virial radius ($R_{vir}$) prior to infall. It distinguishes between "smoothly" accreted particles (never part of another halo) and "non-smoothly" accreted particles, tracking both to allow for nested substructure analysis.
3. Core Identification: At the snapshot of first infall, the $N_{core}$ most gravitationally bound smoothly accreted particles are identified as "core" particles.
4. Density Peak Selection: After infall, the algorithm uses an existing density-based finder (currently Subfind) to identify density peaks only within the tracked particle set. The true subhalo center is defined as the peak containing the highest number of the original "core" particles.
5. Property Calculation: Subhalo properties (mass, $v_{max}$, etc.) are calculated using all gravitationally bound tracked particles relative to this selected peak.
6. Disruption Criteria: A subhalo is flagged as disrupted/merged if it contains no bound core particles within its half-mass radius or if its half-mass radius intersects the host center.

The method was applied to the Symphony simulation suite (including Milky Way-mass, LMC-mass, group, and cluster scales) using $k=16$ nearest neighbors for density estimation and $N_{core}=32$.

Key Results

• Extended Survival Times: Symfind tracks subhalos to orders-of-magnitude lower masses than RCT. In the Symphony suite, Symfind finds $\approx 15\%–40\%$ more subhalos within the virial radius ($R_{vir}$) and $\approx 35\%–120\%$ more subhalos within $R_{vir}/4$ at a fixed peak subhalo mass ($m_{peak}$).
• Resolution Dependence: Unlike RCT, which appears converged at smaller subhalo counts, Symfind finds an increasing number of subhalos as resolution improves. RCT disruption thresholds are largely independent of resolution, leading to false convergence in mass functions and radial distributions.
• Numerical Reliability Limits: The authors establish specific resolution limits for reliable analysis:
  • $v_{max}$: To resolve the maximum circular velocity of disrupting subhalos until the point of likely galaxy disruption, a resolution of $n_{peak} \gtrsim 3 \times 10^4$ particles is required. Below this, $v_{max}$ is systematically biased low.
  • Mass Loss Rates: Mass loss rates and abundances are resolved at more modest resolutions, requiring $n_{peak} \gtrsim 4 \times 10^3$.
• Orphan Modeling: For subhalos with $n_{peak} > 4 \times 10^3$, Symfind can track subhalos until the point of likely galaxy disruption (based on hydrodynamic and empirical models) without needing "orphan" modeling. This suggests that the need for orphans in previous studies may have been driven by finder limitations rather than physical necessity.
• Error Rates: RCT exhibits significant error rates in its final snapshots, particularly for subhalos at small radii ($r/R_{vir} \lesssim 1/20$), where it incorrectly associates subhalo branches with unrelated density peaks. These errors affect $\approx 25\%–30\%$ of disrupted subhalos, leading to incorrect positions and masses for "orphan" initialization.

Significance and Claims
The paper claims that Symfind represents a significant step toward resolving the "fragility" of subhalo finders. By demonstrating that subhalos are far more durable than previously thought when tracked via particle methods, the authors argue that:

1. Subhalo Durability: Low-mass subhalos in pure $\Lambda$CDM can survive as bound remnants for essentially arbitrarily long periods, provided numerical resolution is sufficient.
2. Methodological Benchmark: The authors provide a concrete set of tests (survival thresholds, convergence of $v_{max}$ vs. mass loss, and radial distribution convergence) to determine if other subhalo finders meet the criteria for "good enough" performance.
3. Reduction of Systematic Uncertainty: By eliminating the need for orphan modeling for resolved subhalos ($n_{peak} > 4 \times 10^3$), the method reduces systematic uncertainties in predicting satellite galaxy populations and their radial distributions.
4. Data Availability: The authors publicly release Symfind catalogs and particle data for the Symphony suite, enabling the community to re-evaluate subhalo statistics without relying on the potentially flawed RCT pipeline.

The authors remain modest regarding their claims, noting that their analysis is specific to dark-matter-only simulations and that hydrodynamic effects or alternative cosmologies could alter subhalo durability. They also defer quantitative predictions for the converged stellar mass function to future work, acknowledging that galaxy disruption models still carry uncertainties. However, they assert that for the purpose of modeling satellite abundances in $\Lambda$CDM, Symfind is likely "good enough" to capture all numerically resolved, galaxy-hosting subhalos.