Symfind: Particle-Tracking Subhalo Finder

• Symfind is a particle-tracking subhalo finder that identifies subhalos by tracking their most-bound core particles across simulation snapshots.
• It employs methods such as fixed-core tagging, iterative unbinding, and density peak matching to maintain temporal continuity and improve recovery in both CDM and SIDM contexts.
• Quantitative studies reveal significant gains in subhalo detection and tracking longevity, guiding resolution thresholds and hybrid catalog strategies in cosmological simulations.

Searching arXiv for the cited Symfind papers and closely related context. Symfind is a particle-tracking-based subhalo finder developed for cosmological $N$-body simulations to address known failure modes of conventional single-epoch halo-finding pipelines, especially artificial subhalo disruption and false convergence in inferred subhalo statistics. In its original $\Lambda$CDM formulation, Symfind begins from a conventional halo catalog and merger tree, tags the most-bound particles of a subhalo at first infall, and subsequently identifies descendants by locating the density peak containing the majority of those tagged particles, followed by iterative unbinding (Mansfield et al., 2023). Subsequent work has shown that the same fixed-core strategy that is advantageous in cold dark matter can become problematic in self-interacting dark matter (SIDM), where self-interactions and tides can diffuse originally tagged core particles outward and strip them from the remnant, leading to premature loss of otherwise surviving subhalos (Kong et al., 13 Jul 2025).

1. Conceptual basis and motivation

Symfind was introduced to overcome two specific failings attributed to traditional “single-epoch” pipelines such as Rockstar + consistent-trees (RCT): artificial disruption of resolved subhalos at masses orders of magnitude above those predicted by idealized, high-resolution simulations, and false convergence of subhalo statistics with increasing simulation resolution (Mansfield et al., 2023). The central premise is that a subhalo should be identified by temporal continuity of its most tightly bound material rather than solely by instantaneous phase-space overdensity.

In this framework, the defining object is not merely a density peak at a given snapshot, but a tracked remnant anchored to a pre-selected “core” of bound particles. This design is intended to reduce confusion between a genuine subhalo remnant and surrounding tidal debris. In cold dark matter simulations, the method is reported to be insensitive to temporary confusion between the true subhalo core and tidal material and to recover more highly stripped subhalos at small host-centric radii than conventional phase-space methods such as Rockstar (Kong et al., 13 Jul 2025).

A plausible implication is that Symfind shifts the ontology of subhalo identification from snapshot-local classification to branch-continuous remnant tracking. That distinction is central to why its convergence properties differ from those of RCT in the published comparisons (Mansfield et al., 2023).

2. Algorithmic pipeline

Symfind begins with a conventional halo catalog and merger tree, specifically Rockstar + consistent-trees in the published implementation, and corrects merger-tree errors such as spurious short-lived branches and aphysical central-subhalo label swapping during mergers (Mansfield et al., 2023). For each branch that eventually becomes a subhalo, it walks the branch backward in time and collects every $N$-body particle that was ever within the branch’s virial radius, $R_{\rm vir}$, before first infall, separating smoothly accreted from non-smoothly accreted particles (Mansfield et al., 2023).

At the snapshot of first infall, Symfind computes binding energies and flags the $N_{\rm core}$ most-bound particles as the subhalo core. The fiducial choice is $N_{\rm core}=32$ (Mansfield et al., 2023). The SIDM analysis describes the same step as ranking all particles belonging to a newly detected subhalo by their binding energy and tagging the top $N_{\rm core}=32$ most-bound particles at the “infall snapshot” (Kong et al., 13 Jul 2025).

At each later snapshot, Symfind re-identifies candidate density peaks and uses the pre-selected core particles to decide which peak is the descendant. In the 2023 description, candidate peaks are identified among smoothly accreted particles using Subfind with kernel-smoothed density over the $k$ nearest neighbors, and the peak containing the largest number of core particles is taken as the subhalo center of mass and velocity (Mansfield et al., 2023). The fiducial neighbor count is $k=16$, and the pair $(k,N_{\rm core})=(16,32)$ yields an estimated instantaneous error rate below $\Lambda$0 for subhalos with $\Lambda$1 (Mansfield et al., 2023). The SIDM study describes an equivalent descendant-identification stage as a local-density-peak search using a small Friends-of-Friends run applied to the tagged particles and their neighbors (Kong et al., 13 Jul 2025). In both descriptions, the descendant is defined by the density peak containing the largest fraction of the original tagged core.

After the center is identified, Symfind iteratively unbinds tracked particles and computes halo properties from the resulting bound set. The SIDM description gives the unbinding loop explicitly: gather all particles within $\Lambda$2 the tidal radius or within $\Lambda$3 if available, compute each particle’s total energy relative to the peak, remove particles with $\Lambda$4, and repeat until convergence (Kong et al., 13 Jul 2025). The tracked bound set is then used to derive quantities such as mass $\Lambda$5, half-mass radius $\Lambda$6, $\Lambda$7, and $\Lambda$8 (Mansfield et al., 2023).

Symfind declares a subhalo disrupted if any of the following hold: all core particles lie outside $\Lambda$9, the subhalo’s distance to its host drops below its own $N$0, or it is completely unbound (Mansfield et al., 2023). It also continues searching in later snapshots to recover transient misassignments and interpolates properties across short gaps (Mansfield et al., 2023).

By construction, the tagged core set never grows. New tightly bound particles are incorporated only if they lie near the density peak containing the tagged core particles (Kong et al., 13 Jul 2025). This design is essential to both the method’s robustness in CDM and its vulnerability in some SIDM regimes.

3. Quantitative behavior in cold dark matter

The principal quantitative claim for Symfind in $N$1CDM is that it tracks subhalos to substantially lower surviving masses than commonly used tools such as Rockstar and consistent-trees (Mansfield et al., 2023). In the Symphony dark-matter-only simulations, the reported gains are approximately $N$2 more subhalos within the virial radius and approximately $N$3 more subhalos within $N$4 at fixed peak subhalo mass (Mansfield et al., 2023). At eight-times higher resolution in SymphonyMilkyWayHR, the gains increase to approximately $N$5 inside $N$6 and approximately $N$7 inside $N$8 (Mansfield et al., 2023).

The published comparison also emphasizes changes in inferred radial structure. Symfind returns subhalo cumulative radial distributions that steepen with resolution and approach the host dark-matter particle cumulative distribution, whereas RCT shows no change with resolution (Mansfield et al., 2023). In the same study, the low-mass slope of the $N$9 mass function is shallower for Symfind than for Rockstar by approximately $R_{\rm vir}$0 inside $R_{\rm vir}$1 and $R_{\rm vir}$2 inside $R_{\rm vir}$3 (Mansfield et al., 2023).

The interpretation advanced in the source is that single-epoch finders frequently miss low-mass remnants or misidentify them during disruption because subhalos can lose large fractions of their mass before disappearing (Mansfield et al., 2023). Symfind’s particle-tracking scheme is intended to maintain continuity through precisely this regime. The same study argues that Symfind can trace resolved subhalos until the point of typical galaxy disruption without invoking orphan modeling, provided the numerical resolution is sufficient (Mansfield et al., 2023).

4. Resolution thresholds, convergence, and validation

A major contribution of the original Symfind paper is the distinction between resolving mass loss and resolving internal structural quantities. Idealized simulations are used to argue that resolving subhalo mass loss rates requires $R_{\rm vir}$4 particles at peak, whereas structural properties such as $R_{\rm vir}$5 require $R_{\rm vir}$6 (Mansfield et al., 2023). These thresholds are reiterated as recommended best practice for sample selection (Mansfield et al., 2023).

The same work formulates numerical disruption thresholds through fitted functions

$R_{\rm vir}$7

with

$R_{\rm vir}$8

where the best-fit coefficients are given in Table 4 of the source paper (Mansfield et al., 2023). The disruption analysis uses survival-analysis methodology. Letting $R_{\rm vir}$9 and $N_{\rm core}$0 denote the minimum $N_{\rm core}$1 before a branch disappears, the Kaplan-Meier estimator is written as

$N_{\rm core}$2

with Greenwood variance

$N_{\rm core}$3

These formulae are used to account for censored subhalos surviving to $N_{\rm core}$4 (Mansfield et al., 2023).

In the reported comparison for subhalos with $N_{\rm core}$5, Symfind’s median $N_{\rm core}$6 is approximately $N_{\rm core}$7–$N_{\rm core}$8 times smaller than Rockstar’s (Mansfield et al., 2023). Rockstar’s disruption fraction is described as essentially independent of $N_{\rm core}$9, producing a flat $N_{\rm core}=32$0; this is identified as a textbook example of false convergence (Mansfield et al., 2023). Symfind, by contrast, is reported not to falsely converge because $N_{\rm core}=32$1 decreases with $N_{\rm core}=32$2 until numerical limits are reached (Mansfield et al., 2023).

The Symfind framework also proposes four validation tests for any subhalo finder: Kaplan-Meier survival curves for disruption thresholds, structural convergence using the $N_{\rm core}=32$3 versus $N_{\rm core}=32$4 relation, mass-loss convergence at fixed $N_{\rm core}=32$5, and core-particle consistency during disruption (Mansfield et al., 2023). This suggests that Symfind is not only an algorithm but also a methodological program for certifying subhalo catalogs against numerical and physical criteria.

5. Reformulation in self-interacting dark matter

The 2025 SIDM study re-examines Symfind in a regime where the physics alters the behavior of the very particles used to define the tracked core (Kong et al., 13 Jul 2025). The simulations adopt a velocity-dependent scattering cross section with Rutherford-like angular dependence,

$N_{\rm core}=32$6

where $N_{\rm core}=32$7 is the normalization, $N_{\rm core}=32$8 is the turnover velocity, and $N_{\rm core}=32$9 is the relative speed of colliding particles (Kong et al., 13 Jul 2025). An approximate phenomenological form is also given: $N_{\rm core}=32$0 The study compares Symfind with RCT on Milky-Way- and Group-mass zoom hosts in four models: SIDM70, SIDM147-Group, SIDM147-MW, and a CDM baseline (Kong et al., 13 Jul 2025).

Several auxiliary quantities are defined to characterize why Symfind can fail in SIDM. The instantaneous tidal radius is

$N_{\rm core}=32$1

for subhalo mass $N_{\rm core}=32$2 at host-centric radius $N_{\rm core}=32$3 (Kong et al., 13 Jul 2025). A diffusion radius is introduced to describe heat-conduction-driven migration of core particles,

$N_{\rm core}=32$4

with diffusion coefficient

$N_{\rm core}=32$5

and $N_{\rm core}=32$6 (Kong et al., 13 Jul 2025). In practice, $N_{\rm core}=32$7 is measured as the radius enclosing half of the originally tagged cores after time $N_{\rm core}=32$8 (Kong et al., 13 Jul 2025). The study also defines a core-particle-loss fraction after pericenter,

$N_{\rm core}=32$9

The key physical result is that the fixed-core technique does not always yield accurate results in SIDM (Kong et al., 13 Jul 2025). Self-interactions transfer heat from hotter outer regions to colder inner regions, causing originally tagged core particles to move onto larger orbits; if those particles reach radii $k$0, the host tidal field can strip them away (Kong et al., 13 Jul 2025). The same mechanism can cause Symfind to lose the tracked core even though a bound remnant survives.

The paper distinguishes two regimes. In the core-expansion phase, subhalos develop large constant-density inner cores, with $k$1–$k$2 for massive $k$3 systems; after tidal pruning of the outer NFW wings, the remaining isothermal core particles diffuse outward and are rapidly stripped, leading Symfind to lose the object prematurely (Kong et al., 13 Jul 2025). In the core-collapse phase, central densities rise and diffusion is subdominant, so core particles remain bound through repeated pericenters; here Symfind can track farther into the host center than RCT, which often confuses the subhalo with host outskirts at small radii (Kong et al., 13 Jul 2025).

6. Comparative performance and hybrid catalog construction

The SIDM study condenses the comparison between Symfind and RCT into four metrics: mass completeness, tracking longevity, false-loss rate, and model dependence on $k$4 and $k$5 (Kong et al., 13 Jul 2025). The reported behavior is summarized below.

Metric	Reported result	Regime
Mass completeness	Symfind recovers $k$6 more subhalos within $k$7 than RCT	CDM
Mass completeness	Symfind’s gain falls to $k$8	SIDM70
Mass completeness	Symfind under-performs RCT by $k$9 for massive subhalos in the inner $k=16$0	SIDM147-Group
Mass completeness	Symfind outperforms by $k=16$1	SIDM147-MW
Tracking longevity	Symfind is $k=16$2 longer than RCT for $k=16$3	CDM
Tracking longevity	Symfind can be lost $k=16$4 earlier than RCT for core-expansion subhalos	SIDM147-Group
False-loss rate	$k=16$5	CDM
False-loss rate	rises to $k=16$6	SIDM70
False-loss rate	can exceed $k=16$7 for the most massive core-expansion subhalos	SIDM147-Group

The model dependence is stated explicitly: higher $k=16$8 and higher $k=16$9 produce larger isothermal cores, more core-particle migration, larger $(k,N_{\rm core})=(16,32)$0, larger $(k,N_{\rm core})=(16,32)$1, and degraded Symfind performance, whereas smaller $(k,N_{\rm core})=(16,32)$2 places many low-mass subhalos in core collapse, where tightly bound cores suffer little diffusion and Symfind excels (Kong et al., 13 Jul 2025).

Because neither finder is uniformly superior across all SIDM regimes, the study recommends a hybrid workflow that merges Symfind and RCT outputs (Kong et al., 13 Jul 2025). The procedure is: run both finders; pre-match subhalos one-to-one by particle IDs or most-bound center; if Symfind’s core-loss fraction after infall exceeds approximately $(k,N_{\rm core})=(16,32)$3 and $(k,N_{\rm core})=(16,32)$4, adopt the RCT descendant; else if $(k,N_{\rm core})=(16,32)$5 and the subhalo is in core collapse with rising $(k,N_{\rm core})=(16,32)$6, adopt the Symfind result; otherwise use whichever finder reports the later disruption time; finally, include subhalos found in only one catalog but flag the finder of origin (Kong et al., 13 Jul 2025). The resulting combined catalog recovers approximately $(k,N_{\rm core})=(16,32)$7–$(k,N_{\rm core})=(16,32)$8 more total subhalos and up to approximately $(k,N_{\rm core})=(16,32)$9 more subhalos at $\Lambda$00 than either method alone across a wide range of SIDM parameters (Kong et al., 13 Jul 2025).

This suggests that Symfind’s methodological value persists outside CDM, but only when paired with diagnostics sensitive to the underlying microphysics. In SIDM, the core particles are not merely tracers; their transport properties become part of the failure analysis.

7. Relation to orphan modeling and broader significance

A recurring implication of the Symfind literature is that the longevity of tracked subhalos bears directly on the need for orphan prescriptions in satellite-galaxy modeling. The 2023 study argues that, for $\Lambda$01CDM applications, one can avoid orphan modeling whenever $\Lambda$02, and that studies requiring reliable $\Lambda$03 should ensure $\Lambda$04 (Mansfield et al., 2023). If orphans are still required, the recommendation is to generate them at the simulation’s numerical disruption threshold rather than at the last surviving snapshot reported by the halo finder, and to use multiple core particles to track positions so as to mitigate diffusion errors (Mansfield et al., 2023).

The SIDM results qualify that conclusion. In CDM, fixed core-particle tracking is a source of robustness because it resists confusion with tidal debris and host background (Kong et al., 13 Jul 2025). In SIDM, the same fixed core set can become physically non-representative of the surviving remnant after heat conduction and tidal stripping (Kong et al., 13 Jul 2025). Thus, the general lesson is not that particle tracking is universally superior, but that its validity depends on whether the tagged particles remain a stable proxy for remnant identity.

Within the subhalo-finding literature, Symfind is therefore significant in two senses. First, it provides a concrete alternative to single-epoch finders, with explicit numerical tests, survival-analysis diagnostics, and published resolution criteria (Mansfield et al., 2023). Second, its later SIDM reassessment clarifies the boundary conditions of that alternative: the durability of the tracked core is model-dependent, and catalog construction may require hybridization with phase-space methods when new physics alters core transport (Kong et al., 13 Jul 2025).