Kinematically-Persistent Planes

• Kinematically-Persistent Planes (KPPs) are defined as fixed groups of co-orbiting satellite galaxies showing long-term kinematic coherence rather than mere positional alignment.
• Identification methods leverage orbital-pole clustering within a fixed aperture and use metrics like tensor-of-inertia ratios to confirm persistent membership over time.
• Research connects KPP formation to early anisotropic collapse in the cosmic web, enhancing our understanding of satellite dynamics in ΛCDM cosmology.

Searching arXiv for the main KPP paper and related work to ground the article in current literature. Kinematically-Persistent Planes (KPPs) are fixed sets of satellite galaxies co-orbiting around their host galaxy, whose orbital poles are conserved and clustered across long cosmic time intervals. In the recent satellite-plane literature, they are treated as long-lived kinematic structures rather than as merely thin positional alignments at one snapshot, and they have been described as “skeletons”, ensuring the long-term durability of positional planes (Gámez-Marín et al., 2024). A stricter formulation defines them as satellite sets with fixed-in-time identities whose orbital poles remain clustered around a fixed-in-time direction over long time intervals, thereby separating them from transient planar configurations or from system-level “planarity” diagnostics that do not track a unique, persistent member set (Gámez-Marín et al., 17 Sep 2025).

1. Definition and conceptual boundaries

The defining property of a KPP is not geometric thinness alone, but long-term kinematic coherence. In the modern TNG50-based formulation, the relevant axis is the direction of maximum co-orbitation, denoted $\vec{J}_{\rm stack}$, and co-orbitation is defined through orbital-pole clustering within an aperture

$\alpha_{\rm co-orbit}=36.87^\circ.$

A “significant” KPP is then required to contain at least

$N_{\rm KPP}^{\rm min}=5$

satellites and to satisfy

$$f_{\rm KPP}=\frac{N_{\rm KPP}}{N_{\rm sat}}\ge 25\%,$$

with hosts having $N_{\rm sat}<9$ treated as non-eligible in that framework (Gámez-Marín et al., 17 Sep 2025). In a closely related operationalization, a satellite is classified as a KPP member if its orbital pole lies within $36.87^\circ$ of $\hat{n}_{\rm KPP}$ for at least 50% of the analyzed timesteps (Rodríguez-Cardoso et al., 20 Mar 2026).

This usage is deliberately narrower than several adjacent notions in the literature. “Planarity” in the NewHorizon analysis is a system-level measure of how strongly a satellite population is “explained by planes” without recourse to the number or thickness of planes, and “kinematically supported planes” there are assessed through consistency between position and velocity plane spaces rather than through fixed-member persistence (Uzeirbegovic et al., 2024). A positional plane can therefore be thin and statistically prominent without qualifying as a KPP.

2. Emergence of the KPP framework

The immediate precursor to the KPP concept was the realization that positional analyses alone were insufficient. A positional-only study of two hydrodynamical zoom simulations showed that high-quality positional planes could be found at all analyzed timesteps and could match the spatial characteristics of observed MW/M31 planes, but also concluded that the fraction of co-orbiting satellites within them was in general low, suggesting time-varying satellite membership and motivating a full six-dimensional phase-space treatment (Santos-Santos et al., 2020).

The term itself was then formalized in a 2022 study of two zoom-in $\Lambda$CDM hydrodynamical simulations, which identified three fixed satellite groups whose orbital angular momenta are conserved over long time intervals and whose orbital poles remain clustered, defining “kinematically-coherent, time-persistent planes” lasting at least from virialization to $z=0$, i.e. more than 7 Gyr (Santos-Santos et al., 2022). This moved the subject from snapshot planarity to persistent orbital structure.

A later statistical step came with the first TNG50 census of KPPs in 190 MW/M31-like hosts, which identified KPPs around 46 systems, corresponding to $46/190=24.2\%$ of the full sample and $\alpha_{\rm co-orbit}=36.87^\circ.$0 of the eligible systems with $\alpha_{\rm co-orbit}=36.87^\circ.$1 (Gámez-Marín et al., 17 Sep 2025). The subsequent companion paper then connected these early KPPs to the evolution of the local Cosmic Web through Lagrangian Volumes and reduced tensor-of-inertia analysis (Gámez-Marín et al., 7 May 2026).

Paper	System/sample	KPP-related contribution
“Planes of satellites around simulated disk galaxies II” (Santos-Santos et al., 2022)	2 zoom-in hydro simulations	Defined KPPs and identified 3 examples lasting $\alpha_{\rm co-orbit}=36.87^\circ.$2 Gyr
“A statistical look on kinematic planes of satellite galaxies I” (Gámez-Marín et al., 17 Sep 2025)	190 TNG50 MW/M31-like hosts	First frequency estimate: 46 KPP hosts
“A statistical look on kinematic planes of satellite galaxies II” (Gámez-Marín et al., 7 May 2026)	46 early KPPs in TNG50	Linked KPP origin to early local Cosmic Web collapse
“VINTERGATAN-GM: long-lived satellite planes induced by a massive GSE-like merger” (Rodríguez-Cardoso et al., 20 Mar 2026)	5 genetically modified MW-mass zooms	Showed a controlled merger-driven route to KPPs

3. Identification strategies and quantitative diagnostics

The core KPP-identification machinery is orbital-pole based. In the TNG50 studies, one follows the same $\alpha_{\rm co-orbit}=36.87^\circ.$3 satellites backward in time, computes their orbital poles, and scans the sphere to identify the fixed axis $\alpha_{\rm co-orbit}=36.87^\circ.$4 around which the maximum number of poles remain clustered over time (Gámez-Marín et al., 17 Sep 2025). In the VINTERGATAN-GM analysis, the orbital angular momentum of each satellite is written explicitly as

$\alpha_{\rm co-orbit}=36.87^\circ.$5

and the preferred KPP axis $\alpha_{\rm co-orbit}=36.87^\circ.$6 is found by scanning the time-stacked orbital-pole distribution with a fixed aperture $\alpha_{\rm co-orbit}=36.87^\circ.$7 (Rodríguez-Cardoso et al., 20 Mar 2026).

Positional structure is usually characterized separately. The main geometric quantities are the tensor-of-inertia axis ratios $\alpha_{\rm co-orbit}=36.87^\circ.$8 and $\alpha_{\rm co-orbit}=36.87^\circ.$9, the root-mean-square thickness $N_{\rm KPP}^{\rm min}=5$0, the plane centroid offset $N_{\rm KPP}^{\rm min}=5$1, and the plane normal $N_{\rm KPP}^{\rm min}=5$2. A particularly systematic positional search is the extended 4-galaxy-normal density plot method, which fits a plane to every 4-satellite combination, projects the corresponding normals onto the sphere, weights each normal by

$N_{\rm KPP}^{\rm min}=5$3

identifies peaks in normal space, and then builds ranked plane families as a function of member count $N_{\rm KPP}^{\rm min}=5$4 and fraction $N_{\rm KPP}^{\rm min}=5$5 (Santos-Santos et al., 2020).

A distinct but adjacent methodology is the “planarity” framework, which constructs a plane space from all planes implied by pairs of position or velocity vectors and summarizes the resulting histogram by a Gini coefficient,

$N_{\rm KPP}^{\rm min}=5$6

with high $N_{\rm KPP}^{\rm min}=5$7 interpreted as stronger plane-supported structure. That framework is deliberately agnostic about how many planes exist and does not center the analysis on a single fixed-member plane, which is why it should be regarded as KPP-adjacent rather than as a direct KPP definition (Uzeirbegovic et al., 2024).

4. Dynamical structure and physical origin

A central physical result is that KPPs are linked to the early anisotropic collapse of the local Cosmic Web. In the TNG50 “physics behind their early formation” study, the local environment of each host is represented by a Lagrangian Volume (LV), whose deformation is characterized through the reduced tensor of inertia

$N_{\rm KPP}^{\rm min}=5$8

with eigenvectors $N_{\rm KPP}^{\rm min}=5$9 defining the principal directions of deformation (Gámez-Marín et al., 7 May 2026). Among the 46 KPP-hosting systems in that sample, 31 systems ($$f_{\rm KPP}=\frac{N_{\rm KPP}}{N_{\rm sat}}\ge 25\%,$$0) align best with $$f_{\rm KPP}=\frac{N_{\rm KPP}}{N_{\rm sat}}\ge 25\%,$$1, 9 ($$f_{\rm KPP}=\frac{N_{\rm KPP}}{N_{\rm sat}}\ge 25\%,$$2) with $$f_{\rm KPP}=\frac{N_{\rm KPP}}{N_{\rm sat}}\ge 25\%,$$3, 2 ($$f_{\rm KPP}=\frac{N_{\rm KPP}}{N_{\rm sat}}\ge 25\%,$$4) with $$f_{\rm KPP}=\frac{N_{\rm KPP}}{N_{\rm sat}}\ge 25\%,$$5, and 4 systems ($$f_{\rm KPP}=\frac{N_{\rm KPP}}{N_{\rm sat}}\ge 25\%,$$6) show no clear alignment. The KPP versus non-KPP alignment curves are distinguishable from random at confidence $$f_{\rm KPP}=\frac{N_{\rm KPP}}{N_{\rm sat}}\ge 25\%,$$7 (Gámez-Marín et al., 7 May 2026). The earlier two-host analysis already found an outstanding alignment between LV principal directions and KPP satellites’ orbital poles, with the $$f_{\rm KPP}=\frac{N_{\rm KPP}}{N_{\rm sat}}\ge 25\%,$$8-structure collapse marking the end of the early compressive regime and the establishment of orbital-pole clustering when the Universe is $$f_{\rm KPP}=\frac{N_{\rm KPP}}{N_{\rm sat}}\ge 25\%,$$9 Gyr old (Gámez-Marín et al., 2024).

The mature kinematic state is rotation-dominated. In the TNG50 study, the velocity field is decomposed in a cylindrical frame aligned with $N_{\rm sat}<9$0, and the energy fractions in vertical, radial, and azimuthal motion are tracked through $N_{\rm sat}<9$1, $N_{\rm sat}<9$2, and $N_{\rm sat}<9$3. Systems are termed “disky” once

$N_{\rm sat}<9$4

and the median equilibrium rotational support over the 46 KPPs is reported as

$N_{\rm sat}<9$5

The characteristic timescales for orbital-pole clustering, settlement onto the KPP plane, and LV shape evolution are quasi-coeval and peak around $N_{\rm sat}<9$6 Gyr, during the fast mass assembly phase of the host halo (Gámez-Marín et al., 7 May 2026).

KPP members are also dynamically distinct from satellites outside KPPs. In the original two-zoom study they show higher specific orbital angular momenta, orbit more perpendicularly to the central disk galaxy, and have larger pericentric distances than non-KPP satellites, with the null hypothesis rejected at $N_{\rm sat}<9$7 confidence for $N_{\rm sat}<9$8, $N_{\rm sat}<9$9, and $36.87^\circ$0 (Santos-Santos et al., 2022). The first statistical TNG50 paper reached a closely related conclusion, finding that KPP satellites are located at further distances from the host center and maintain higher specific angular momentum since high redshift (Gámez-Marín et al., 17 Sep 2025).

5. Positional planes, observational analogues, and major controversies

One of the most consequential claims in the KPP literature is that KPPs are the long-lived kinematic backbone of positional planes. The 2022 two-host study states that KPPs and the best-quality positional planes share the same space configuration across time, such that KPPs act as “skeletons” preventing the latter from being washed out in short timescales (Santos-Santos et al., 2022). The statistical TNG50 follow-up generalized that statement, reporting that KPPs form a kind of backbone of observationally-detected positional planes; in the subset of 752 cases where both KPP and co-orbiting-satellite planes are simultaneously thin and oblate, only $36.87^\circ$1 have $36.87^\circ$2 (Gámez-Marín et al., 17 Sep 2025).

Several recurrent controversies concern whether observed satellite planes are already established as KPPs. One is methodological: line-of-sight co-rotation is not a robust proxy for full 3D kinematic coherence. In simulated Andromeda analogues, line-of-sight co-rotation shows large viewing-angle dependence, is consistent with randomized velocities, and coexists with a fraction of $36.87^\circ$3 chance-aligned satellites; tracking those systems backward shows that they are transient and not kinematically coherent as wholes (Buck et al., 2015). A related CLUES analysis similarly concluded that many vast planes are partly fortuitous and are not kinematically coherent structures as a whole, with $36.87^\circ$4 to $36.87^\circ$5 of satellites expected to leave the plane on $36.87^\circ$6 Myr timescales (Gillet et al., 2014).

A second controversy is observational. The NewHorizon “planarity” study found that the Milky Way satellite positions exhibit strong planarity, but the velocity vectors do not, and therefore kinematic coherence cannot be confirmed from current observational data; more than 99% of position-vector replications exceed the isotropic 95th percentile, but only 20% of velocity-vector replications do so (Uzeirbegovic et al., 2024). A more general methodological critique had already stressed that conclusions about dynamical stability require statistical significance tests, explicit treatment of observational biases, and proper propagation of proper-motion errors, and argued that orbit integrations cannot disprove long-lived coherence unless they exclude all allowed initial conditions and all allowed host potentials (Pawlowski et al., 2017). That caution was reinforced by a 2025 mock-observation study showing that an intrinsically stable plane can appear to widen under backward integration purely بسبب measurement uncertainty: for $36.87^\circ$7, roughly the Gaia systematic-error level, the inferred width ratio at 3 Gyr is

$36.87^\circ$8

even though the underlying plane is stable (Kumar et al., 2 Jun 2025).

A third controversy concerns the meaning of “persistent.” A 2025 TNG50 analysis argued that planes are transient in a host-centric frame, where the current satellite system of a host is reselected at each epoch and remains strongly anisotropic for only a few hundred Myr, but can be persistent in a satellite-centric frame, where the progenitors of the same present-day satellites retain spatial coherence for several Gyr when traced backward (Sawala, 1 Oct 2025). This distinction is compatible with the KPP program only if persistence is reserved for fixed-member orbital coherence rather than for snapshot anisotropy of a changing host population.

6. Formation channels in $36.87^\circ$9CDM and outstanding problems

The literature does not support a single universal formation route. In the controlled VINTERGATAN-GM suite, more massive GSE-like mergers produce more planar and more kinematically coherent satellite systems, with KPP fractions rising monotonically from 24% and 26% in the $\hat{n}_{\rm KPP}$0 and $\hat{n}_{\rm KPP}$1 runs to 44%, 46%, and 49% in the $\hat{n}_{\rm KPP}$2, $\hat{n}_{\rm KPP}$3, and $\hat{n}_{\rm KPP}$4 runs; the proposed mechanism combines preferential equatorial infall and anisotropic dynamical friction in a flattened halo whose minor axis is aligned with the merger direction and with the direction of maximum compression of the surrounding Lagrangian volume (Rodríguez-Cardoso et al., 20 Mar 2026). By contrast, a statistical IllustrisTNG study of mergers concluded that major mergers with mass ratios above $\hat{n}_{\rm KPP}$5 generally have a negligible or adverse impact on present-time phase-space correlation, do not statistically form highly flattened and orbitally coherent configurations, and that any merger imprint is washed out within 2–5 Gyr by post-merger accretion and orbital evolution (Kanehisa et al., 2023). In the FIRE-2 suite, MW-like thin and/or coherent planes exist but are generally transient, surviving for $\hat{n}_{\rm KPP}$6 Myr; the main positive exception is a recent LMC-like first pericentric passage, which raises the incidence of MW-like planes to 7–16% of snapshots and can extend lifetimes to 0.7–3 Gyr, likely because of group accretion of satellites (Samuel et al., 2020).

The strongest common ground across the KPP-specific papers is early formation. In the TNG50 statistical study, the KPP formation time $\hat{n}_{\rm KPP}$7 peaks near Universe age $\hat{n}_{\rm KPP}$8 Gyr and predates the end of the host halo’s fast assembly phase, indicating that halo processes do not drive the original orbital-pole clustering (Gámez-Marín et al., 17 Sep 2025). The companion physical-origin paper makes the same point in a more mechanistic language, arguing that early KPPs are fossil remnants of high-redshift anisotropic mass collapse driven by local Cosmic Web formation in $\hat{n}_{\rm KPP}$9CDM and noting explicitly that a full explanation for why $\Lambda$0 of eligible systems do not host early KPPs remains for future work (Gámez-Marín et al., 7 May 2026).

This suggests that KPPs are best understood not as generic properties of all satellite systems, but as a specific dynamical class requiring both a persistent orbital-pole backbone and a favorable assembly history. Their current literature role is therefore double. On one hand, they sharpen the distinction between positional planes, system-level planarity, and true long-lived kinematic coherence. On the other hand, they provide an explicitly $\Lambda$1CDM-internal framework in which at least some MW/M31-like satellite structures can be interpreted as long-lived products of early anisotropic structure formation rather than as exclusively transient alignments or as immediate contradictions of the standard cosmological model.