Plane of Satellites (PoS) Insights

• Plane of Satellites (PoS) is defined as a thin, extended configuration of dwarf satellites exhibiting both spatial flattening and orbital coherence.
• Researchers quantify PoS through metrics like the c/a ratio, rms thickness, and orbital pole clustering to assess both geometry and dynamics.
• Analyses of PoS in systems such as the Milky Way, Andromeda, and Cen A offer vital insights into anisotropic accretion, simulation biases, and challenges for ΛCDM.

Plane of Satellites (PoS) denotes a configuration in which the dwarf satellites of a more massive host are distributed in a geometrically thin, extended structure that can be approximated by a plane and, in the strongest cases, also exhibit coherent orbital motion within that plane. In contemporary usage, the term refers not only to spatial flattening but to the conjunction of geometry and dynamics: small thickness, large radial extent, and some degree of common orbital sense or orbital-pole clustering. Because the Milky Way, Andromeda, and Centaurus A all host prominent examples, PoS have become a focal point in the small-scale assessment of $\Lambda$CDM, with disagreement centered less on their existence than on their frequency, longevity, and physical interpretation (1904.02719, Müller, 2023).

1. Definition and formal characterization

A PoS is usually specified by the 3D satellite positions $\mathbf{r}_i$ relative to the host and by the orbital angular momenta $\mathbf{L}_i = \mathbf{r}_i \times \mathbf{v}_i$. Spatial flattening is commonly quantified through an inertia tensor or an equivalent least-squares plane fit. In one standard form,

$$I_{\alpha\beta} = \sum_i r_{i,\alpha}\,r_{i,\beta},$$

whose eigenvalues $\lambda_a \ge \lambda_b \ge \lambda_c$ define principal axes and axis ratios

$$\frac{c}{a} = \sqrt{\frac{\lambda_c}{\lambda_a}}, \qquad \frac{b}{a} = \sqrt{\frac{\lambda_b}{\lambda_a}}.$$

A small $c/a$ indicates a thin, plane-like configuration. An alternative geometric measure is the rms thickness,

$\Delta_{\rm rms} = \sqrt{\frac{1}{N}\sum_i d_i^2},$

where $d_i$ is the perpendicular distance of satellite $i$ from a best-fit plane (Müller, 2023).

The dynamical aspect is encoded in orbital poles, the directions of $\mathbf{r}_i$0. A subset of satellites may share a common orbital plane even if one or more members counter-rotate, because co- and counter-rotators can lie in the same geometrical plane. In EAGLE, the clustering of orbital poles is measured through

$\mathbf{r}_i$1

and the opening angle $\mathbf{r}_i$2, defined as the smallest cone needed to enclose the best-chosen subset of $\mathbf{r}_i$3 orbital poles around some axis. Small $\mathbf{r}_i$4 corresponds to strong orbital coplanarity (1904.02719).

This distinction between geometry and dynamics is central. A system can be thin in configuration space yet dynamically heterogeneous; conversely, a system can host a dynamically coherent orbital plane even if a few satellites lie well away from the fitted spatial slab. Multiple simulation studies explicitly separate purely flattened configurations from orbitally coherent planes, and that separation underlies much of the modern literature (1904.02719).

2. Nearby systems and observed manifestations

The Milky Way’s Vast Polar Structure (VPOS) remains the archetypal PoS. Using the 11 classical satellites, the spatial distribution has $\mathbf{r}_i$5, and 8 of the 11 have orbital poles within a cone of opening angle $\mathbf{r}_i$6 centered at $\mathbf{r}_i$7. Of these 8, 7 are co-rotating and one, Sculptor, is counter-rotating but still lies in the same orbital plane. Pawlowski further argued that the SDSS footprint biases away from a close alignment between the SDSS satellites and the classical-satellite plane, and that the combined phase-space alignment of classical and SDSS satellites is a $\mathbf{r}_i$8 event with respect to isotropy (1904.02719, Pawlowski, 2015).

Andromeda’s Great Plane of Andromeda (GPoA) is the best-studied external case. Buck, Macciò, and Dutton adopt the observational characterization of 15 of 27 PAndAS satellites in a plane with

$\mathbf{r}_i$9

projected extent $\mathbf{L}_i = \mathbf{r}_i \times \mathbf{v}_i$0, and $\mathbf{L}_i = \mathbf{r}_i \times \mathbf{v}_i$1 of the 15 sharing the same sign of line-of-sight velocity across the galaxy. Other analyses use 14 or 15 members depending on membership criteria, but the basic phenomenology is unchanged: a thin, extended, apparently rotating plane (Buck et al., 2015).

Beyond the Local Group, Müller reviews the Centaurus Group, where Cen A shows a strongly flattened satellite distribution with 14/16 and later 21/28 satellites following a common kinematic trend consistent with co-motion, and NGC 253, where a thin spatial alignment of nine satellites has preliminary kinematic support from 4 of 5 line-of-sight velocities. By contrast, MATLAS provides evidence that about 30% of host halos show statistically significant 2D flattening, but without distances and velocities it cannot distinguish true 3D planes from chance alignments (Müller, 2023).

System	Reported signature	Source
Milky Way (classical sample)	$\mathbf{L}_i = \mathbf{r}_i \times \mathbf{v}_i$2; 8 of 11 orbital poles within $\mathbf{L}_i = \mathbf{r}_i \times \mathbf{v}_i$3	(1904.02719)
Milky Way (classical + SDSS)	$\mathbf{L}_i = \mathbf{r}_i \times \mathbf{v}_i$4 against isotropy	(Pawlowski, 2015)
M31 / GPoA	15 of 27; $\mathbf{L}_i = \mathbf{r}_i \times \mathbf{v}_i$5 kpc; $\mathbf{L}_i = \mathbf{r}_i \times \mathbf{v}_i$6 co-rotating	(Buck et al., 2015)
Cen A	14/16, later 21/28, co-moving	(Müller, 2023)
NGC 253	9-satellite alignment; 4 of 5 LOS velocities consistent with co-rotation	(Müller, 2023)

3. Metrics, inference strategies, and methodological issues

PoS analyses are sensitive to the choice of statistic. Spatial flattening can be measured by $\mathbf{L}_i = \mathbf{r}_i \times \mathbf{v}_i$7, by $\mathbf{L}_i = \mathbf{r}_i \times \mathbf{v}_i$8, or by direct plane-finding with fixed slab thickness. EAGLE instead emphasized the joint use of $\mathbf{L}_i = \mathbf{r}_i \times \mathbf{v}_i$9 and orbital-pole opening angle $$I_{\alpha\beta} = \sum_i r_{i,\alpha}\,r_{i,\beta},$$0, showing that many thin systems are not orbitally coherent and many orbitally coherent systems are not especially thin (1904.02719).

The radial distribution of satellites also matters. Sawala and collaborators introduced a Gini coefficient of inertia,

$$I_{\alpha\beta} = \sum_i r_{i,\alpha}\,r_{i,\beta},$$1

to quantify how strongly a few distant satellites dominate the inertia tensor. In their Milky Way reanalysis, the reported exceptional anisotropy was strongly contingent on a lopsided radial distribution combined with the close but fleeting conjunction of Leo I and Leo II; in their interpretation, short-lived planes are common in new $$I_{\alpha\beta} = \sum_i r_{i,\alpha}\,r_{i,\beta},$$2CDM simulations (Sawala et al., 2022).

Kinematic inference is more contentious. Buck, Dutton, and Macciò showed that the number of co-rotating satellites inferred from the sign of the line-of-sight velocity varies strongly with viewing angle and can be reproduced by samples with randomized velocities. They concluded that line-of-sight velocity is not well suited as a proxy for kinematic coherence, and that clustering of angular momentum vectors is the better measure (Buck et al., 2015).

This methodological distinction motivates proper-motion forecasts for M31. If the Andromeda plane is non-transient, then the allowed proper-motion space of each satellite is tightly constrained by the requirement that the orbit remain bound, avoid strong tidal destruction, and stay within $$I_{\alpha\beta} = \sum_i r_{i,\alpha}\,r_{i,\beta},$$3, $$I_{\alpha\beta} = \sum_i r_{i,\alpha}\,r_{i,\beta},$$4, or $$I_{\alpha\beta} = \sum_i r_{i,\alpha}\,r_{i,\beta},$$5 times the observed plane thickness over 10 periapses. That program was formulated explicitly for 19 M31 satellites, with HST, JWST, and THEIA identified as the relevant tests (Hodkinson et al., 2019).

4. Formation channels within $$I_{\alpha\beta} = \sum_i r_{i,\alpha}\,r_{i,\beta},$$6CDM

A large part of the recent literature converges on anisotropic accretion as a necessary ingredient. In EAGLE, MW-like satellite systems were on average always flatter than the full halo population and corresponded to systems with a high degree of anisotropic accretion. Their median $$I_{\alpha\beta} = \sum_i r_{i,\alpha}\,r_{i,\beta},$$7 reached a minimum around $$I_{\alpha\beta} = \sum_i r_{i,\alpha}\,r_{i,\beta},$$8 Gyr look-back time, coincident with the typical infall time of the classical satellites, and the orbital poles of co-planar satellites were tightly aligned with the minor axis of the host halo, consistent with torques from the host’s aspherical potential channeling orbits into the host’s equatorial plane (1904.02719).

Buck, Macciò, and Dutton made the Andromeda connection more explicit. In high-resolution collisionless zooms, thin, extended, rotating planes resembling M31’s appeared preferentially in high-concentration, early-forming halos, and the satellites that ended up in the plane were traced back to two main filaments at $$I_{\alpha\beta} = \sum_i r_{i,\alpha}\,r_{i,\beta},$$9. In that framework, the plane is fossil evidence for early filamentary accretion in an early-forming halo (Buck et al., 2015).

Horizon-AGN broadened the discussion from discrete PoS analogues to statistical coplanarity. Between $\lambda_a \ge \lambda_b \ge \lambda_c$0, satellites tend on average to lie in the galactic plane of the central galaxy, especially for massive red centrals, while filamentary alignment dominates at large halo-centric radii and fades toward the center. The proposed mechanism is infall along quasi-polar flows followed by torquing within the halo, which progressively bends satellite orbits toward the central galactic plane (Welker et al., 2015).

Group infall is another recurring channel. In Auriga, an LMC-mass primary is expected to host about 3 satellites with stellar masses $\lambda_a \ge \lambda_b \ge \lambda_c$1, and Gaia-based orbital reconstructions place Fornax and Carina on orbits closely aligned with the orbital plane of the Magellanic Clouds, supporting a Magellanic association. This provides a concrete $\lambda_a \ge \lambda_b \ge \lambda_c$2CDM mechanism by which a coherent subgroup contributes to the MW plane (Pardy et al., 2019).

A merger-driven route has also been proposed. In an idealized collisionless scenario, a merging secondary galaxy can bring in its own satellite population, which is spread into an extended, flattened, predominantly prograde disk of satellites during coalescence. The mechanism requires a sufficiently circular merger orbit and a subset of initially prograde satellites with small vertical dispersion relative to the interaction plane (Smith et al., 2015).

IllustrisTNG extends these themes by suggesting that a PoS can form from one or more of at least five different processes, including accretion along filaments, cluster-related flows, and filament mergers. In that sample, a massive Magellanic Cloud-like satellite appears in roughly one third of the most MW-like systems and probably plays an important role in PoS formation (Zhao et al., 2 Oct 2025).

5. Lifetimes, transience, and dynamical state

The longevity of PoS depends on which property is being tracked. In EAGLE, purely flattened systems selected only by $\lambda_a \ge \lambda_b \ge \lambda_c$3 are short-lived chance alignments and persist for less than $\lambda_a \ge \lambda_b \ge \lambda_c$4. By contrast, orbitally coherent subsets are longer lived: using $\lambda_a \ge \lambda_b \ge \lambda_c$5 as a formation criterion, half of MW-like orbit planes have been in place for at least $\lambda_a \ge \lambda_b \ge \lambda_c$6, with some surviving for $\lambda_a \ge \lambda_b \ge \lambda_c$7 Gyr (1904.02719).

M31 analogues show a stronger transient component. In the Buck, Dutton, and Macciò analysis, planes that look M31-like in line-of-sight velocity contain a fraction of $\lambda_a \ge \lambda_b \ge \lambda_c$8 chance-aligned satellites, their orbital poles are only moderately clustered in 3D, and tracking them backward shows that the thin planes are transient rather than globally coherent structures (Buck et al., 2015).

The Milky Way has been interpreted in both ways. Sawala and collaborators argue that the present-day extreme thinness of the classical satellites is transient rather than rotationally supported, largely contingent on the lopsided radial distribution and the fleeting conjunction of Leo I and Leo II, and that such short-lived planes are common in new $\lambda_a \ge \lambda_b \ge \lambda_c$9CDM simulations (Sawala et al., 2022). By contrast, Taibi and collaborators, using Gaia-based orbital classifications, emphasize that co-orbiting VPOS satellites are almost all approaching pericenters while the two counter-orbiting members are leaving their last pericenters, and that the on-plane sample tends to occupy the lowest orbital energies for a given angular momentum. They interpret these patterns as hints that the VPOS is a young structure produced by late accretion, plausibly of a dwarf group (Taibi et al., 2023).

IllustrisTNG points in a similar direction. In the most MW-like PoS systems, about half of the satellites have recently arrived at $$\frac{c}{a} = \sqrt{\frac{\lambda_c}{\lambda_a}}, \qquad \frac{b}{a} = \sqrt{\frac{\lambda_b}{\lambda_a}}.$$0, and the aspect ratio evolves accordingly, indicating that a MW-like PoS is a recent and transient phenomenon (Zhao et al., 2 Oct 2025).

6. Controversies, alternatives, and present status

The PoS problem remains unsettled because the literature disagrees on both statistics and interpretation. Müller summarizes one side of the debate by treating the MW, M31, and Cen A systems as a severe challenge to standard cosmology, especially when spatial flattening and kinematic coherence are required simultaneously across multiple hosts rather than for the Milky Way alone (Müller, 2023). Other simulation-based analyses instead argue that MW-like planes are rare but natural in $$\frac{c}{a} = \sqrt{\frac{\lambda_c}{\lambda_a}}, \qquad \frac{b}{a} = \sqrt{\frac{\lambda_b}{\lambda_a}}.$$1CDM and that exact-tail comparisons overstate the tension (1904.02719, Sawala et al., 2022).

Baryons complicate the comparison. In paired DM-only and hydrodynamic simulations, Ahmed, Brooks, and Christensen found that baryons change which satellites survive, reduce radial concentration through enhanced destruction near the host, and therefore alter the statistical significance of maximum planes. They concluded that DM-only PoS studies are misleading because they analyze different satellite populations, yet also reported that none of their baryonic runs reproduced the combined positional and co-rotation significance of the observed MW and M31 systems (Ahmed et al., 2016).

Alternative explanations remain in circulation. Tidal dwarf scenarios and modified gravity are reviewed by Müller as non-standard responses to the PoS problem (Müller, 2023). Pawlowski and Kroupa argued that the coherent orbital alignment of 7 to 9 of the 11 classical MW satellites supports a rotationally stabilized VPOS and is a very significant challenge for $$\frac{c}{a} = \sqrt{\frac{\lambda_c}{\lambda_a}}, \qquad \frac{b}{a} = \sqrt{\frac{\lambda_b}{\lambda_a}}.$$2CDM, while being a natural consequence of tidal dwarf galaxies formed together in the debris of a galaxy collision (Pawlowski et al., 2013). A more specialized alternative is dissipative dark matter: Randall and Scholtz proposed that a thin dark disk embedded in the baryonic disk could supply dark matter to tidal dwarf galaxies pulled out in a merger, potentially generating Andromeda-plane dwarfs with $$\frac{c}{a} = \sqrt{\frac{\lambda_c}{\lambda_a}}, \qquad \frac{b}{a} = \sqrt{\frac{\lambda_b}{\lambda_a}}.$$3 ratios as high as $$\frac{c}{a} = \sqrt{\frac{\lambda_c}{\lambda_a}}, \qquad \frac{b}{a} = \sqrt{\frac{\lambda_b}{\lambda_a}}.$$4 (Randall et al., 2014).

The present state of the subject is therefore plural rather than settled. Several nearby galaxies host flattened and in some cases kinematically coherent satellite structures; spatial thinness alone is not a sufficient dynamical diagnostic; anisotropic accretion, group infall, halo torques, and massive companions can all contribute within $$\frac{c}{a} = \sqrt{\frac{\lambda_c}{\lambda_a}}, \qquad \frac{b}{a} = \sqrt{\frac{\lambda_b}{\lambda_a}}.$$5CDM; and both observational selection effects and metric choice materially affect inferred tensions. The decisive next steps are uniform plane definitions, full 6D phase-space information where possible, and direct observation–simulation comparisons that treat geometry, orbital-pole coherence, radial structure, and environment on the same footing.