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Tracing the W3/W4/W5 and Perseus complex dynamical evolution with star clusters

T0 review · 3 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read The Perseus complex is not dispersing: the paper argues that the apparent Hubble-like expansion is a projection effect caused by stars at different line-of-sight depths orbiting the Galaxy at different speeds.

desk verdict A solid, honest paper that makes a plausible case that the Perseus complex's apparent expansion is a projection effect, though the argument leans on a contested SAI 24 velocity and the abstract slightly overstates the constraint. read the letter →

arxiv 2504.16159 v1 pith:HQPNVFLC submitted 2025-04-22 astro-ph.GA

A. Della Croce , E. Dalessandro , E. Vesperini , M. Bellazzini , C. Fanelli , L. Origlia , N. Sanna This is my paper · ORCID
classification astro-ph.GA
keywords starclustersPerseuscomplexW3/W4/W5regionGaiaDR3clusterkinematicsorbitintegrationspiralarmsyoungstellarobjects
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that the Perseus complex—a large star-forming region spanning the W3/W4/W5 clouds and the LISCA I and LISCA II cluster aggregates—is not flying apart, contrary to the Hubble-like expansion flow of about 15 km/s/kpc reported for its young stars. The authors use Gaia DR3 data to recover five star clusters in the W345 region, attach six-dimensional phase-space information to clusters across the whole complex, and integrate their orbits in a Galactic potential. They find that the apparent expansion vanishes when the 1.2 kpc line-of-sight depth of the complex is accounted for: the on-sky velocity pattern is what you expect from stars orbiting the Galaxy at slightly different Galactocentric distances and speeds. The same orbits place LISCA I and W345 within a few hundred parsecs of each other 20–30 Myr ago and suggest spiral-arm perturbations can keep the pieces closer for longer. The reason to care is that it separates genuine internal dispersal of young clusters from the shearing view of a large complex seen through projection.

What carries the argument

The load-bearing tool is the star cluster used as a six-dimensional tracer: each cluster supplies a 3D position (sky position plus parallax-based distance) and a 3D velocity (proper motion plus line-of-sight velocity), so the same data can be viewed as a projected flow or as true Galactic orbits. The decisive comparison is the projected velocity–distance diagram versus the intrinsic (3D) velocity–distance diagram, computed after de-projecting cluster positions relative to IC 1805; the first shows an expansion-like slope, the second does not. The orbit integrations themselves are carried out in a Galactic potential using an action–angle-based integration scheme, with 500 resamplings of distance and line-of-sight velocity errors, and the backward integrations reverse the velocity vectors to trace where the cluster aggregates came from. For internal kinematics, the paper uses the mean radial velocity to velocity dispersion ratio $\langle v_R\rangle/\sigma_R$ to quantify how strongly a young cluster is expanding.

What would settle it

Take high-resolution spectra of SAI 24 and of the three clusters with no line-of-sight velocity at all (UBC 420, Basel 10, NGC 637), and recompute the 3D velocity–distance slope and the backward orbits. If the true SAI 24 velocity comes out near +52 km/s rather than −48 km/s, or the newly measured velocities shift the W345–LISCA I convergence time by much more than the quoted few-Myr errors, the claim that the complex is not dispersing loses its support.

Watch

Extended reading notes

Core claim

Stated on the paper's own terms: the Perseus complex is not undergoing a bulk expansion. When the clusters' on-sky proper motions are plotted against projected distance from the putative expansion center, the data reproduce the previously claimed 15 km/s/kpc (here 14 ± 6 km/s/kpc) trend; but when the same clusters are placed in three dimensions using parallaxes and line-of-sight velocities, the intrinsic velocity–distance relation is 7 ± 10 km/s/kpc, consistent with no net divergence. The complex spans about 1.2 kpc along the line of sight, so stars at different Galactic radii simply orbit at different speeds, and projection manufactures the appearance of a flow. Backward orbit integrations add a formation statement: LISCA I and the W345 system were a few hundred parsecs apart roughly 25 Myr ago, while LISCA II was born roughly 0.6–1 kpc away. Adding spiral-arm perturbations to the Galactic potential does not change the short-term picture and tends to drag clusters toward arm-density peaks, which can keep the components closer together for longer than an axisymmetric potential would.

Load-bearing premise

The whole orbit-based story leans on the adopted line-of-sight velocities, and the most fragile single number is the velocity chosen for the cluster SAI 24, whose two catalog values (+52 ± 22 km/s and −48 ± 5 km/s) disagree by 3.7 sigma and pull the W345 mean in opposite directions.

Editorial extensions

If this is right

  • The 15 km/s/kpc Hubble-like expansion reported for the Perseus complex is a projection artifact; the complex itself shows no net 3D divergence (7 ± 10 km/s/kpc).
  • LISCA I and the W345 system were separated by only a few hundred parsecs about 20–30 Myr ago; LISCA II formed roughly 0.6–1 kpc from them.
  • Spiral-arm perturbations drag star clusters toward higher-density regions and can keep the components of the complex closer together for over 200 Myr compared to the axisymmetric case.
  • The three youngest W345 clusters (IC 1805, IC 1848, SAI 24, age ≈ 5 Myr) are internally expanding with $\langle v_R\rangle/\sigma_R$ up to about 1–2, while the older Berkeley 65 and UBC 420 are near equilibrium, matching the age trend for young clusters.
  • Aggregating clusters into the W345, LISCA I, and LISCA II systems gives cleaner orbits than individual clusters, whose 6D initial conditions are too sensitive to line-of-sight velocity errors.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: if the projection interpretation is right, other young complexes seen through a large line-of-sight depth inside spiral arms may show spurious Hubble flows; re-doing such analyses with 3D velocities would reveal how common shear artifacts are.
  • Editorial inference: the SAI 24 velocity disagreement is the first place to look for a revision; a decisive measurement would either confirm the adopted W345 mean or reopen the formation-scenario conclusion.
  • Editorial inference: the spiral-arm toy model predicts that arm trapping can keep clusters together for hundreds of Myr, which would make hierarchical merging among the Perseus components more likely; this could be tested with self-consistent N-body simulations of cluster aggregates in the same potential.
  • Editorial inference: the same cluster-as-6D-tracer method could be applied to other Galactic star-forming complexes to quantify the fraction of observed 'expansions' that are actually Galactic shear projection.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper presents a multi-scale study of the W3/W4/W5 (W345) region and the larger Perseus complex using Gaia DR3 and complementary catalogs. The authors identify five known clusters in W345, characterize their structure, ages, and internal kinematics, and find that the three youngest clusters show expansion while the two older ones are near equilibrium. They then assemble 6D phase-space data for 15 clusters across W345, LISCA I, and LISCA II, and integrate cluster aggregate orbits in the axisymmetric McMillan (2017) potential, as well as in models with spiral-arm perturbations and a bar. The central claims are that the Hubble-like expansion reported by Román-Zúñiga et al. (2019) is likely a projection effect caused by different orbital velocities of stars at slightly different Galactocentric distances; that LISCA I and W345 formed 20--30 Myr ago only a few hundred parsecs apart; and that spiral-arm perturbations can keep the aggregates closer for longer.

Significance. If the conclusions hold, the paper provides a novel and important reinterpretation of the kinematics of the Perseus complex, replacing an internal-expansion interpretation with a Galactic-orbit interpretation. The work is careful in several respects: it uses homogeneous astrometric selections and membership criteria, it propagates distance and line-of-sight velocity errors into orbit integrations via Monte Carlo sampling, it makes the AGAMA orbit integrations reproducible, and it explores perturbations of the Galactic potential (spiral arms, bar, varying perturbation strength) in appendices. The cluster characterization in Section 3 is a useful contribution in its own right, and the YSO kinematic analysis in Section 4 adds value. The main weakness is that the dynamical conclusions, especially the no-expansion statement and the LISCA I--W345 co-formation epoch, rest on a small number of line-of-sight velocity measurements, one of which (SAI 24) shows a 3.7-sigma discrepancy between two catalogs. The authors acknowledge this discrepancy but do not demonstrate that their conclusions are robust to the alternative value.

major comments (3)
  1. [Section 5.1, Table 4] The choice of vLOS for SAI 24 is load-bearing for the paper's central conclusion. Tarricq et al. (2021) report +52 ± 22 km/s while Hunt & Reffert (2023) report -48 ± 5 km/s, and the authors adopt the latter because it is closer to the W345 mean velocity. This selection is based on consistency with the quantity being averaged rather than on an independent validation of either measurement. SAI 24 enters the W345 aggregate; switching to the Tarricq value changes the four-cluster W345 mean vLOS from approximately -47 km/s to approximately -22 km/s. Since the backward orbit integrations in Section 5.3 (Fig. 14) drive the claim of a LISCA I--W345 minimum distance 20--30 Myr ago, the authors should repeat the aggregate mean and orbit integrations using the Tarricq value, and also with SAI 24 excluded, and show whether the conclusions survive.
  2. [Section 5.2, Fig. 10] The direct 3D distance--velocity regression gives 7 ± 10 km/s/kpc, which is formally consistent with both zero expansion and a mild expansion at the level claimed by Román-Zúñiga et al. (2019). The statement that 'we do not observe a Hubble-like expansion' is therefore not established by this regression alone; it rests on the orbit-integration analysis. Moreover, the regression is performed on absolute 3D velocities in the Galactocentric frame, which include the large common orbital velocity of the complex. The slope could be dominated by the gradient of Galactic rotation across the ~1.2 kpc line-of-sight depth rather than by any internal expansion. I ask the authors to add a test using velocities relative to the complex mean motion, or an explicit forward model of the projection signature, to demonstrate that the absence of a 3D slope is specifically informative about internal dispersal.
  3. [Section 5.1 and 5.3] Three clusters in Table 4 (UBC 420, Basel 10, and NGC 637) have no line-of-sight velocity measurement in any catalog, yet they are included in the aggregate positions and velocities used for the orbit integrations. The paper does not state which clusters actually contribute to each aggregate's vLOS, nor does it quantify the sensitivity of the aggregate means or the resulting inter-aggregate distances to excluding these clusters (or to assigning them the aggregate mean as a proxy). Given that vLOS is explicitly identified as a primary uncertainty source in the orbit reconstruction, this missing sensitivity analysis compounds the SAI 24 concern and should be reported.
minor comments (4)
  1. [Throughout] There are several typographical and formatting issues: 'Identifing' in the Section 2 title, 'genearlly' in Section 5.3, 'Persues' in Section 5.3, 'Publicy' in a footnote, and frequent 'di fferent' (spurious spaces) throughout the text. These should be corrected in a final pass.
  2. [Section 3.3] The text says that for clusters not in Tarricq et al. (2021), the authors adopt a mean LOS velocity of -39 km/s from Fanelli et al. (2022b). It would help to state explicitly that this adopted value is used only for the internal expansion analysis (Fig. 8) and not for the orbit integrations in Section 5.3, since the latter require per-cluster vLOS values.
  3. [Section 5.3, Fig. 12-14] The captions and text refer to 'median orbits' but it is not always clear whether the medians are taken across the 500 initial-condition realizations at each time step or across time. A one-sentence clarification in the caption of Fig. 12 would resolve this.
  4. [Section 5.4] The discussion of spiral-arm perturbation strength (f) is clear, but the choice f = 0.3 as the 'reference model' is presented without a quantitative justification beyond the statement that f_HI = 0.53-0.66 is an upper limit. The authors should briefly restate why 0.3 is a reasonable intermediate value for the stellar arm-to-interarm contrast.

Circularity Check

1 steps flagged · score 2.0 of 10

Mild consistency-based selection of SAI 24 vLOS is the only circularity-adjacent step; the no-dispersal and formation conclusions are not forced by construction.

  1. other [Section 5.1, SAI 24 vLOS selection (Table 4; used in Section 5.3 orbit initial conditions).]
    "Tarricq et al. (2021) measured vLOS = +52± 22 km s−1 (using 8 stars), whereas Hunt & Reffert (2023) found vLOS = −48±5 km s−1 (using 7 stars). The two measurements are highly discrepant (3.7σ), possibly due to different membership compilations. However, the measurement from Hunt & Reffert (2023) is closer to the mean LOS velocity of the W345 complex (around −40 km s−1, Fanelli et al. 2022b) it belongs to. We thus adopted the value by Hunt & Reffert (2023)."

    The SAI 24 vLOS is selected because it is close to the W345 complex mean vLOS, and SAI 24 is then included in the W345 aggregate whose mean vLOS feeds the orbit integrations (Section 5.3, Figs. 12-14). The input is therefore chosen for consistency with the aggregate property it helps determine, making the W345 aggregate kinematics partly self-referential. However, the main no-expansion/projection-effect conclusion also rests on the 15-cluster sample and the comparison of projected vs 3D slopes, so this is a mild consistency-based circularity rather than a full reduction of the central claim.

full rationale

The paper's central claims are not circularly forced. The no-dispersal conclusion comes from comparing the projected distance-velocity slope (14±6 km/s/kpc) with the intrinsic 3D slope (7±10 km/s/kpc) computed from cluster distances and vLOS, and from direct backward orbit integrations in the McMillan (2017) potential. These are measured outputs, not identities with the inputs. The LISCA I/II definitions (Dalessandro et al. 2021; Della Croce et al. 2023), the cumulative-luminosity age method (Della Croce et al. 2023), and the ⟨vR⟩/σR expansion metric (Della Croce et al. 2024) are inherited from the authors' prior work, but they are used as inputs or diagnostic tools rather than as the conclusions being derived. The one mild circularity-adjacent step is the SAI 24 vLOS choice: the paper rejects Tarricq et al. (2021) in favor of Hunt & Reffert (2023) because the latter is closer to the W345 complex mean vLOS, and SAI 24 subsequently enters the W345 aggregate mean used for orbit integrations. This makes the aggregate kinematics partially self-consistent by selection; the paper itself identifies vLOS as a primary uncertainty source. Repeating the aggregate analysis with the Tarricq value would be the appropriate robustness test. Because the central projection-effect and LISCA I-W345 proximity claims depend on the full 15-cluster sample and on orbit integrations that do not algebraically reduce to the adopted input, this is a minor consistency-based input selection rather than a load-bearing circularity.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claims rest on the adopted line-of-sight velocities, especially the disputed SAI 24 value, the completeness of vLOS coverage for the aggregates, and the choice of Galactic potential. The spiral perturbation amplitude f and the average pitch angle are free parameters in the model. No new physical entities are introduced.

free parameters (3)
  • Spiral perturbation amplitude f = 0.3 (reference), explored over 0.1 to 0.5
    Section 5.4: the density amplitude of the Cox and Gomez (2002) spiral perturbation relative to the axisymmetric potential is largely unconstrained; the paper adopts f = 0.3 as a reference and tests 0.1 and 0.5. The spiral-arm effect on cluster distances depends on this value.
  • Perseus arm average pitch angle psi = 9.5 degrees
    Section 5.4: the Cox and Gomez (2002) potential model does not allow a changing pitch angle, so the paper assumes the average value for the Perseus arm from Reid et al. (2019).
  • HDBSCAN clustering parameters = min_cluster_size = 50, min_samples = 30
    Section 2: these parameters were chosen after several tests to recover known clusters; they determine which overdensities are identified and hence the cluster member catalogs that feed all subsequent analysis.
assumptions (4)
  • domain assumption The adopted line-of-sight velocity for SAI 24 from Hunt and Reffert (2023) is correct despite a 3.7-sigma disagreement with Tarricq et al. (2021).
    Invoked in Section 5.1 and Table 4; the paper selects the Hunt and Reffert value because it is closer to the W345 mean velocity. This choice directly affects the cluster's 3D velocity and the orbit integrations that underpin the formation-distance claims.
  • domain assumption Clusters with missing or single-star line-of-sight velocities can be included in aggregate mean velocities without biasing the result.
    Section 5.3: UBC 420, Basel 10, and NGC 637 have no vLOS in Table 4, and some clusters have vLOS based on one or two stars. The averaging procedure for aggregates is not fully specified.
  • domain assumption The McMillan (2017) axisymmetric potential, with Cox and Gomez (2002) spiral perturbations, adequately describes Galactic forces over 200 Myr for orbits near the Perseus arm.
    Adopted in Sections 5.3 and 5.4; the bar is tested separately in Appendix B and found negligible, but the spiral amplitude f is unconstrained and the potential model does not include a changing pitch angle or multiple pattern speeds.
  • domain assumption Extinction coefficients calibrated for effective temperatures 3500 to 10000 K can be extrapolated to 30000 K for the youngest clusters.
    Section 3.2: the authors explicitly note that the Danielski et al. (2018) relations are extrapolated for hot stars in 5 Myr clusters; this affects differential reddening corrections and inferred ages.

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Pith. "Pith review of Tracing the W3/W4/W5 and Perseus complex dynamical evolution with star clusters." pith.science (2026). https://pith.science/paper/HQPNVFLC

@misc{pith2026250416159,
  author       = {Pith},
  title        = {Pith review of: Tracing the W3/W4/W5 and Perseus complex dynamical evolution with star clusters},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HQPNVFLC}},
  note         = {Machine review of arXiv:2504.16159}
}
abstract

The Perseus complex offers an ideal testbed to study cluster formation and early evolution as it hosts two major hierarchical structures (namely LISCA I and LISCA II) and the W3/W4/W5 (W345) region characterized by recent star formation. This work aims to provide a full characterization of the population of star clusters in the W345 region, in terms of their structural, photometric, and kinematic properties. Clusters are then used to probe the dynamical properties of the W345 region and, on a larger scale, to investigate the evolution of the Perseus complex. We used Gaia DR3 data to search for star clusters in the W345 region and characterize them in terms of their density structure, ellipticity, internal dynamical state, and ages. We identified five stellar clusters belonging to the W345 complex. The three younger clusters are still partially embedded in the gas and show evidence of expansion, while the older ones cleared the surrounding gas. We also found that YSOs trace the parent gas structure and possibly its kinematics. Thanks to the 6D information available for star clusters, we followed their orbital evolution to assess the formation conditions and evolution of the complex. When accounting for the Galactic potential, we find that the Perseus complex is not dispersing. The observed expansion might be a projection effect due to stars orbiting the Galaxy at different velocities. In addition, we find that the LISCA I and W345 systems formed some $20-30$ Myr ago just a few hundred parsecs away, while LISCA II was originally $\simeq 0.75-1$ kpc apart. Finally, we also assessed the impact of spiral arm perturbations by constructing tailored Galactic potential which matches the observed Galactic spiral arm structure. We find spiral structures drag star clusters toward higher-density regions, possibly keeping clusters closer for longer than the unperturbed, axisymmetric case.

Figures

Figures reproduced from arXiv: 2504.16159 by the authors.

Figure 1
Figure 1. Intrinsic, i.e. deconvolved, parallax (top panel), and PM (bottom panel) distributions for the eight clusters in the region defined by the preliminary Galactic coordinates ranges. Cluster names are reported in the top left panel. Black lines show the parallax and PM ranges adopted for selecting Gaia sources. The top right panel shows a narrower paral￾lax range centered around the W345 star clusters to visualize the … view at source ↗
Figure 2
Figure 2. Two-dimensional density map in Galactic coordinates of Gaia sources after the parallax and PM selections. Darker colors for denser regions. Iso-density contours at 0.5σ (solid), 1σ (dashed), and 1.5σ (dash-dotted) are shown in black. The cluster positions and names are marked. The density map was obtained through Gaussian kernel density estimate using the gaussian_kde function of the scipy Python pack￾age (Virtanen … view at source ↗
Figure 3
Figure 3. Projected number density profiles for the five clusters analyzed in this study. Distances from the center were normalized to R50. Errors in each evenly-populated bin were computed as the standard deviation of density measurements in different angular sectors (concerning the y axis) and as the quantiles of the radial distribution within the bin (for the x axis). The solid lines show the median Plummer model fit of th… view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: On-sky spatial distribution of cluster members. For each cluster star, PM vectors are shown on top of the RGB image of the region from the allWISE survey. We mapped the W3 band in red, W2 in green, and W1 in blue. The W3 filter mainly traces small grain dust and polycy…
Figure 5
Figure 5. Figure 5: Spatial distribution in Galactic coordinates of Gaia DR3 sources, selected according to Sect. 2. Each star is color-coded according to its reddening value. Crosses show the centers of the five stellar clusters analyzed in this work (SAI 24 in purple, IC 1848 in red, Be…
Figure 6
Figure 6. Figure 6: Color magnitude diagrams in the Gaia filters for cluster members. The best-fit isochrones from differential-reddening-corrected, G-band luminosity function fits are shown using the same color palette as cluster members. In black are multiple isochrones from literature …
Figure 7
Figure 7. Figure 7: Mean radial velocity to the radial velocity dispersion ratio profiles. Cluster-centric distances were normalized to R50. The integrated values using all the cluster members are shown as horizontal lines (along with errors depicted as shaded areas). A black dashed line …
Figure 8
Figure 8. Figure 8: The ratio between the radial mean velocity and velocity disper￾sion as a function of the cluster age. Underlying data are from Della Croce et al. (2024). Different colors highlight the position and results for the clusters analyzed in this work. checked that perspectiv…
Figure 9
Figure 9. Figure 9: Spatial distribution of the Gaia YSO sample, with PMs depicted with arrows. PMs were referred to the clusters mean motion in the regions (see Sect. 2). The background image is the composite RGB image of the W345 complex using data from the allWISE survey. With the star…
Figure 10
Figure 10. Figure 10: Projected kinematic properties for the Perseus star clusters. Left panel: spatial distribution of the Perseus complex star clusters. Arrows show the PM vectors, converted in km s−1 according to the cluster distance (mapped into the size of markers, the smaller, the cl…
Figure 13
Figure 13. Figure 13: Galactocentric coordinates time evolution for the star cluster aggregates. Darker lines are the forward in time (i.e., t > 0) integrations while lighter ones are backward (i.e., t < 0). The present-day positions are at t = 0. Initial conditions were sampled 500 times …
Figure 12
Figure 12. Figure 12: XY projection for individual cluster orbits (left panel) and stel￾lar cluster aggregates (right panel). Darker lines trace the orbits for￾ward in time, whereas lighter ones are backward. Thin lines show or￾bit integrations from multiple initial condition extractions w…
Figure 15
Figure 15. Figure 15: Density map on the XY Galactic plane (i.e., computed at Z = 0) for a spiral perturbation with f = 0.3 (used as a reference model). The Sun is located at X = −8.178 kpc and Y = 0. The different colored lines present the different spiral arm models according to Reid et …
Figure 16
Figure 16. Figure 16: The same as [PITH_FULL_IMAGE:figures/full_fig_p014_16.png]
Figure 17
Figure 17. Figure 17: The same as [PITH_FULL_IMAGE:figures/full_fig_p015_17.png]

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    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.