pith. sign in

arxiv: 2605.01076 · v1 · submitted 2026-05-01 · 🌌 astro-ph.GA

Analysis of spatial velocities of several samples of open star clusters

Vadim V. Bobylev , Anisa T. Bajkova This is my paper

Pith reviewed 2026-05-09 18:29 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords open star clustersspiral density wavesgalactic rotationcorotation radiusradial velocitiesMilky Way kinematicsFourier analysis
0
0 comments X

The pith

Analysis of open star clusters shows the Sun lies very close to the Milky Way's corotation radius.

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

The paper examines the velocities of thousands of young open star clusters to map the Milky Way's rotation and its spiral density waves. It identifies periodic patterns in radial velocities that appear in clusters up to 600 million years old and shift their locations as the samples get older. Measuring these shifts yields the relative angular speed between the spiral pattern and the galactic disk, which in turn locates the corotation radius where the pattern and stars rotate at the same rate. This location matters because it determines how long stars and gas remain in spiral arms and influences the overall structure of the galaxy.

Core claim

Fourier analysis of radial velocities in three age-grouped samples of open star clusters gives a wavelength near 2 kpc and perturbation amplitudes that rise from 4.3 to 9.6 km/s with increasing age. The positions of the wave maxima and minima move systematically with sample age; the rate of this movement implies |ΔΩ| = 2.0 km/s/kpc between the spiral pattern speed and galactic rotation, producing possible corotation radii of 8.6 kpc or 7.6 kpc.

What carries the argument

The systematic age-dependent shift in the locations of maxima and minima of radial-velocity waves, which is converted into the absolute difference |ΔΩ| between spiral pattern angular velocity and galactic rotation velocity.

If this is right

  • The Sun sits close enough to corotation that its orbital speed nearly matches the spiral pattern speed.
  • Spiral density waves remain detectable in cluster kinematics for at least 600 million years.
  • The galactic rotation curve parameters refine the local angular velocity and its first two derivatives.
  • Two discrete corotation distances arise from the sign ambiguity in the measured difference |ΔΩ|.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Confirmation would suggest the solar neighborhood experiences slower arm crossings than regions inside or outside corotation.
  • Higher-precision ages for the same clusters could test whether the wave amplitude grows linearly with time as predicted by simple density-wave theory.

Load-bearing premise

The observed changes in wave positions across age samples arise only from the spiral pattern rotating at a steady speed different from the galactic disk, without large effects from catalog biases, measurement errors, or unrelated motions.

What would settle it

An independent measurement of radial velocities in a new sample of clusters that shows no age-dependent wave shift, or a |ΔΩ| value clearly different from 2 km/s/kpc from gas or stellar stream data, would contradict the derived corotation radii.

read the original abstract

An analysis of the kinematics of open star clusters (OSCs) using their characteristics from the new Hunt and Reffert catalog was conducted. Based on 4003 OSCs younger than 200 million years, the following values for the angular velocity of the Galaxy's rotation were found: $\Omega_0 = 28.99\pm0.11$ km/s/kpc, $\Omega^{'}_0 = -3.909\pm0.026$ km/s/kpc$^{2}$ and $\Omega^{''}_0 = 0.5662\pm0.018$ km/s/kpc$^{3}$, where $V_0=234.8\pm3.0$ km/s for $R_0=8.1\pm0.1$ kpc. It was found that periodicity in the radial velocities of OSCs is manifested in clusters younger than 600 Myr, while a wave in residual tangential velocities is observed only in the youngest ones, younger than 40 Myr. A spectral Fourier analysis of the radial velocities of three OSC samples with average ages of 18, 72, and 143 Myr was used to obtain the following values of the wavelength $\lambda$ and the velocity perturbation amplitude $f_R$: $\lambda=2.0$ kpc and $f_R=4.3$ km/s, $\lambda=2.2$ kpc and $f_R=8.2$ km/s, $\lambda=2.1$ kpc and $f_R=9.6$ km/s, respectively. A systematic change in the positions of the maxima and minima of the waves in the radial velocities of OSCs was found depending on the age of the sample. From the analysis of these shifts, the value of the absolute value of the difference $|\Delta\Omega|$ between the angular velocity of rotation of the spiral pattern $\Omega_p$ and the rotation velocity of the Galaxy was found, $|\Delta\Omega|=2.0\pm0.5_{stat}\pm2.3_{syst}$ km/s/kpc. Based on this, an estimate of two possible values of the corotation radius was obtained: $8.6\pm0.2$ kpc and $7.6\pm0.2$ kpc, which indicates that the Sun is very close to the corotation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper analyzes kinematics of 4003 open star clusters younger than 200 Myr from the Hunt & Reffert catalog. It derives Galactic rotation parameters Ω₀ = 28.99 ± 0.11 km/s/kpc, Ω'₀ = -3.909 ± 0.026 km/s/kpc², Ω''₀ = 0.5662 ± 0.018 km/s/kpc³ (with V₀ = 234.8 ± 3.0 km/s at R₀ = 8.1 ± 0.1 kpc). Fourier analysis of radial velocities in three age-binned samples (mean ages 18, 72, 143 Myr) yields wavelengths λ ≈ 2.0–2.2 kpc and amplitudes f_R = 4.3–9.6 km/s. Systematic shifts in wave extrema positions with sample age are used to measure |ΔΩ| = 2.0 ± 0.5_stat ± 2.3_syst km/s/kpc between spiral pattern speed and Galactic rotation, implying corotation radii of 8.6 ± 0.2 kpc or 7.6 ± 0.2 kpc and placing the Sun near corotation. Periodicity in radial velocities appears for clusters <600 Myr and in residual tangential velocities only for <40 Myr.

Significance. If the age-dependent shifts in Fourier wave positions reliably trace the spiral pattern speed difference without dominant artifacts, the result supplies an independent |ΔΩ| constraint from a large OSC sample and supports the Sun lying close to corotation, with implications for Galactic dynamics and density-wave theory. The provision of explicit fitted values with separate statistical and systematic errors, plus the use of multiple age bins, strengthens the analysis relative to single-sample studies.

major comments (3)
  1. [Fourier analysis and |ΔΩ| derivation] The extraction of wave-maxima/minima positions from the Fourier fits and the subsequent calculation of their age-dependent shifts to obtain |ΔΩ| (abstract and the Fourier-analysis section) is not described: no explicit phase-extraction formula, time baseline (using the 18/72/143 Myr means), or conversion from positional shift to |ΔΩ| is given. This step is load-bearing for the central claim.
  2. [Corotation radius estimates] The dominant systematic uncertainty ±2.3 km/s/kpc on |ΔΩ| is comparable to the measured value 2.0 km/s/kpc, yet the derived corotation radii are reported to ±0.2 kpc precision (abstract). No explicit propagation of this uncertainty (or of age errors) into the final corotation estimates is shown.
  3. [Sample selection and Fourier analysis] No robustness checks are presented against typical OSC age uncertainties (20–50 Myr), spatially varying catalog completeness in Hunt & Reffert, or possible selection effects that could mimic age-dependent wave shifts. These tests are required to support the assumption that the observed periodicity and shifts arise purely from spiral density waves.
minor comments (2)
  1. [Fourier analysis] The number of clusters in each of the three age bins and the precise radial range used for the Fourier fits should be stated explicitly to allow assessment of statistical power.
  2. [Introduction and methods] Notation for the rotation-curve derivatives (Ω'₀, Ω''₀) and the perturbation amplitude f_R is introduced without a dedicated definitions subsection; a short table of symbols would improve clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive review. The comments highlight important gaps in methodological detail and validation that we will address in a revised manuscript. We provide point-by-point responses below and will incorporate the necessary clarifications, formulas, error propagations, and robustness tests.

read point-by-point responses

  1. Referee: The extraction of wave-maxima/minima positions from the Fourier fits and the subsequent calculation of their age-dependent shifts to obtain |ΔΩ| (abstract and the Fourier-analysis section) is not described: no explicit phase-extraction formula, time baseline (using the 18/72/143 Myr means), or conversion from positional shift to |ΔΩ| is given. This step is load-bearing for the central claim.

    Authors: We agree that the original manuscript omitted the explicit steps for extracting wave positions and deriving |ΔΩ|. In the revision we will add a dedicated subsection with: (i) the phase-extraction formula ϕ = atan2(Im(F), Re(F)) evaluated at the dominant Fourier frequency; (ii) time baselines computed from the sample mean ages (Δt = 54 Myr between first and second bin, 71 Myr between second and third); (iii) the conversion |ΔΩ| = (Δr / λ) / Δt where Δr is the observed shift in wave extrema position. We will tabulate the measured extrema positions for each age bin and show the arithmetic leading to |ΔΩ| = 2.0 ± 0.5_stat ± 2.3_syst km s⁻¹ kpc⁻¹. revision: yes

  2. Referee: The dominant systematic uncertainty ±2.3 km/s/kpc on |ΔΩ| is comparable to the measured value 2.0 km/s/kpc, yet the derived corotation radii are reported to ±0.2 kpc precision (abstract). No explicit propagation of this uncertainty (or of age errors) into the final corotation estimates is shown.

    Authors: The referee is correct that error propagation was not shown. We will insert an explicit calculation of the corotation radius R_cr = R_0 × Ω_0 / (Ω_0 ± |ΔΩ|) together with standard analytic propagation of both statistical and systematic uncertainties on |ΔΩ|, plus the contribution from age-bin uncertainties. The resulting uncertainties on R_cr will be reported (likely larger than ±0.2 kpc) and the abstract will be updated to reflect the propagated errors. revision: yes

  3. Referee: No robustness checks are presented against typical OSC age uncertainties (20–50 Myr), spatially varying catalog completeness in Hunt & Reffert, or possible selection effects that could mimic age-dependent wave shifts. These tests are required to support the assumption that the observed periodicity and shifts arise purely from spiral density waves.

    Authors: We acknowledge the absence of these checks. In the revision we will add a new subsection containing: (1) Monte-Carlo resampling of cluster ages within the quoted 20–50 Myr uncertainties and re-derivation of Fourier parameters and shifts; (2) a quantitative assessment of Hunt & Reffert completeness for clusters <200 Myr as a function of Galactic longitude; (3) a test excluding the inner-Galaxy region most affected by selection. We will report the outcome of these tests and, if they alter the results, qualify the conclusions accordingly. Full exhaustive simulations of all possible selection biases are beyond the scope of the present work but the added checks will strengthen the analysis. revision: partial

Circularity Check

0 steps flagged

No significant circularity in derivation of |ΔΩ| from observed wave shifts

full rationale

The paper conducts independent Fourier fits to radial-velocity data in three separate age-binned OSC samples (mean ages 18, 72, 143 Myr), extracts λ and f_R directly from those fits, measures the empirical shifts in the locations of wave maxima/minima across the bins, and converts the observed shift rate into |ΔΩ| via the standard density-wave phase relation. This chain uses data-driven measurements at each step and does not reduce any claimed result to a tautology, a fitted parameter renamed as a prediction, or a self-citation whose content is presupposed. The rotation-curve parameters (Ω0, Ω'0, Ω''0) are obtained from a separate least-squares fit to the same catalog and are not used to force the |ΔΩ| value. No load-bearing self-citation, uniqueness theorem, or ansatz smuggling is present in the derivation.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard galactic kinematics assumptions and the interpretation of velocity periodicity as spiral waves. No new physical entities are postulated. Two free parameters are adopted from prior work to scale the results.

free parameters (2)
  • R0 = 8.1 kpc
    Adopted galactocentric distance of the Sun used to convert angular velocities to linear velocities and to locate corotation radii.
  • V0 = 234.8 km/s
    Linear rotation velocity at R0 derived from the fitted Ω0.
axioms (2)
  • domain assumption The galactic rotation curve can be locally approximated by a Taylor expansion in (R - R0) to obtain Ω0, Ω'0, and Ω''0.
    Invoked to fit the three angular velocity parameters from the cluster velocity data.
  • domain assumption Periodic variations in radial velocities of young clusters are produced by spiral density waves whose pattern speed differs from the local stellar rotation.
    Underlies the Fourier analysis and the interpretation of age-dependent wave shifts as a measure of |ΔΩ|.

pith-pipeline@v0.9.0 · 5747 in / 1663 out tokens · 34346 ms · 2026-05-09T18:29:07.866472+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

65 extracted references · 65 canonical work pages

  1. [1]

    L. H. Amaral, J. R. D. Lepine, Mon. Not. R. Astron. Soc. 286, 885 (1997)

    work page 1997

  2. [2]

    Antoja, A

    T. Antoja, A. Helmi, M. Romero-G´ omez, et al., Nature 561, 360 (2018)

    work page 2018

  3. [3]

    Antoja, P

    T. Antoja, P. Ramos, B. Garcia-Conde, et al., Astron. Astro phys. 673, A115 (2023)

    work page 2023

  4. [4]

    Armstrong, J.C

    J.J. Armstrong, J.C. Tan, N.J. Wright, et al., Mon. Not. R. Astron. Soc. 543, 2349 (2025)

    work page 2025

  5. [5]

    Babusiaux, C

    C. Babusiaux, C. Fabricius, S. Khanna, et al., Astron. Astr ophys. 674, A32 (2023). 12

    work page 2023

  6. [6]

    Bajkova, V.V

    A.T. Bajkova, V.V. Bobylev, Astron. Lett. 38, 549 (2012)

    work page 2012

  7. [7]

    Barnes, K

    A.T. Barnes, K. Morii, J. E. Pineda, et al., arXiv: 2601.209 28 (2026)

    work page 2026

  8. [8]

    Bobylev, A.T

    V.V. Bobylev, A.T. Bajkova, and S.V. Lebedeva. Astron. Lett . 33, 720 (2007)

    work page 2007

  9. [9]

    Bobylev, A.T

    V.V. Bobylev, A.T. Bajkova, and A.S. Stepanishchev, Astron . Lett. 34, 515 (2008)

    work page 2008

  10. [10]

    Bobylev, A.T

    V.V. Bobylev, A.T. Bajkova, Mon. Not. R. Astron. Soc. 437, 1549 (2014)

    work page 2014

  11. [11]

    Bobylev, A.T

    V.V. Bobylev, A.T. Bajkova, Astron. Lett. 42, 90 (2016)

    work page 2016

  12. [12]

    V. V. Bobylev, A. T. Bajkova, Astron. Lett. 45,109 (2019)

    work page 2019

  13. [13]

    Bobylev, A.T

    V.V. Bobylev, A.T. Bajkova, Astron. Rep. 65, 498 (2021)

    work page 2021

  14. [14]

    Bobylev, A.T

    V.V. Bobylev, A.T. Bajkova, Astron. Lett., 48, 9 (2022)

    work page 2022

  15. [15]

    Bobylev, A.T

    V.V. Bobylev, A.T. Bajkova, Astron. Lett. 49, 320 (2023)

    work page 2023

  16. [16]

    Bobylev, A.T

    V.V. Bobylev, A.T. Bajkova, A.A. Smirnov, Astron. Lett. 51, 278 (2025)

    work page 2025

  17. [17]

    G. A. Gontcharov, A. A. Marchuk, S. S. Savchenko, et al., R es. Astron. Astrophys. 25, id.125016 (2025)

    work page 2025

  18. [18]

    G. M. Green, E. Schlafly, C. Zucker, et al., Astrophys. J. 887, 93 (2019)

    work page 2019

  19. [19]

    W. S. Dias, J. R. D. Lepine, and B. S. Alessi, Astron. Astrop hys. 376, с. 441 (2001)

    work page 2001

  20. [20]

    W. S. Dias, M. Assafin, V. Florio, et al., Astron. Astrophy s. 446, 949 (2006)

    work page 2006

  21. [21]

    W. S. Dias, H. Monteiro, A. Moitinho, et al., Mon. Not. R. A stron. Soc. 504, 356 (2021)

    work page 2021

  22. [22]

    T. C. Junqueira, C. Chiappini, J. R. D. Lepine, et al., Mon . Not. R. Astron. Soc. 449, 2336 (2015)

    work page 2015

  23. [23]

    M. V. Zabolotskikh, A. S. Rastorguev, and A. K. Dambis, As tron. Lett. 28, 454 (2002)

    work page 2002

  24. [24]

    Joshi, S

    Y.C. Joshi, S. Malhotra, Astron. J. 166, 170 (2023)

    work page 2023

  25. [25]

    Camargo, C

    D. Camargo, C. Bonatto, and E. Bica, Mon. Not. R. Astron. Soc . 450, 4150 (2015)

    work page 2015

  26. [26]

    Cantat-Gaudin, A

    T. Cantat-Gaudin, A. Jordi, A. Vallenari, et al., Astron . Astrophys. 618, A93 (2018)

    work page 2018

  27. [27]

    Cantat-Gaudin, F

    T. Cantat-Gaudin, F. Anders, A. Castro-Ginard, et al., A stron. Astrophys. 640, A1 (2020)

    work page 2020

  28. [28]

    Prusti, et al.), Astron

    Gaia Collab (T. Prusti, et al.), Astron. Astrophys. 595, 1 (2016)

    work page 2016

  29. [29]

    Brown, et al.), Astron

    Gaia Collab ( A.G.A. Brown, et al.), Astron. Astrophys. 616, 1 (2018)

    work page 2018

  30. [30]

    Brown, et al.), Astron

    Gaia Collab (A.G.A. Brown, et al.), Astron. Astrophys. 649, 1 (2021)

    work page 2021

  31. [31]

    Vallenari, et al.), Astron

    Gaia Collab (A. Vallenari, et al.), Astron. Astrophys. 674, 1 (2023)

    work page 2023

  32. [32]

    J. R. D. Lepine, W. S. Dias, and Y. Mishurov, Mon. Not. R. As tron. Soc. 386, 2081 (2008)

    work page 2081

  33. [33]

    Lindegren, S.A

    L. Lindegren, S.A. Klioner, J. Hern´ andez, et al., Astro n. Astrophys. 649, A2 (2021)

    work page 2021

  34. [34]

    R.A. Lee, E. Gaidos, J. van Saders, et al., Mon. Not. R. Ast ron. Soc. 528, 4760 (2024). 13

    work page 2024

  35. [35]

    A. V. Loktin, M. E. Popova, Astron. Rep. 51, 364 (2007)

    work page 2007

  36. [36]

    A. V. Loktin, M. E. Popova, Astrophys. Bull. 74, 270 (2019)

    work page 2019

  37. [37]

    Luhman, Astron

    K.L. Luhman, Astron. J. 165, 269 (2023)

    work page 2023

  38. [38]

    Pang, Astrophys

    L Liu, X. Pang, Astrophys. J. Suppl. 245, 32 (2019)

    work page 2019

  39. [39]

    S. R. Majewski, R. P. Schiavon, P. M. Frinchaboy, et al., A stron. J. 154, 94 (2017)

    work page 2017

  40. [40]

    Mr´ oz, A

    P. Mr´ oz, A. Udalski, D.M. Skowron, et al., Astrophys. J. 870, L10. (2019)

    work page 2019

  41. [41]

    Perryman, Physics Reports 1150, 1 (2026)

    M. Perryman, Physics Reports 1150, 1 (2026)

    work page 2026

  42. [42]

    A. E. Piskunov, N. V. Kharchenko, S. R¨ oser, et al., Astro n. Astrophys. 445, 545 (2006)

    work page 2006

  43. [43]

    Poggio, R

    E. Poggio, R. Drimmel, R. Andrae, et. al., Nature Astron. 4, 590 (2020)

    work page 2020

  44. [44]

    M. E. Popova, A. V. Loktin, Astron. Lett. 31, 171 (2005)

    work page 2005

  45. [45]

    Ratzenb¨ ock, J.E

    S. Ratzenb¨ ock, J.E. Grosschedl, T. M¨ oller, et al., Ast ron. Astrophys. 677, A59 (2023)

    work page 2023

  46. [46]

    Reid, K.M

    M.J. Reid, K.M. Menten, A. Brunthaler, et al., Astrophys. J. 885, 131 (2019)

    work page 2019

  47. [47]

    Skowron, J

    D.M. Skowron, J. Skowron, P. Mr´ oz, et al., Science 365, 478 (2019a)

    work page

  48. [48]

    Skowron, J

    D.M. Skowron, J. Skowron, P. Mr´ oz, et al., Acta Astron. 69, 305 (2019b)

    work page

  49. [49]

    Tarricq, C

    Y. Tarricq, C. Soubiran, L. Casamiquela, et al., Astron. Astrophys. 647, A19 (2021)

    work page 2021

  50. [50]

    Tepper-Garcia, J

    T. Tepper-Garcia, J. Bland-Hawthorn, T. R. Bedding, et al. , Mon. Not. R. Astron. Soc. 542, 1987 (2025)

    work page 1987

  51. [51]

    Q. Feng, Y. Huang, H. Zhang, and J. Liu, Mon. Not. R. Astron . Soc. 546, id.stag011 (2025)

    work page 2025

  52. [52]

    Fedorov A

    P.N. Fedorov A. M. Dmytrenko, V. S. Akhmetov, et al., arXi v: 2511.22295 (2025)

    work page arXiv 2025

  53. [53]

    C.J. Hao, Y. Xu, L.G. Hou, et al., Astron. Astrophys. 652, 102 (2021)

    work page 2021

  54. [54]

    Hamilton, A

    C. Hamilton, A. Mummery, and J. Bland-Hawthorn, arXiv: 26 02.06182 (2026)

    work page 2026

  55. [55]

    E.L. Hunt, S. Reffert, Astron. Astrophys. 646, A104 (2021)

    work page 2021

  56. [56]

    E.L. Hunt, S. Reffert, Astron. Astrophys. 673, A114 (2023)

    work page 2023

  57. [57]

    E.L. Hunt, S. Reffert, Astron. Astrophys. 696, A42 (2024)

    work page 2024

  58. [58]

    Kharchenko, A

    N.V. Kharchenko, A. E. Piskunov, S. R¨ oser, et al., Astro n. Astrophys. 438, 1163 (2005)

    work page 2005

  59. [59]

    Kharchenko, R.-D

    N.V. Kharchenko, R.-D. Scholz, A. E. Piskunov, et al., As tron. Nachr. 328, 889 (2007)

    work page 2007

  60. [60]

    Kharchenko, A

    N.V. Kharchenko, A. E. Piskunov, E. Schilbach, et al., As tron. Astrophys. 558, A53 (2013)

    work page 2013

  61. [61]

    Horta, A

    D. Horta, A. M. Price-Whelan, S.E. Koposov, et al., Xiv: 2 601.18876 (2026)

    work page 2026

  62. [62]

    Chiba, N

    R. Chiba, N. Frankel, and C. Hamilton, Mon. Not. R. Astron . Soc. 543, 2159 (2025)

    work page 2025

  63. [63]

    Scholz, N

    R.-D. Scholz, N. V. Kharchenko, A. E. Piskunov, et al., As tron. Astrophys. 581, A39 (2015)

    work page 2015

  64. [64]

    Sch¨ onrich, J.J

    R. Sch¨ onrich, J.J. Binney, and W. Dehnen, Mon. Not. R. Ast ron. Soc. 403, 1829 (2010)

    work page 2010

  65. [65]

    Yamsiri, J

    P. Yamsiri, J. Bland-Hawthorn, and T. Tepper-Garcia, arX iv: 2602.05296 (2026). 14

    work page arXiv 2026