Effects on vsini determinations of O stars from 3D model atmospheres with high turbulent velocities

D. Debnath; F. Backs; J.O. Sundqvist; L. Delbroek; P. Schillemans; T. Ceulemans

arxiv: 2604.25391 · v2 · pith:VWT7JURFnew · submitted 2026-04-28 · 🌌 astro-ph.SR

Effects on vsini determinations of O stars from 3D model atmospheres with high turbulent velocities

L. Delbroek , J.O. Sundqvist , F. Backs , T. Ceulemans , D. Debnath , P. Schillemans This is my paper

Pith reviewed 2026-05-21 08:22 UTC · model grok-4.3

classification 🌌 astro-ph.SR

keywords O starsprojected rotational velocitymacroturbulencespectral line broadening3D model atmospheresstellar spectroscopyrotation rates

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The pith

Standard methods cannot separately determine O-star rotation and macroturbulence from spectra

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

The paper investigates the reliability of common techniques for measuring projected rotational velocities in O-type stars when significant macroturbulent velocities are also present. By synthesizing spectra from three-dimensional model atmospheres that incorporate high turbulent velocities and applying the Fourier transform and goodness-of-fit methods to these mock observations, the authors demonstrate a strong degeneracy. They establish that only the quantity sqrt(v_mac^2/2 + vsini^2/4) can typically be constrained, with reliable individual values possible only when one velocity clearly exceeds the other. This result shows that earlier measurements of rotation rates and their reported correlations with turbulence in O-star populations will require reinterpretation.

Core claim

When rotation is included in spectral synthesis from 3D O-star model atmospheres showing significant photospheric turbulent velocities, the FT and GOF methods generally constrain only the sum sqrt(v_mac^2/2 + vsini^2/4) rather than the separate values of vsini and v_mac; good individual constraints arise only when one parameter clearly dominates.

What carries the argument

The degeneracy between rotational and macroturbulent line broadening, recovered as a broad region of acceptable fits that closely follows the empirical relation sqrt(v_mac^2/2 + vsini^2/4).

If this is right

Empirical correlations between vsini and v_mac from prior studies must be re-examined for bias.
Statistical distributions of observed rotation rates for O-star populations require reinterpretation.
The FT method still produces reasonable vsini results when vsini clearly exceeds v_mac.
GOF best-fit values occupy a large degenerate region independent of the true inputs when the parameters are similar.

Where Pith is reading between the lines

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

The same degeneracy could affect parameter estimates for other hot stars that show strong turbulence, broadening the impact on stellar spectroscopy.
Complementary methods such as time-series variability or polarimetry might be needed to separate the two contributions in targeted cases.
Evolutionary models that use observed O-star rotation distributions as input may need adjustment to account for this measurement limitation.

Load-bearing premise

The turbulent velocity fields chosen in the 3D model atmospheres accurately represent the line-broadening physics in real O-star photospheres.

What would settle it

Spectra of O stars with independent evidence that vsini greatly exceeds v_mac should return consistent individual vsini values from the standard methods, while stars with comparable values should exhibit the predicted broad degeneracy region.

Figures

Figures reproduced from arXiv: 2604.25391 by D. Debnath, F. Backs, J.O. Sundqvist, L. Delbroek, P. Schillemans, T. Ceulemans.

**Figure 1.** Figure 1: Visualisation of LoS velocities (at the optical photo view at source ↗

**Figure 2.** Figure 2: O III 5594 Å line from a 3D O-star model atmosphere, view at source ↗

**Figure 3.** Figure 3: Results for view at source ↗

**Figure 4.** Figure 4: 3sin i determined by the FT method for different 3rot,in (indicated in each lower left corner of each panel); angles are inclination angles i of the observer. The first number in between brackets () displays3sin i found by the FT method, also indicated in the figure by vertical dotted lines, whereas the second number is the expected value at the photosphere. fit value lies. Depending on rotation rate and o… view at source ↗

**Figure 5.** Figure 5: 3sin i and 3macro determined by the GOF method. The observer inclination angle i is shown in each top right corner of the panels; 3rot,in in each lower left corner. The red cross indicates best-fit values, while the magenta pentagon shows what the expected values are. Note that the colour scaling of this chi-squared distribution function is in log space, not linear space. 4. Conclusions Both the FT and G… view at source ↗

read the original abstract

When studying massive stars and their life cycles, rotation plays a key role. Hence, understanding the rotation of these stars is crucial when determining their properties, or for constraining evolutionary models. We examine the reliability of the standard methods to derive projected rotation speeds vsini from photospheric spectra of hot, massive stars in the presence of large turbulent velocities. We include rotation in the spectral synthesis of O-stars by means of three-dimensional model atmospheres showing significant photospheric turbulent velocities. We then use these as mock-observations to back-test the Fourier Transform and goodness-of-fit methods commonly used for empirical determination of vsini when the turbulent velocity field is not known. When the expected vsini>v_mac, with v_mac the macroturbulent velocity, FT vsini determinations (most of the time) give reasonable results. However, if vsini < v_mac the method is no longer reliable. Results from the GOF method show that if one parameter is not significantly larger than the other, empirical best-fit values may be located in a large region of the vsini-v_mac parameter space, independent of the true values. The degenerate region follows well the empirical formula found by Howarth et al. (2007), sqrt(v_mac^2/2+vsini^2/4). In other words, only this sum can be constrained by GOF observational analysis. Our analysis shows clearly that, generally, only the sum sqrt(v_mac^2/2+vsini^2/4) can be constrained through the standard spectroscopic methods used to infer these parameters individually. Only in the case where one of the two clearly dominates, can good constraints on the dominating parameter be derived. This demonstrates that previously found empirical correlations between vsini and v_mac as well as derived statistical distributions of observed rotation rates for O-star populations will need to be re-analysed and interpreted.

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.

Desk Editor's Note private letter to a colleague

Tests with 3D atmospheres show standard vsini methods for O stars mainly constrain a vsini-v_mac combination when turbulence matters.

read the letter

The punchline for this paper is that the usual ways to measure projected rotation from O-star spectra don't separate vsini from macroturbulence when the turbulence is strong. What you mostly get is a constraint on that particular combination sqrt(v_mac^2/2 + vsini^2/4), and only when one parameter dominates do you get a good handle on the larger one. They generate mock observations by taking 3D model atmospheres that already show high turbulent velocities, then include rotation in the spectral synthesis. After that they apply the Fourier transform and goodness-of-fit methods that people normally use on real data. This setup lets them see directly what the methods return when the underlying physics comes from 3D calculations rather than 1D assumptions. The work does well at mapping out the region where the fits become unreliable and at showing that it lines up with the relation Howarth et al. found empirically in 2007. The soft spot is the realism of the turbulent velocity fields in the 3D models. The degeneracy result only transfers to actual observations if those models produce line broadening that matches real O-star photospheres in spectrum and depth dependence. If the simulated turbulence differs, the conclusion that past vsini distributions need re-analysis loses some force. The paper is upfront about using the models as given, but this remains the key assumption to check. This kind of targeted method test is mainly for researchers who extract stellar parameters from hot-star spectra or who rely on rotation statistics for evolution calculations. A reader looking for evidence on how robust current vsini values are will get something concrete here. It is not a complete overhaul of the field, but the approach is direct and the outcome is clear enough to warrant a serious referee. I would recommend sending it out for review rather than desk rejecting it.

Referee Report

1 major / 3 minor

Summary. The manuscript uses 3D model atmospheres with high photospheric turbulent velocities to synthesize mock spectra of O stars that include rotation. These are then analyzed with standard Fourier Transform (FT) and goodness-of-fit (GOF) methods to recover vsini and v_mac. The central result is that the methods generally constrain only the combination sqrt(v_mac^2/2 + vsini^2/4), with reliable individual constraints possible only when one parameter clearly dominates; this matches the empirical relation of Howarth et al. (2007) and implies that prior vsini distributions for O-star populations require re-analysis.

Significance. If the 3D turbulence fields are representative, the work demonstrates a fundamental limitation of current 1D-based spectroscopic techniques for separating rotation and macroturbulence in hot stars. The forward-modeling approach with independent 3D simulations followed by standard recovery codes provides a non-circular test, and explicit reproduction of the Howarth et al. degeneracy formula adds weight. The finding could affect statistical studies of massive-star rotation and evolutionary models.

major comments (1)

Discussion section: the claim that 'previously found empirical correlations between vsini and v_mac as well as derived statistical distributions of observed rotation rates for O-star populations will need to be re-analysed' is load-bearing for the broader impact but rests on the assumption that the chosen 3D turbulent velocity fields (spectrum and depth dependence) match real O-star photospheres; without sensitivity tests or direct profile comparisons to observations, transferability to real data remains unquantified.

minor comments (3)

Abstract: the phrasing 'Our analysis shows clearly that, generally, only the sum...' could be tempered to reflect that the result is demonstrated specifically for the 3D models employed rather than universally.
Results section on FT method: quantify the fraction of cases where vsini > v_mac yields 'reasonable results' and report the typical recovered uncertainties to allow readers to assess the practical reliability.
Figure captions and text: ensure consistent notation for the degenerate combination (e.g., always write sqrt(v_mac^2/2 + vsini^2/4)) and add a reference to the exact Howarth et al. (2007) equation being matched.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive review and for recognizing the significance of our findings. We address the major comment below and propose a targeted revision to strengthen the discussion of limitations.

read point-by-point responses

Referee: Discussion section: the claim that 'previously found empirical correlations between vsini and v_mac as well as derived statistical distributions of observed rotation rates for O-star populations will need to be re-analysed' is load-bearing for the broader impact but rests on the assumption that the chosen 3D turbulent velocity fields (spectrum and depth dependence) match real O-star photospheres; without sensitivity tests or direct profile comparisons to observations, transferability to real data remains unquantified.

Authors: We agree that the broader implications hinge on the representativeness of the adopted 3D turbulent velocity fields. These fields are drawn from established 3D radiation-hydrodynamic simulations of O-star atmospheres that produce high photospheric turbulent velocities consistent with observed macroturbulence. While the present study does not include additional sensitivity experiments varying the turbulent spectrum or its depth dependence, the reported degeneracy between vsini and v_mac is a robust outcome of the forward-modeling procedure and reproduces the empirical relation of Howarth et al. (2007). We will revise the discussion to add an explicit statement that the results apply specifically to the turbulent properties realized in the chosen 3D models, to note that quantitative transferability would benefit from future direct comparisons with observed line profiles, and to frame the call for re-analysis as applying to O-star populations where significant turbulence is present. This revision will clarify the scope without altering the central conclusion. revision: partial

Circularity Check

0 steps flagged

No circularity: result obtained from forward-modeling with independent 3D simulations and standard recovery methods

full rationale

The paper constructs mock spectra from 3D model atmospheres that incorporate known values of vsini and turbulent velocities, then applies the external standard FT and GOF analysis procedures to those mocks. The reported degeneracy region and the conclusion that only the combination sqrt(v_mac^2/2 + vsini^2/4) is constrained follow directly from comparing the recovered parameters against the known input values in the simulations. No step reduces a fitted quantity to the target result by construction, and the cited Howarth et al. (2007) formula serves as an external empirical reference rather than a load-bearing self-citation or ansatz. The derivation chain therefore remains independent of the final claim.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the 3D model atmospheres correctly capture the line-broadening effects of turbulence in real stars; no new free parameters are introduced beyond those already present in the cited 3D modeling framework, and no new physical entities are postulated.

axioms (1)

domain assumption The 3D model atmospheres with high turbulent velocities accurately reproduce the photospheric line profiles of real O stars.
Invoked when the models are treated as mock-observations whose true vsini and v_mac are known.

pith-pipeline@v0.9.0 · 5902 in / 1399 out tokens · 46185 ms · 2026-05-21T08:22:00.573565+00:00 · methodology

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Works this paper leans on

3 extracted references · 3 canonical work pages

[1]

J., & Scott, P

Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009, ARA&A, 47, 481–522 Bodenheimer, P. 1995, ARA&A, 33, 199 Conti, P. S. & Ebbets, D. 1977, ApJ, 213, 438 Delbroek, L., Sundqvist, J. O., Debnath, D., et al. 2025, A&A, 704, A104 Dutta, Jayanta. 2016, A&A, 585, A59 Gray, D. F. 1975, ApJ, 202, 148 Gray, D. F. 2005, The Observation and Analysis of Stel...

work page 2009
[2]

Since we work with3 rot,in, the rotation at the inner bound- ary, we also refer to this method as the ‘inner boundary rotation’ method

for each point in our grid, which is in the spherical coordinate sys- tem (r, θ, ϕ) with r in range (R0,R max),θin range (0, π) andϕin range (0,2π): 3rot =3 rot,in sin(θ) R0 r (A.1) 3x =3 x −3 rot sin(ϕ) (A.2) 3y =3 y +3 rot cos(ϕ) (A.3) 3z =3 z (A.4) Here,3 rot is the calculated rotation at a specific grid point,3 rot,in is the rotation at the inner boun...

work page 2005
[3]

C1: Average LoS velocities at the optical photosphere of in- dividual snapshots, used to construct our spherical models

Appendix C: Figures Fig. C1: Average LoS velocities at the optical photosphere of in- dividual snapshots, used to construct our spherical models. Each snapshot is separated by approximately 500 seconds in time, showing the variability of these simulations in time. The posi- tive LoS velocities correspond to a general inward-falling mo- tion at the photosp...

work page 2025

[1] [1]

J., & Scott, P

Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009, ARA&A, 47, 481–522 Bodenheimer, P. 1995, ARA&A, 33, 199 Conti, P. S. & Ebbets, D. 1977, ApJ, 213, 438 Delbroek, L., Sundqvist, J. O., Debnath, D., et al. 2025, A&A, 704, A104 Dutta, Jayanta. 2016, A&A, 585, A59 Gray, D. F. 1975, ApJ, 202, 148 Gray, D. F. 2005, The Observation and Analysis of Stel...

work page 2009

[2] [2]

Since we work with3 rot,in, the rotation at the inner bound- ary, we also refer to this method as the ‘inner boundary rotation’ method

for each point in our grid, which is in the spherical coordinate sys- tem (r, θ, ϕ) with r in range (R0,R max),θin range (0, π) andϕin range (0,2π): 3rot =3 rot,in sin(θ) R0 r (A.1) 3x =3 x −3 rot sin(ϕ) (A.2) 3y =3 y +3 rot cos(ϕ) (A.3) 3z =3 z (A.4) Here,3 rot is the calculated rotation at a specific grid point,3 rot,in is the rotation at the inner boun...

work page 2005

[3] [3]

C1: Average LoS velocities at the optical photosphere of in- dividual snapshots, used to construct our spherical models

Appendix C: Figures Fig. C1: Average LoS velocities at the optical photosphere of in- dividual snapshots, used to construct our spherical models. Each snapshot is separated by approximately 500 seconds in time, showing the variability of these simulations in time. The posi- tive LoS velocities correspond to a general inward-falling mo- tion at the photosp...

work page 2025