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arxiv: 2604.11189 · v1 · pith:E56WULSXnew · submitted 2026-04-13 · 🌌 astro-ph.SR

Fundamental properties of two rapidly rotating stars: Rasalhague and Alkaid

Axel Lazzarotto , Alain Hui-Bon-Hoa , Torsten Boehm , Matthew Gent , Michel Rieutord This is my paper

Pith reviewed 2026-05-10 16:18 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords rapidly rotating starsfundamental parameterstwo-dimensional modelsRasalhagueAlkaidstellar inclinationstellar evolution
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The pith

A method using infrared temperatures, projected velocities, and luminosities with grids of two-dimensional stellar models determines masses, rotation rates, ages, and spin-axis inclinations for fast-rotating stars.

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

The paper presents a technique to extract the mass, rotation rate, core hydrogen fraction, and viewing angle for rapidly rotating stars by comparing five spectrophotometric measurements to a grid of steady two-dimensional models. Temperature comes from the infrared flux method, combined with the projected equatorial speed and apparent luminosity to pick consistent models and report the most probable values. The approach is demonstrated on Rasalhague and Alkaid, improving earlier results for the first star and supplying new numbers for the second, including its young age. Accurate parameters for such stars matter because rotation alters their structure, mixing, and evolutionary paths in ways one-dimensional models cannot capture.

Core claim

Using the temperature derived by the infrared flux method, the Vsini and the apparent luminosity, along with a grid of 2D steady state models, we select models that are compatible with all observational constraints, and derive the most probable mass, rotation rate, core hydrogen mass fraction relative to that of the envelope, and inclination of the rotation axis on the line of sight of the targeted star. For Rasalhague the inclination is found to be approximately 69 degrees. For Alkaid the mass is 5.071 solar masses, the equatorial rotation period is 14.6 hours, the inclination is about 42 degrees, and the star lies between 2 and 8 million years past the zero-age main sequence.

What carries the argument

Grid of steady two-dimensional stellar models matched against five spectrophotometric observables including infrared-flux temperature, projected rotational velocity, and apparent luminosity to resolve degeneracies among mass, rotation rate, age, and inclination.

Load-bearing premise

The steady two-dimensional models must accurately capture the internal structure and surface properties of real stars, and the five chosen observables must be sufficient to distinguish among different combinations of mass, rotation rate, age, and viewing angle.

What would settle it

Interferometric measurements of equatorial and polar radii or surface temperature maps for either star that lie outside the range predicted by the selected best-fit models would falsify the derived parameters and ages.

Figures

Figures reproduced from arXiv: 2604.11189 by Alain Hui-Bon-Hoa, Axel Lazzarotto, Matthew Gent, Michel Rieutord, Torsten Boehm.

Figure 1
Figure 1. Figure 1: Ratio Qeq(ω, i) = TIRFM/T eq eff as a function of the rotation axis inclination i on the line of sight, for various rotation rates ω between 0.2 and 0.7. The thickness of the lines represents the effects of mass and Xcore/Xenv variations in the intervals [2.0,2.4] and [0.25,0.45], respec￾tively. c2 = − 5 2   log   R FF220 R FF250   − log   R FF250 R FF419     mag (… view at source ↗
Figure 2
Figure 2. Figure 2: Mean line profile of Rasalhague obtained with the Least Square Deconvolution method (Donati et al. 1997) with a rotationally broad￾ened profile fit to the data (top panel), and its residuals (bottom panel). The resulting projected equatorial velocity is 224.3 ± 2.6 km/s [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Combined spectra of Rasalhague. The spectrophotometric part #1401 is shown by the black solid line. Its extension towards the UV is in magenta. The 5%-uncertainty of these data is shown by the greyed zone around the spectrum. The bandpasses of the filters used in the c ′ 1 and c2 indices are shown in red and blue, respectively. The infrared extension is not shown. The green line shows the synthetic spectru… view at source ↗
Figure 4
Figure 4. Figure 4: Histograms of the distributions of mass M, rotation rate with respect to the critical one Ω/Ωc(= ω), equatorial radius Req, relative hy￾drogen mass fraction in the core Xc , inclina￾tion of the rotation axis i, apparent luminos￾ity Lapp and spectroscopic quantities TIRFM, c ′ 1 and c2. The blue histograms show the distri￾bution when the interferometric constraint on Req from Monnier et al. (2010) is used, … view at source ↗
Figure 5
Figure 5. Figure 5: Diagrams summarising the histograms of [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Mean line profile of Alkaid obtained with the Least Square De￾convolution method with a rotationally broadened profile fit to the data (top panel), and its residuals (bottom panel). The resulting projected velocity is 154.3 ± 9.1 km/s. course. They also showed that the two photometric indices, c ′ 1 and c2, do not participate in the selection of the models in the present case. As a side note, we also remar… view at source ↗
Figure 7
Figure 7. Figure 7: Histograms of the parameter distribu￾tions of steady 2D-ESTER models for Alkaid that match the observational constraints. Red lines have the same meaning as in [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Evolutionary track in a Hertzsprung-Russell-like diagram show￾ing the evolution the best ESTER Alkaid model during the first 12 Myrs on the main sequence. The red cross represents the mean observed value and its uncertainty box is depicted by the pink area. the spectral energy distribution dependent on the orientation of the rotation axis and on the rotational flattening. This allowed us to infer the param… view at source ↗
read the original abstract

Abridged : The fundamental parameters of rapidly rotating stars are key quantities to understand the impact of rotation on stellar evolution. A few nearby early-type stars offer the possibility of precise measurements of these parameters, which will help us constrain newly available two-dimensional models. We propose a method to retrieve the fundamental parameters of a fast rotating star (mass, rotation rate, and age), and also the inclination of its rotation axis on the line of sight, using five spectrophotometric observables along with a set of steady 2D-models. Using the temperature derived by the infrared flux method, the Vsini and the apparent luminosity, along with a grid of 2D steady state models, we select models that are compatible with all observational constraints, and derive the most probable mass, rotation rate, core hydrogen mass fraction relative to that of the envelope, and inclination of the rotation axis on the line of sight of the targetted star. We apply this method to two stars: Rasalhague (alpha Oph) and Alkaid (eta UMa). We confirm and improve the fundamental parameters of Rasalhague and provide a new determination of its rotation axis inclination on the line-of-sight, which we find to be $\sim69$ degrees. Concerning Alkaid, we infer a mass of $5.071\pm0.023 M_\odot$, a rotation rate corresponding to an equatorial rotation period of 14.6 hours. We also find an inclination of the rotation axis of $\sim42$ degrees. We show that Alkaid is a very young star, presumably between 2 and 8 Myrs off the Zero-Age Main Sequence. As a side result, using high resolution spectra and the Least Square Deconvolution method, we determined a precise value of the Vsini of Rasalhague, namely $224.3\pm2.6$ km/s. Similarly, we find $V\sin i=154.3\pm9.1$ km/s for Alkaid.

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 manuscript proposes a method to derive the mass, rotation rate, core hydrogen mass fraction (relative to envelope), and inclination of rapidly rotating stars by identifying models from a grid of steady-state 2D stellar models that match five observational constraints: effective temperature from the infrared flux method, projected rotational velocity V sin i, apparent luminosity, and two additional spectrophotometric quantities. The method is applied to Rasalhague (α Oph) and Alkaid (η UMa). For Rasalhague, it confirms and improves previous parameters and determines an inclination of approximately 69 degrees. For Alkaid, it yields a mass of 5.071 ± 0.023 solar masses, an equatorial rotation period of 14.6 hours, an inclination of about 42 degrees, and indicates the star is very young (2-8 Myr since ZAMS). As a byproduct, precise V sin i values are measured using high-resolution spectra and the Least Squares Deconvolution technique: 224.3 ± 2.6 km/s for Rasalhague and 154.3 ± 9.1 km/s for Alkaid.

Significance. If the results hold, the paper offers useful empirical constraints on two well-observed rapid rotators that can help test and refine 2D stellar models. The model-selection procedure is a reasonable way to handle the underconstrained problem of fitting multiple parameters to limited data. The new V sin i measurements from LSD are a clear observational contribution. The work highlights the potential of combining IRFM temperatures with 2D models for stars like these, but its broader impact depends on demonstrating that the steady-state approximation does not introduce significant biases for young objects like Alkaid.

major comments (3)
  1. [Methods (model grid description)] The paper does not detail the parameter space covered by the grid of steady 2D models (e.g., mass range, rotation rates from 0 to critical, core-to-envelope hydrogen ratios) or the numerical method used to generate them. This information is essential to assess whether the selection process can uniquely determine the four parameters from the five observables and to reproduce the quoted uncertainties.
  2. [Results for Alkaid] Alkaid is concluded to be only 2–8 Myr old, yet the analysis relies exclusively on steady-state 2D models. No comparison is made to evolutionary sequences that self-consistently evolve angular momentum and chemical mixing from the ZAMS. This assumption is load-bearing for the derived mass and inclination, as time-dependent effects could alter the predicted surface properties and internal profiles used in the matching.
  3. [Observables used in model selection] While the abstract refers to five spectrophotometric observables, only the IRFM temperature, V sin i, and apparent luminosity are named explicitly. The identities and uncertainties of the remaining two quantities must be stated clearly to evaluate the constraining power of the dataset.
minor comments (2)
  1. [Abstract] Spelling: 'targetted' should be corrected to 'targeted'.
  2. [Abstract] The core hydrogen mass fraction is described as 'relative to that of the envelope'; please specify whether this is a ratio or a difference, and how it is implemented in the models.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which have helped us identify areas for improvement. We address each major comment below and will revise the manuscript to provide the requested clarifications and additional discussion.

read point-by-point responses

  1. Referee: The paper does not detail the parameter space covered by the grid of steady 2D models (e.g., mass range, rotation rates from 0 to critical, core-to-envelope hydrogen ratios) or the numerical method used to generate them. This information is essential to assess whether the selection process can uniquely determine the four parameters from the five observables and to reproduce the quoted uncertainties.

    Authors: We agree that a detailed description of the model grid is essential for reproducibility and to evaluate the robustness of the parameter determination. In the revised manuscript, we will expand the Methods section to fully specify the parameter space of the grid (including mass range, rotation rates up to critical, and core-to-envelope hydrogen ratios) and describe the numerical method used to compute the steady-state 2D models. We will also explain how the model selection yields the quoted uncertainties on mass, rotation period, inclination, and core hydrogen fraction. revision: yes

  2. Referee: Alkaid is concluded to be only 2–8 Myr old, yet the analysis relies exclusively on steady-state 2D models. No comparison is made to evolutionary sequences that self-consistently evolve angular momentum and chemical mixing from the ZAMS. This assumption is load-bearing for the derived mass and inclination, as time-dependent effects could alter the predicted surface properties and internal profiles used in the matching.

    Authors: The referee correctly notes that our age estimate for Alkaid relies on the core hydrogen fraction in steady-state models without direct comparison to full evolutionary calculations. Our approach matches current observables to the present-day structure, using the hydrogen ratio as a proxy for evolutionary state. We acknowledge this as a limitation for very young stars. In the revision, we will add a paragraph discussing the steady-state approximation, its potential impact on the derived parameters, and the justification for its use here, while noting that self-consistent evolutionary modeling would be a valuable extension but lies beyond the scope of the present work. revision: partial

  3. Referee: While the abstract refers to five spectrophotometric observables, only the IRFM temperature, V sin i, and apparent luminosity are named explicitly. The identities and uncertainties of the remaining two quantities must be stated clearly to evaluate the constraining power of the dataset.

    Authors: We will revise both the abstract and the main text to explicitly identify all five spectrophotometric observables, including the two additional quantities, and to provide their measured values along with uncertainties. This will allow readers to better assess the constraining power of the full dataset used in the model selection. revision: yes

Circularity Check

0 steps flagged

No significant circularity: independent model grid matched to external observables

full rationale

The derivation selects compatible models from a pre-existing grid of steady 2D models using five independent external observables (IRFM temperature, V sin i, apparent luminosity, and spectrophotometric quantities). No free parameters are fitted inside the derivation such that a 'prediction' reduces to the input by construction. No self-citations, uniqueness theorems, or ansatzes from prior author work are invoked to justify the central steps. The grid is treated as given and independent of the target stars' data, making the procedure a standard forward-model comparison rather than a tautological loop.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the existence and accuracy of a pre-computed grid of steady 2D stellar models whose internal physics (equation of state, opacities, convection treatment) are taken as given; the only free parameters introduced by the method itself are the discrete choices of which models survive the five observational cuts.

free parameters (1)
  • core hydrogen mass fraction relative to envelope
    Treated as a free parameter that is read off from the surviving models rather than predicted from first principles.
axioms (1)
  • domain assumption Steady-state 2D models with given mass, rotation rate, and core hydrogen fraction accurately reproduce the surface temperature distribution, luminosity, and projected rotation velocity of real stars.
    Invoked when the authors state that models compatible with the five observables yield the true stellar parameters.

pith-pipeline@v0.9.0 · 5688 in / 1630 out tokens · 60706 ms · 2026-05-10T16:18:32.228209+00:00 · methodology

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Works this paper leans on

2 extracted references · 2 canonical work pages

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