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arxiv: 1906.11591 · v1 · pith:TNXR5HF3new · submitted 2019-06-27 · 🌌 astro-ph.HE · astro-ph.SR

Modelling decretion discs in Be/X-ray binaries

R. O. Brown , M. J. Coe , W. C. G. Ho , A. T. Okazaki This is my paper

Pith reviewed 2026-05-25 14:31 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.SR
keywords Be/X-ray binariesdecretion discssmoothed particle hydrodynamicscircumstellar discsneutron star accretionorbital period dependencedisc truncation
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The pith

Smoothed particle hydrodynamics simulations support that Be star circumstellar disc size depends on orbital period in X-ray binaries.

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

This paper uses smoothed particle hydrodynamics to simulate decretion discs in Be/X-ray binaries by changing parameters including orbital period, eccentricity, mass ejection rate, viscosity and disc orientation. It measures how these changes affect the disc base density, neutron star accretion rate and disc size. The results back up observations that disc size increases with longer orbital periods and larger semi-major axes. This matters because it provides a way to link binary orbit properties to disc behavior and accretion in these common high-mass X-ray binary systems.

Core claim

The simulations demonstrate relationships between the varied parameters and the disc characteristics, specifically supporting the observational evidence that the size of the Be star's circumstellar disc depends on the orbital period and semi-major axis.

What carries the argument

Smoothed particle hydrodynamics simulations varying orbital period, eccentricity, mass ejection rate, viscosity and disc orientation to find effects on base gas density, accretion rate and disc size.

If this is right

  • Disc size increases with orbital period and semi-major axis.
  • The accretion rate onto the neutron star is influenced by the disc parameters.
  • Base gas density at the disc depends on the mass ejection rate and viscosity.
  • The model explains several observable phenomena in Be/X-ray binaries.

Where Pith is reading between the lines

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

  • If the size-orbital period relation holds, observers could estimate disc properties from orbital data alone in unmodeled systems.
  • Future simulations could test whether including magnetic fields changes the reported size dependency.
  • Similar modeling might apply to other types of decretion discs in stellar binaries.

Load-bearing premise

The smoothed particle hydrodynamics model with its viscosity prescription, mass-ejection boundary condition, and neglect of magnetic fields and radiative transfer captures the main physics controlling disc size.

What would settle it

Finding a Be/X-ray binary system where the circumstellar disc size does not increase with orbital period as the simulations predict would challenge the result.

Figures

Figures reproduced from arXiv: 1906.11591 by A. T. Okazaki, M. J. Coe, R. O. Brown, W. C. G. Ho.

Figure 1
Figure 1. Figure 1: An illustration of the geometry used in this paper. The Be star’s circumstellar disc is shown in red and the neutron star is represented by the solid blue circle. The orbit of the neutron star is in the x-y plane. The two angles, θ and φ, show the inclination and azimuthal angles, respectively. The inclination and azimuthal angle are defined as the rotation about the x axis and z axis, respectively. Perias… view at source ↗
Figure 2
Figure 2. Figure 2: The relationship between the base gas density and the viscosity parameter of the disc. The bars show the minimum and maximum values of the base gas density around an orbital cycle. The bars are comparable to or smaller than the size of the sym￾bols. This is for systems with a 40 day period and eccentricities of e = 0 and 0.4 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The relationship between the base gas density and the mass ejection rate of the Be star. The bars show the minimum and maximum values of the base gas density around an orbital cycle. The bars are comparable to or smaller than the size of the sym￾bols. This is for systems with a 40 day period and eccentricities of e = 0 and 0.4. and Taylor 1992). The size of the circumstellar disc in Be/X￾ray binaries is de… view at source ↗
Figure 4
Figure 4. Figure 4: The relationship between the time-averaged size of the disc and viscosity parameter for systems with an orbital period of 40 days and eccentricities of e = 0 and 0.4. The solid and dashed lines show the maximum and minimum disc sizes, respectively. rate yields a generally higher density of the disc (see Fig￾ure 3). When the truncation radius remains the same, the neutron star interacts at the same distance… view at source ↗
Figure 5
Figure 5. Figure 5: Top: Time-averaged size of the disc for various orien￾tations. The systems shown have an orbital period of 40 days and eccentricities of e = 0.0 and 0.2. The solid and dashed lines show the maximum and minimum disc sizes, respectively. The values of maximum and minimum disc size are for simulations of any φ at each eccentricity. Bottom: Time-averaged size of the disc for various disc orientations. φ indica… view at source ↗
Figure 6
Figure 6. Figure 6: The relationship between the time-averaged size of the disc and the orbital parameters of the Be/neutron star binaries. The data points have a range of eccentricities from e = 0.0 to 0.6. The solid and dashed lines show the maximum and minimum disc sizes, respectively [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: shows the relationship between the size of the Be star’s circumstellar and orbital period. The data and fits shown in [PITH_FULL_IMAGE:figures/full_fig_p006_8.png] view at source ↗
Figure 7
Figure 7. Figure 7: The relationship between the maximum accretion rate of the neutron star and the orbital period [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: The relationship between the Be star’s circumstellar disc size and semi-major axis of the neutron star’s orbit. The black squares show the observational data from CK15. The coloured bars represent the simulation data and have a range of eccentric￾ities from e = 0.0 to 0.6. The bars show the minimum and max￾imum values of disc size. The quadratic fit from CK15 (dashed black line) is given by Equation 3. 0.0… view at source ↗
read the original abstract

As the largest population of high mass X-ray binaries, Be/X-ray binaries provide an excellent laboratory to investigate the extreme physics of neutron stars. It is generally accepted that Be stars possess a circumstellar disc, providing an additional source of accretion to the stellar winds present around young hot stars. Interaction between the neutron star and the disc is often the dominant accretion mechanism. A large amount of work has gone into modelling the properties of these circumstellar discs, allowing for the explanation of a number of observable phenomena. In this paper, smoothed particle hydroynamics simulations are performed whilst varying the model parameters (orbital period, eccentricity, the mass ejection rate of the Be star and the viscosity and orientation of the disc). The relationships between the model parameters and the disc's characteristics (base gas density, the accretion rate of the neutron star and the disc's size) are presented. The observational evidence for a dependency of the size of the Be star's circumstellar disc on the orbital period (and semi-major axis) is supported by the simulations.

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

1 major / 1 minor

Summary. The paper performs smoothed particle hydrodynamics (SPH) simulations of decretion discs in Be/X-ray binaries, varying orbital period, eccentricity, mass-ejection rate, viscosity parameter, and disc orientation. It reports relationships between these inputs and outputs including base gas density, neutron-star accretion rate, and disc size, and states that the simulations support the observational claim of a disc-size dependence on orbital period (and semi-major axis).

Significance. If the reported size-period scaling is robust to the numerical choices, the work would supply theoretical backing for an observed correlation in Be/X-ray binaries and help interpret accretion onto the neutron star. The simulations are forward-modelled from independent parameters and compared to separate observations, avoiding direct circularity.

major comments (1)
  1. [Abstract] Abstract: the central claim that the simulations support an orbital-period dependence of disc size requires that the measured truncation radius is set by tidal interaction rather than by the fixed Shakura-Sunyaev viscosity prescription or the inner-boundary mass-injection condition. No convergence tests on the viscosity parameter, its functional form, or the mass-ejection rate are described, so it is unclear whether the reported correlation would survive changes in these load-bearing numerical choices.
minor comments (1)
  1. [Abstract] Abstract, line 3: 'hydroynamics' is a typographical error and should read 'hydrodynamics'.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful review and constructive comments on the manuscript. We respond to the major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the simulations support an orbital-period dependence of disc size requires that the measured truncation radius is set by tidal interaction rather than by the fixed Shakura-Sunyaev viscosity prescription or the inner-boundary mass-injection condition. No convergence tests on the viscosity parameter, its functional form, or the mass-ejection rate are described, so it is unclear whether the reported correlation would survive changes in these load-bearing numerical choices.

    Authors: We agree that the robustness of the reported disc-size versus orbital-period correlation to the numerical setup is central to the claim. The simulations vary both the Shakura-Sunyaev viscosity parameter and the mass-ejection rate as independent inputs (Table 1 and Sections 3.2–3.3), and the positive correlation between measured truncation radius and orbital period persists across these variations. The truncation itself is produced by the tidal torque from the neutron star opposing viscous spreading, a standard outcome in such SPH models rather than an imposed inner-boundary artifact. That said, the referee correctly observes that dedicated convergence tests on the functional form of the viscosity or finer sampling of the mass-ejection rate were not presented. We will revise the manuscript to include an explicit discussion of parameter sensitivity together with additional test simulations demonstrating that the scaling remains unchanged under reasonable variations in these quantities. revision: partial

Circularity Check

0 steps flagged

No circularity: forward simulations compared to independent observations

full rationale

The paper executes SPH simulations with input parameters (orbital period, eccentricity, mass-ejection rate, viscosity, disc orientation) and reports emergent quantities (base density, accretion rate, disc size). These outputs are compared to separate observational data on disc-size vs. orbital-period trends. No equation or result is defined in terms of itself, no fitted parameter is relabeled as a prediction, and no load-bearing premise reduces to a self-citation chain. The derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

3 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of standard SPH fluid equations plus domain-specific assumptions about how Be-star mass ejection and disc viscosity are implemented; no new entities are introduced.

free parameters (3)
  • viscosity parameter
    Varied across runs to explore its effect on disc structure; value chosen within conventional range for Be discs.
  • mass ejection rate
    Varied as an input boundary condition; not derived from first principles.
  • orbital period and eccentricity
    Sampled from observed ranges but treated as free inputs for each simulation.
axioms (1)
  • domain assumption Smoothed particle hydrodynamics with the adopted artificial viscosity and boundary conditions sufficiently approximates the hydrodynamics of a decretion disc.
    Invoked by the choice of numerical method in the abstract.

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