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arxiv: 1906.09420 · v1 · pith:XWWSG5ENnew · submitted 2019-06-22 · 🌌 astro-ph.HE

Theoretical model of hydrodynamic jet formation from accretion disks with turbulent viscosity

E. Arshilava , M. Gogilashvili , V. Loladze , I. Jokhadze , B. Modrekiladze , N.L. Shatashvili , A.G. Tevzadze This is my paper

Pith reviewed 2026-05-25 18:18 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords hydrodynamic jetsaccretion disksturbulent viscosityBeltrami-Bernoulli flowself-similar solutionsprotostellar jetsjet formationanalytic solutions
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The pith

Analytic solutions connect jet ejection velocities directly to accretion disk turbulence and flow properties.

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

The paper constructs a theoretical model for hydrodynamic jets emerging from protostellar accretion disks by adopting a Beltrami-Bernoulli flow structure. It extends the usual turbulent viscosity prescription and obtains analytic solutions through self-similar variable parametrization. These solutions establish an explicit analytic connection between jet characteristics and the underlying disk accretion flow for the first time. The ratio of ejection velocity to accretion velocity depends on the turbulence parameter, and the ejection speed rises as the local sound speed or the launch radius falls. The resulting expressions offer a way to relate observed jet outflows to measurable disk properties.

Core claim

We develop the theoretical model for the analytic description of hydrodynamic jets from protostellar disks employing the Beltrami-Bernoulli flow configuration of disk-jet structure. For this purpose we extend the standard turbulent viscosity prescription and derive several classes of analytic solutions using the flow parametrization in self-similar variables. Derived solutions describe the disk-jet structure, where for the first time jet properties are analytically linked with the properties of the accretion disk flow. The ratio of the jet ejection and disk accretion velocities is controlled by the turbulence parameter, while the ejection velocity increases with the decrease of local sound 2

What carries the argument

The Beltrami-Bernoulli flow configuration parametrized in self-similar variables combined with an extended turbulent viscosity prescription, which together permit closed-form analytic solutions for the coupled disk-jet system.

If this is right

  • The ratio of jet ejection velocity to disk accretion velocity is set by the turbulence parameter.
  • Ejection velocity rises as local sound velocity decreases or as the jet launching radius decreases.
  • Jet properties are analytically linked to accretion disk flow properties for the first time.
  • Derived solutions can be applied to analyze astrophysical jets from protostellar disks and connect outflows to local disk observations.

Where Pith is reading between the lines

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

  • If the model applies, measurements of jet speeds in protostellar systems could be used to infer the turbulence strength in the parent disks.
  • The self-similar assumption suggests the solutions might apply across different scales of accretion systems if the flow configuration remains similar.
  • Direct comparison with numerical simulations of turbulent accretion disks could test whether the analytic velocity relations hold in more general cases.

Load-bearing premise

The disk-jet structure must follow a Beltrami-Bernoulli flow that can be parametrized with self-similar variables to yield analytic solutions from the extended viscosity prescription.

What would settle it

Finding that the observed ratio of jet ejection to disk accretion velocities does not depend on the turbulence level inferred from disk observations would contradict the model's central linkage.

Figures

Figures reproduced from arXiv: 1906.09420 by A.G. Tevzadze, B. Modrekiladze, E. Arshilava, I. Jokhadze, M. Gogilashvili, N.L. Shatashvili, V. Loladze.

Figure 1
Figure 1. Figure 1: The Beltrami parameters λ(τ) for the disk (top) and the jet (bottom) solutions are shown vs τ for the case when β = 0.01. Notice that Beltrami parameter for the disk solution is negligible for low poloidal angles (τ 1). Eqs. (49-51) together with radial profiles (41) and appropriate choice of the solution for W (see Eq. (44) give the full solution for the disk-jet flow for different types of density profil… view at source ↗
Figure 2
Figure 2. Figure 2: W(τ) (solid black line) vs τ in three region solution. W+(τ) and W−(τ) are shown by blue and red dashed lines, respectively. W(τ) follows W+ in the disk region and W− in the jet region. Transition region in this models starts at τd = 1 and ends at τj = 2. Within the transition region, where flow is effectively ballistic, disk solution can continuously switch into the jet solution. and the jet flow: VrJ (σ,… view at source ↗
Figure 3
Figure 3. Figure 3: Velocity streamlines of the disk-jet structure illustrating accretion [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Total density ρ(r, z) distribution of the disk-jet structure is shown for: Ad = 1, Aj = 1, md = −1, mj = 1 (top) and Ad = 3, Aj = 3, md = −3, mj = 3 (bottom). n all cases τ0 = 0.01. The topology of the density distribution is set by the disk (md < 0) and the jet (mj > 0) power indices; for ρ2(τ) the power-law distribution (59) was used . Specific value of the β parameter can be inferred from observa￾tions,… view at source ↗
Figure 5
Figure 5. Figure 5: Vertical jet velocity of the jet solution [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Vertical Mach number of the jet flow log(Mz(r, z)) when Ad = 3, Aj = 3, md = −3, mj = 3. τ0 = 0.01, β = 0.01, σ0 = 1 and P0/p0 = 106 . Vertical dashed line shows area, where the Mach number reveals supersonic flow: Mz > 1. For density the distribution presented in [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
read the original abstract

We develop the theoretical model for the analytic description of hydrodynamic jets from protostellar disks employing the Beltrami-Bernoulli flow configuration of disk-jet structure. For this purpose we extend the standard turbulent viscosity prescription and derive several classes of analytic solutions using the flow parametrization in self-similar variables. Derived solutions describe the disk-jet structure, where for the first time jet properties are analytically linked with the properties of the accretion disk flow. The ratio of the jet ejection and disk accretion velocities is controlled by the turbulence parameter, while the ejection velocity increases with the decrease of local sound velocity and the jet launching radius. Derived solutions can be used to analyze the astrophysical jets from protostellar accretion disks and link the properties of outflows with the local observational properties of accretion disk flows.

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

2 major / 1 minor

Summary. The paper develops a theoretical model for the analytic description of hydrodynamic jets from protostellar accretion disks by employing the Beltrami-Bernoulli flow configuration of the disk-jet structure. The authors extend the standard turbulent viscosity prescription and derive several classes of analytic solutions via flow parametrization in self-similar variables. The derived solutions are claimed to analytically link jet properties with accretion disk flow properties for the first time, with the ratio of jet ejection to disk accretion velocities controlled by the turbulence parameter, and the ejection velocity increasing as local sound velocity and jet launching radius decrease.

Significance. If the analytic solutions are verified to satisfy the full viscous hydrodynamic equations, the work would provide a useful analytic framework for connecting observable properties of protostellar accretion disks with jet outflows. The explicit control of the velocity ratio by the turbulence parameter and the dependence on sound speed and radius could aid in modeling and interpreting astrophysical jets, offering falsifiable predictions for observations.

major comments (2)
  1. [Derivation of analytic solutions (self-similar parametrization)] The central claim rests on whether the Beltrami-Bernoulli self-similar ansatz combined with the extended turbulent viscosity prescription yields exact solutions to the steady axisymmetric hydrodynamic equations (continuity, momentum including viscous stress tensor, and energy). If the ansatz causes the viscous term to drop out or to violate momentum balance except at isolated parameter values, the claimed analytic linkage between ejection/accretion velocity ratio and the turbulence parameter is not generally valid. This must be demonstrated explicitly with the full derivations.
  2. [Abstract and solution classes] The turbulence parameter is stated to control key velocity ratios in the solutions, but it is unclear whether this parameter is independently constrained from disk physics or leads to circular dependence on quantities fitted to observations. The abstract notes it controls the ratio, but the manuscript must show how it is fixed without reducing to a fitting parameter.
minor comments (1)
  1. [Abstract] The abstract mentions 'several classes of analytic solutions' but does not specify how many or their distinguishing features; a brief enumeration in the abstract or introduction would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. We address each major comment below and have made revisions to improve the clarity and explicitness of the derivations and the role of the turbulence parameter.

read point-by-point responses

  1. Referee: [Derivation of analytic solutions (self-similar parametrization)] The central claim rests on whether the Beltrami-Bernoulli self-similar ansatz combined with the extended turbulent viscosity prescription yields exact solutions to the steady axisymmetric hydrodynamic equations (continuity, momentum including viscous stress tensor, and energy). If the ansatz causes the viscous term to drop out or to violate momentum balance except at isolated parameter values, the claimed analytic linkage between ejection/accretion velocity ratio and the turbulence parameter is not generally valid. This must be demonstrated explicitly with the full derivations.

    Authors: The manuscript derives the solutions by direct substitution of the Beltrami-Bernoulli self-similar ansatz into the complete steady axisymmetric viscous hydrodynamic equations, with the extended turbulent viscosity prescription incorporated into the stress tensor. This substitution reduces the system to ordinary differential equations whose analytic solutions satisfy continuity, momentum (including viscous contributions), and energy balance identically for the identified classes of flows. The viscous terms remain active and are balanced by the chosen functional form of the viscosity within the self-similar framework; they do not drop out. We have added an expanded subsection in the revised manuscript that walks through the substitution and verification steps for the momentum equation to make the satisfaction of the full equations fully explicit. revision: yes

  2. Referee: [Abstract and solution classes] The turbulence parameter is stated to control key velocity ratios in the solutions, but it is unclear whether this parameter is independently constrained from disk physics or leads to circular dependence on quantities fitted to observations. The abstract notes it controls the ratio, but the manuscript must show how it is fixed without reducing to a fitting parameter.

    Authors: The turbulence parameter is the standard dimensionless coefficient in the turbulent viscosity prescription (ν = α c_s H), treated as an independent input characterizing the strength of disk turbulence, exactly as in the Shakura-Sunyaev model. It is constrained by disk observables such as measured accretion rates, surface density profiles, or effective temperatures, independent of jet data. Once specified, the analytic solutions then determine the jet-to-accretion velocity ratio and other jet properties. We have revised the abstract and added a clarifying paragraph in Section 2 to emphasize that the parameter is fixed from disk physics alone and does not involve fitting to jet observations. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain.

full rationale

The paper extends the turbulent viscosity prescription and adopts the Beltrami-Bernoulli configuration with self-similar variables to obtain analytic solutions for the disk-jet structure. The reported linkage (velocity ratio controlled by the turbulence parameter) is presented as a derived outcome from the extended equations rather than a fit or self-definition. No load-bearing self-citations, uniqueness theorems from prior author work, or reductions of predictions to inputs by construction are evident from the abstract and description. The model is self-contained as a theoretical ansatz-based derivation.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on extending an existing viscosity model and assuming self-similar flow parametrization to obtain closed-form solutions.

free parameters (1)
  • turbulence parameter
    Determines the ratio of jet ejection to disk accretion velocities in the derived solutions.
axioms (2)
  • domain assumption Beltrami-Bernoulli flow configuration of disk-jet structure
    Employed as the basis for the analytic description of the disk-jet structure.
  • domain assumption Standard turbulent viscosity prescription can be extended
    Extended to derive the analytic solutions in self-similar variables.

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discussion (0)

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