[Paper Review] A model for the cross section of a turbulent, radiative jet or wake

J. Cantó, A. C. Raga+1 more|arXiv (Cornell University)|Jun 4, 2003

Solar and Space Plasma Dynamics3 citations

TL;DR

This paper presents a simple analytical model for the cross-sectional structure of turbulent, radiative astrophysical jets or wakes, assuming a parabolic mean velocity profile and Gaussian-distributed turbulent motions. It successfully fits observed radial velocity and line width profiles of the HH 110 jet using only four free parameters, demonstrating good agreement with data despite inherent asymmetries in real turbulent flows.

ABSTRACT

We present an analytical model for the cross section of a turbulent, radiative jet or wake. This model is appropriate for modeling HH jets, or "wakes" left behind by "astrophysical bullets". Even though the model is very simple, it has the benign property of only having four free parameters (the outer radius of the beam, the axial velocity, the velocity at the edge of the beam, and the turbulent velocity width), which can be derived by fitting the radial velocity and line width cross sections of an observed outflow. We illustrate how to do such fits using previously published spectroscopic data of the HH 110 jet.

Motivation & Objective

• To develop a simple, analytically tractable model for the cross section of a turbulent, radiative jet or wake in astrophysical outflows.
• To enable direct comparison between theoretical predictions and observed spectroscopic data of HH jets, particularly in radial velocity and line width profiles.
• To extract four key physical parameters—outer beam radius, central axial velocity, edge velocity, and turbulent velocity width—from observed cross sections.
• To assess the validity of mean-flow plus turbulent eddy models in capturing the essential kinematic features of turbulent astrophysical outflows.
• To explore the limitations of axisymmetric models when compared to asymmetric, real-world observations of HH jets.

Proposed method

• Assumes a parabolic mean velocity profile across the jet beam: $ v_j(r) = v_0(1 - r^2/h^2) + v_1 $, where $ h $ is the outer radius, $ v_0 + v_1 $ is the central axial velocity, and $ v_1 $ is the edge velocity.
• Incorporates turbulent motions as a Gaussian-distributed velocity component with constant dispersion $ riangle v_T $, independent of position due to isothermal conditions.
• Derives analytical expressions for the first and second moments of the emission line profile (barycenter and line width) as functions of radial position across the jet.
• Performs numerical integration of the line profile equation over the jet cross section to predict observed position-velocity (PV) diagrams.
• Convolved model predictions with a Gaussian seeing function (FWHM = 2.5") to match observational conditions of the HH 110 data.
• Fits the model to long-slit spectroscopic data of HH 110 knots B and C by matching observed radial velocity and line width profiles.

Experimental results

Research questions

• RQ1 Can a simple analytical model with only four free parameters accurately reproduce the observed radial velocity and line width profiles across the cross section of a turbulent astrophysical jet?
• RQ2 To what extent does the axisymmetric mean-flow plus turbulent eddy model capture the kinematic structure of real turbulent outflows like HH 110?
• RQ3 Why do observed PV diagrams show asymmetries not present in the symmetric theoretical model, and what does this imply for modeling turbulent jets?
• RQ4 Can averaged cross sections derived from 2D spectroscopic data (e.g., Fabry-Pérot) better match the predictions of a mean-flow model than single-slit data?
• RQ5 What physical parameters—outer radius, axial velocity, edge velocity, and turbulent width—can be reliably extracted from observed line profiles in HH jets?

Key findings

• The model successfully fits the observed radial velocity and line width cross sections of knots B and C in the HH 110 jet using only four free parameters.
• The observed line broadening in HH 110 is approximately 50 km s⁻¹, significantly exceeding the 20 km s⁻¹ instrumental resolution, indicating dominant turbulent motions.
• While the radial velocity profile of knot C closely matches the model’s parabolic prediction, knot B shows a clear deviation, suggesting non-uniform or asymmetric flow structures.
• The predicted PV diagrams, after convolution with seeing, reproduce the general features of the observed data (radial velocities, line widths, spatial extent), though asymmetries in observations are not captured by the axisymmetric model.
• Averaged cross sections derived from 2D Fabry-Pérot data (as in Riera et al. 2003b) show surprisingly good agreement with the model predictions, supporting its physical relevance.
• The results suggest that despite its simplicity, the model captures essential mean-flow characteristics of turbulent jets when applied to spatially averaged data.