[Paper Review] A turbulent model for the surface brightness of extragalactic jets

Lorenzo Zaninetti|arXiv (Cornell University)|Mar 6, 2009

Astrophysics and Cosmic Phenomena4 references3 citations

TL;DR

This paper proposes a turbulent model for extragalactic jets that links energy dissipation in turbulence to synchrotron emission, using a power-law distribution of turbulent energy to predict surface brightness profiles, spectral indices, and polarization maps. The model reproduces central depressions in intensity and predicts increasing spectral index (in absolute value) along both axial and transverse directions, consistent with observations of 3C273 and 3C296.

ABSTRACT

This paper summarizes the known physics of turbulent jets observed in laboratory experiments. The formula, which gives the power released in turbulence describes the concentration of turbulence/relativistic particles in each point of the astrophysical jets. The same expression is also used to analyze the power released in turbulence in the case of pipe and non Newtonian fluids. Through an integral operation it is possible to deduce the intensity of synchrotron radiation for a profile perpendicular or not to a straight jet, a 2D map for a perpendicular, randomly oriented straight jet as well as a 2D map of complex trajectories such as NCC4061 and 3C31. Presented here is a simulation of the spectral index in brightness of 3C273 as well as a 2D map of the degree of linear polarization. The Sobel operator is applied to the theoretical 2D maps of straight perpendicular jets.

Motivation & Objective

• To develop a physically grounded model linking turbulent energy dissipation to synchrotron emission in extragalactic jets.
• To simulate 2D surface brightness maps for straight, perpendicular, and complexly curved jets (e.g., NGC4061, 3C31) using integral operations on turbulent power laws.
• To reproduce observed spectral index gradients in jets such as 3C273 and 3C296, where the spectral index increases in absolute value outward from the center.
• To apply the Sobel filter to theoretical maps to detect fine structures like 'valley on the top' features caused by gradient reversals in intensity profiles.
• To compute the degree of linear polarization from the spectral index using a derived conversion formula based on electron energy spectral index.

Proposed method

• The model uses a turbulent energy dissipation law proportional to $ r^{-b} $, with $ b \approx 0.35-0.78 $, to describe energy concentration in the jet cross-section.
• Synchrotron intensity $ I_\nu $ is computed via an integral over a 3D cubic grid of $ 400^3 $ pixels, using the turbulent power law and a Fermi acceleration mechanism with variable velocity.
• The spectral index $ \alpha_s $ is derived from the energy spectral index $ \gamma $ using the relation $ \alpha_s = (\gamma - 1)/2 $, with $ \gamma $ linked to turbulent acceleration.
• The degree of linear polarization is computed from $ \prod = \frac{3(1 - \alpha_s)}{3\alpha_s - 5} $, derived from the electron energy distribution and magnetic field uniformity.
• The Sobel operator is applied to theoretical 2D maps to detect edges and intensity gradients, particularly identifying 'valley on the top' features due to sign changes in radial gradients.
• The model is validated by comparing simulated intensity profiles with observed data from M87 (knot D-E) and 3C273 (knot A) at 5 GHz, accounting for beam smoothing effects.

Experimental results

Research questions

• RQ1 Can the physics of laboratory-scale turbulent jets be extended to explain the surface brightness profiles of extragalactic radio jets?
• RQ2 Does a turbulent energy dissipation law naturally produce a central depression in synchrotron intensity, as observed in some jets?
• RQ3 Can the observed radial and axial gradients in spectral index (increasing in absolute value outward) be reproduced by a turbulent model with variable acceleration?
• RQ4 Can the Sobel filter detect fine morphological features like 'valley on the top' in theoretical maps, and does this match observed structures in radio galaxies?
• RQ5 Is the degree of linear polarization in jets predictable from the spectral index distribution under a turbulent acceleration model?

Key findings

• The model predicts a central intensity depression in straight, perpendicular jets, with maximum synchrotron emission occurring at $ r \approx 0.49 b_{1/2} $, not at the center.
• The simulated spectral index of 3C273 (Figure 32) shows a systematic increase in absolute value along both the axial and transverse directions, matching observations of 3C296.
• The 2D map of linear polarization (Figure 33) is directly computed from the spectral index map using $ \prod = \frac{3(1 - \alpha_s)}{3\alpha_s - 5} $, showing higher polarization at the jet edges.
• The Sobel filter applied to theoretical maps successfully reveals 'valley on the top' features due to radial gradient reversals, consistent with observed arcs in radio galaxies like 3C296.
• The model reproduces observed intensity profiles of M87 (knot D-E) and 3C273 (knot A) at 5 GHz, though beam smoothing may obscure fine central depressions in real data.
• The turbulent power input peaks at $ r = 0.69 b_{1/2} $, indicating that the most energetic turbulence is located slightly off-center in the jet cross-section.