Jet MHD analytical model - framework for radiative transfer

TL;DR

This work develops an analytical MHD jet model that reproduces both transverse and longitudinal jet structure and can serve as a fast, flexible setup for solving radiative transfer and producing total intensity and polarization maps. Building on Beskin24, it introduces a non-constant ε to better capture trans-field acceleration, derives expressions for magnetic fields, velocity, and density, and provides a framework to specify jet boundaries via r_jet or external pressure. It explores two emitting-plasma distributions (equipartition and threshold-based) to generate Doppler-boosted synchrotron maps, showing limb-brightened and spine- or triple-ridge emission patterns under varied viewing angles and jet geometries. The framework yields a universal jet-pressure fit and demonstrates close agreement with full MHD solutions, enabling efficient parameter studies and interpretation of VLBI jet observations, while highlighting limitations near the light cylinder and opportunities for future refinement.

Abstract

We developed the full magnetohydrodynamical analytical jet model that allows accurate reproducing of a transversal and longitudinal structure for a highly collimated relativistic jets. This model can be used as a setup for convenient solution of radiative transfer equations and modelling the total intensity and polarization maps. We show that the analytical fits are in excellent agreement with the numerical solutions of full magnetohydrodynamical equations. Our approach allows setting easily different models for an emitting plasma number density. For example, we show that the equipartition number density ranges from several to tens of percent of a total number density. We show that the Doppler-corrected emissivity distribution behave in such a way that we may expect a limb brightened intensity pattern on a sub-parsec scale and a spine-brightened structure downstream. We reproduce the broken power-law dependence of a jet pressure at its boundary from the jet radius. The corresponding power exponents are in agreement with the parabola-to-cone transition observed directly in nearby sources.

Figures (10)

• Figure 1: Solid lines --- $\alpha$, calculated numerically to match the jet pressure at its boundary. Dashed lines --- fits using Equation (\ref{['alpha1']}).
• Figure 2: Poloidal magnetic field in units of $\frac{B_\mathrm{L}}{2\sigma_\mathrm{M}}$ across a jet for four different cross-cuts defined by the local jet radius in units of a light cylinder radius (upper left panel corresponds to $x_\mathrm{jet}=8.2$, upper right panel --- $12.6$, bottom left --- $29.7$ and bottom right --- $165.0$)
• Figure 3: The same as in Figure \ref{['f:Bp']} for a toroidal magnetic field component.
• Figure 4: Bulk plasma motion Lorentz factor across a jet for three different jet cross-cuts. Dotted lines --- numerical calculation. Dashed line --- ideal acceleration given by Equation (\ref{['G']}) with a constant $\varepsilon=1/2\sigma_\mathrm{M}^2$. Solid lines --- analytical ansatz given by Equation (\ref{['G']}) with a non-constant parameter $\varepsilon$ defined by Equation (\ref{['eps']}). Abscissa for each curve designates the jet radius in units of a light cylinder radius.
• Figure 5: The same as in Figure \ref{['f:Bp']} for a total pressure $\frac{B_*^2}{8\pi}$ in units of $\frac{B_\mathrm{L}^2}{4\sigma_\mathrm{M}^2}$.