Two Types of Magnetohydrodynamic Sheath Jets

Recent observations of astrophysical jets emanating from various galactic nuclei strongly suggest that a double layered structure, or a spine-sheath structure, is likely to be their common feature. We propose that such a sheath jet structure can be formed magnetohydrodynamically within a valley of the magnetic pressures, which is formed between the peaks due to the poloidal and toroidal components, with the centrifugal force acting on the rotating sheath plasma is balanced by the hoop stress of the toroidal field. The poloidal field concentrated near the polar axis is maintained by a converging plasma flow toward the jet region, and the toroidal field is developed outside the jet cone owing to the poloidal current circulating through the jet. Under such situations, the set of magnetohydrodynamic (MHD) equations allows two main types of solutions, at least, in the region far from the footpoint. The first type solution describes the jets of marginally bound nature. This type is realized when the jet temperature decreases like viral one, and neither the pressure-gradient nor the MHD forces, which are both determined consistently, cannot completely overcome the gravity even at infinity. The second type is realized under an isothermal situation, and the gravity is cancelled exactly by the pressure-gradient force. Hence, the jets of this type are accelerated purely by the MHD force. It is suggested also that these two types correspond, respectively, to the jets from type I and II radio galaxies in the Fanaroff-Riley classification.

💡 Research Summary

The paper addresses the increasingly common observational evidence that astrophysical jets from active galactic nuclei (AGN) often display a spine‑sheath (double‑layer) morphology. The authors propose a magnetohydrodynamic (MHD) mechanism that naturally produces such a sheath within a “magnetic‑pressure valley” – a region of reduced total magnetic pressure sandwiched between two peaks generated by the poloidal (vertical) and toroidal (azimuthal) field components. In this configuration the rotating sheath plasma experiences an outward centrifugal force, which is balanced by the inward hoop stress of the toroidal field. The poloidal field is concentrated near the jet axis by a converging plasma inflow, while the toroidal field is built up outside the jet cone by a poloidal electric current that circulates through the jet interior.

To explore the consequences of this picture the authors adopt a set of simplifying assumptions: ideal, non‑viscous, non‑resistive MHD; axisymmetry; steady‑state flow; and non‑relativistic speeds. They write down the continuity, momentum, energy, and induction equations in a cylindrical geometry and include the gravitational potential of the central mass. By prescribing plausible radial scalings for the magnetic components (poloidal ∝ r⁻², toroidal ∝ r⁻¹) and focusing on the asymptotic region far from the jet footpoint, they reduce the problem to a set of coupled ordinary differential equations for density, pressure, velocity, and magnetic field.

Two distinct families of solutions emerge.

1. Marginally bound (viral‑temperature) jets – In this class the plasma temperature declines roughly as T ∝ r⁻¹. The pressure gradient and the MHD forces (magnetic tension and centrifugal force) are insufficient to completely overcome gravity, even at arbitrarily large radii. Consequently the jet remains only marginally unbound; its speed asymptotically approaches a finite value and the flow is partially restrained by the central gravitational field.
2. Isothermal jets – Here the plasma is assumed to be isothermal (p ∝ ρ). The pressure gradient exactly cancels the gravitational pull, so gravity disappears from the momentum balance. The jet is then accelerated solely by the MHD forces, primarily the toroidal hoop stress and the centrifugal term. This solution yields a continuously accelerating outflow that can reach high Lorentz factors (in a relativistic extension) and remains well collimated by the toroidal field.

The authors argue that these two theoretical regimes correspond to the two Fanaroff‑Riley (FR) classes of radio galaxies. FR I sources, which display slower, flaring jets that decelerate on kiloparsec scales, are identified with the marginally bound, viral‑temperature solution. FR II sources, characterized by highly collimated, relativistic jets terminating in bright hotspots, are associated with the isothermal, MHD‑driven solution.

The paper also discusses the sensitivity of the pressure‑valley configuration to the details of plasma inflow, the distribution of the poloidal current, and the sign of the toroidal field. It acknowledges several limitations: the neglect of viscosity, resistivity, radiative cooling, and relativistic effects; the assumption of simple power‑law magnetic profiles; and the restriction to a one‑dimensional radial analysis. The authors suggest that future work should involve three‑dimensional relativistic MHD simulations, direct measurements of magnetic field geometry in jets (e.g., via Faraday rotation mapping), and inclusion of realistic thermodynamics to test the robustness of the two‑solution picture.

In summary, the study provides a physically motivated MHD framework that links the observed spine‑sheath morphology to a magnetic‑pressure valley, and it offers a plausible explanation for the dichotomy between FR I and FR II jets through two analytically tractable asymptotic solutions.