Modeling of resistive relativistic astrophysical jets. Semianalytic results following a paraxial formalism

Abstract: Relativistic jets of magnetized plasma are a common high-energy astrophysical phenomenon, observed across a wide range of spatial and energy scales. In the past, semianalytic meridionally self-similar models have proven highly successful in deciphering the intricate mechanisms that determine their acceleration, collimation, and morphological characteristics. In this work, we present a modification of this formalism based on the angular expansion of the equations of general-relativistic resistive magnetohydrodynamics in the vicinity of the jet axis for the description of resistive relativistic spine jets. Our paraxial formalism allows for the inclusion of resistivity and of a realistic, variable adiabatic index equation of state in the mathematical formulation. The electric potential gradient along poloidal magnetic field lines, caused by a gradient in the rotational angular velocity of the field lines, was identified as the mechanism behind the emergence of Ohmic dissipation in resistive jets. The semianalytic solutions that we present demonstrate that Ohmic dissipation is significant only over localized dissipation regions in resistive jets. Over the extent of these regions, Ohmic dissipation weakens the thermal acceleration mechanism and can even lead to the deceleration of these outflows. Additionally, the resistive jets display enhanced collimation and a strengthening of their toroidal magnetic fields over the dissipation regions, resulting in smaller asymptotic opening angles and a more helical magnetic field structure compared to their nonresistive counterparts.