Relativistic Acceleration of Magnetically Driven Jets

Abstract

We present an analytical model for describing highly relativistic acceleration of magnetically driven jets, within the framework of ideal MHD for cold, stationary and axisymmetric outflows. Our novel procedure is to treat the wind equation as an algebraic relation between the relativistic Alfvén Mach-number and the poloidal electric to toroidal magnetic field amplitudes ratio $\xi$. This allows us to obtain easily the wind solutions for trans-fast-magnetosonic flows, together with the required range of $\xi$. Then, to determine the spatial variation of $\xi$, we solve approximately the Grad-Shafranov equation applied to a jet flow ejected with a very large total specific energy $E$ and confined within a very small opening angle. Our trans-fast-magnetosonic model provides a closed-form expression for the transition from a magnetically dominated flow to a kinetic-energy dominated one, which occurs in the sub-asymptotic region far beyond the light cylinder of the radius $R_{\mathrm{L}}$. Importantly, we find that the equipartition between magnetic and kinetic energies is realized at a cylindrical radius of order of $R_{\mathrm{L}}E/c^2$, and confirm that the further conversion of magnetic to kinetic energy proceeds logarithmically with distance in the asymptotic region. Finally, we discuss briefly the astrophysical implications of our model for jets originating from active galactic nuclei.

23 pages, 7 eps figures, submitted to ApJ

References in corpus (4)

• Internal shocks in the jets of radio-loud quasars
• Characteristic X-ray Variability of TeV Blazars: Probing the Link between the Jet and the Central Engine
• Screw instability in black hole magnetospheres and a stabilizing effect of field-line rotation
• Magnetically driven superluminal motion from rotating black holes

Cited by in corpus (21)

• General Relativistic Magnetohydrodynamic Simulations of Jet Formation and Large-Scale Propagation from Black Hole Accretion Systems
• Magnetic acceleration of ultra-relativistic jets in gamma-ray burst sources
• Efficiency of Magnetic to Kinetic Energy Conversion in a Monopole Magnetosphere
• Parabolic Jets from the Spinning Black Hole in M87
• Innermost collimation structure of the M87 jet down to ~ten Schwarzschild radii
• Kinematics of the M87 jet in the collimation zone: gradual acceleration and velocity stratification
• Magnetization degree at the jet base of M87 derived from the event horizon telescope data: Testing magnetically driven jet paradigm
• Ideal MHD solution to the $\sigma$ problem in Crab-like pulsar winds and general asymptotic analysis of magnetized outflows
• Sub-milliarcsecond Imaging of SgrA* and M87
• Fast-spinning black holes inferred from symmetrically limb-brightened radio jets
• Global asymptotic solutions for relativistic MHD jets and winds
• Properties of Trans-fast Magnetosonic Jets in Black Hole Magnetospheres
• Implications from the velocity profile of the M87 jet: a possibility of a slowly rotating black hole magnetosphere
• Relativistic outflows from a GRMHD mean-field disk dynamo
• Signatures of Black Hole Spin and Plasma Acceleration in Jet Polarimetry
• The efficiency of the magnetic acceleration in relativistic jets
• Constraints on the Evolution of Black Hole Spin due to Magnetohydrodynamic Accretion
• Matter density distribution of general relativistic highly magnetized jets driven by black holes
• Relativistic jet acceleration region in a black hole magnetosphere
• On the possible core shift break in relativistic jets
• Formation of relativistic MHD jets: stationary state solutions & numerical simulations