Magnetic acceleration of ultrarelativistic jets in gamma-ray burst sources

Abstract

We present numerical simulations of axisymmetric, magnetically driven outflows that reproduce the inferred properties of ultrarelativistic gamma‐ray burst (GRB) jets. These results extend our previous simulations of outflows accelerated to moderately relativistic speeds, which are applicable to jets of active galactic nuclei. In contrast to several recent investigations, which have employed the magnetodynamics approximation, our numerical scheme solves the full set of equations of special relativistic, ideal magnetohydrodynamics, which enables us to explicitly calculate the jet velocity and magnetic‐to‐kinetic energy conversion efficiency – key parameters of interest for astrophysical applications. We confirm that the magnetic acceleration scheme remains robust into the ultrarelativistic regime, as previously indicated by semi‐analytic self‐similar solutions. We find that all current‐carrying outflows exhibit self‐collimation and consequent acceleration near the rotation axis, but that unconfined outflows lose causal connectivity across the jet and therefore do not collimate or accelerate efficiently in their outer regions. We show that magnetically accelerated jets confined by an external pressure that varies as z−α (0 < α≤ 2) assume a paraboloidal shape z∝ra (where r, z are cylindrical coordinates and a > 1), and we obtain analytic expressions for the one‐to‐one correspondence between the pressure distribution and the asymptotic jet shape. We demonstrate that the acceleration efficiency of jets with paraboloidal streamlines is ≳50 per cent, with the numerical value being higher the lower the initial magnetization. We derive asymptotic analytic expressions for the acceleration of initially cold outflows along paraboloidal streamlines and verify that they provide good descriptions of the simulated flows. Our modelled jets (corresponding to 3/2 < a < 3) attain Lorentz factors Γ≳ 102 on scales ∼ 1010–1012 cm, consistent with the possibility that long/soft GRB jets are accelerated within envelopes of collapsing massive stars, and Γ≳ 30 on scales ∼9 × 108–3 × 1010 cm, consistent with the possibility that short/hard GRB jets are accelerated on scales where they can be confined by moderately relativistic winds from accretion discs. We also find that Γθv∼ 1 for outflows that undergo an efficient magnetic‐to‐kinetic energy conversion, where θv is the opening half‐angle of the poloidal streamlines. This relation implies that the γ‐ray emitting components of GRB outflows accelerated in this way are very narrow, with θv≲ 1° in regions where Γ≳ 100, and that the afterglow light curves of these components would either exhibit a very early jet break or show no jet break at all.

Uncovering the physics behind the blazar sequence using a realistic model for jet emission

“…This is consistent with state of the art numerical simulations which show the jet base starts magnetically dominated and accelerates in the parabolic region reaching a terminal bulk Lorentz factor at equipartition after which the jet becomes ballistic and conical [2], [3], [4] and [5]. Here we use an emission model with a magnetically dominated, accelerating, parabolic base transitioning at equipartition to a slowly decelerating, conical jet to test this emerging picture of jets and to try to determine their properties.…”

“…This can then be used to constrain the radius of the transition region of the jet from fitting to the SED. We find that in order to fit to the synchrotron break in FSRQs we require that the transition region occurs at a 05008-p. 3 The Innermost Regions of Relativistic Jets and Their Magnetic Fields 05008-p. 4 Alternatively, we can consider a universal jet geometry where all jets have the same inner structure as M87 scaling linearly with black hole mass, with a transition region occurring at 10 5 r s . In Figure 3 we show the inferred black hole masses of the blazar fits in this scenario.…”

Acceleration and Collimation of Relativistic Magnetohydrodynamic Disk Winds

“…However, we note that when increasing σ , the energy conversion efficiency decreases, a situation commonly denoted as σ -problem in pulsar winds (Rees & Gunn 1974;Kennel & Coroniti 1984). Several authors have recently addressed this issue with partly controversial results (Komissarov et al 2009;Tchekhovskoy et al 2009;Lyubarsky 2009), so that after the successful acceleration toward relativistic speeds, Poynting flux could still remain and one is tempted to ask: is there a σ -problem for AGN jets? The simulations presented here are not fit to answer this question satisfactory.…”

Polarized Emission from Gamma-Ray Burst Jets

“…In an alternative model, the rotation of a BH-accretion disk system might cause a helical outgoing Magnetohydrodynamic (MHD) wave which accelerates material frozen into the field lines. In a magnetic jet, globally ordered magnetic fields are expected to present [16]. As we discuss below, by measuring the degree of linear polarization in early-time emission, we should be able to distinguish the competing models.…”