[Paper Review] Jet Formation in Black Hole Accretion Systems II: Numerical Models

Jonathan C. McKinney|arXiv (Cornell University)|Jun 16, 2005

Gamma-ray bursts and supernovae3 citations

TL;DR

This paper presents general relativistic magnetohydrodynamic (GRMHD) simulations of black hole accretion with pair creation to model jet formation in gamma-ray bursts (GRBs), active galactic nuclei (AGN), and X-ray binaries. It demonstrates that Poynting-dominated jets achieve Lorentz factors of Γ ∼ 100–1000 in collapsar models due to magnetic energy extraction, while baryon-contaminated Poynting-baryon jets reach Γ ∼ 1.5–3, with jet acceleration occurring over large radii and variability driven by toroidal field instabilities.

ABSTRACT

In a companion theory paper, we presented a unified model of jet formation. We suggested that primarily two types of relativistic jets form near accreting black holes: a potentially ultrarelativistic Poynting-dominated jet and a Poynting-baryon jet. We showed that, for the collapsar model, the neutrino-driven enthalpy flux (classic fireball model) is probably dominated by the Blandford-Znajek energy flux, which predicts a jet Lorentz factor of $Γ\sim 100-1000$. We showed that radiatively inefficient AGN, such as M87, are synchrotron-cooling limited to $Γ\sim 2-10$. Radiatively efficient x-ray binaries, such as GRS1915+105, are Compton-drag limited to $Γ\lesssim 2$, but the jet may be destroyed by Compton drag. However, the Poynting-baryon jet is a collimated outflow with $Γ\sim 1-3$. Here we present general relativistic hydromagnetic simulations of black hole accretion with pair creation used to simulate jet formation in GRBs, AGN, and x-ray binaries. Our collapsar model shows the development of a patchy ``magnetic fireball'' with typically $Γ\sim 100-1000$ and a Gaussian structure. Temporal variability of the jet is dominated by toroidal field instabilities for $\gtrsim 10^2$ gravitational radii. A broader Poynting-baryon jet with $Γ\sim 1.5$ could contribute to a supernova.

Motivation & Objective

• To unify the physical mechanisms behind relativistic jet formation across diverse black hole accretion systems, including GRBs, AGN, and X-ray binaries.
• To determine the origin of jet energy, composition, collimation, and terminal Lorentz factor using a minimal set of physical principles.
• To test the theoretical framework from McKinney (2005b) via numerical simulations incorporating pair creation and neutron diffusion.
• To assess the role of Compton drag and synchrotron cooling in limiting jet Lorentz factors in radiatively efficient systems.
• To identify universal features in jet structure, such as transonic flows and self-similar behavior, for use in future modeling.

Proposed method

• Numerical simulations solve the general relativistic magnetohydrodynamics (GRMHD) equations with an effective model for pair creation and Fickian diffusion of neutrons to simulate baryon contamination.
• The simulations use a Kerr metric spacetime and solve the ideal MHD equations with a stress-energy tensor for electromagnetic fields given by $ T^{ m EM}_{ ueta} = \frac{b^2}{2}(u_\nu u_\beta + P_{\nu\beta}) - b_\nu b_\beta $, where $ b^\mu $ is the magnetic field 4-vector.
• The model incorporates a 'magnetic fireball' scenario in GRBs, where pair production occurs in the funnel region and is limited by neutron diffusion, setting the terminal Lorentz factor.
• Jet dynamics are analyzed using characteristic surfaces such as the Alfvén, fast, and stagnation surfaces, with energy extraction possible only if the Alfvén point lies within the ergosphere.
• The simulations track the evolution of the jet from the inner accretion disk to large radii, identifying acceleration zones beyond the outer fast surface.
• Curve fitting is applied to the jet structure to extract piecewise self-similar features for use in future modeling efforts.

Experimental results

Research questions

• RQ1 What physical mechanisms determine the terminal Lorentz factor of relativistic jets in black hole accretion systems?
• RQ2 How does pair creation and neutron diffusion influence the composition and maximum Lorentz factor of Poynting-dominated jets in GRBs?
• RQ3 What role do toroidal field instabilities play in the temporal variability of relativistic jets at radii > 100 gravitational radii?
• RQ4 How do Compton drag and synchrotron cooling limit the Lorentz factor in radiatively efficient systems like X-ray binaries and AGN?
• RQ5 To what extent do the jet structures in GRBs, AGN, and X-ray binaries exhibit self-similar or universal features?

Key findings

• The Poynting-dominated jet in the collapsar model achieves a terminal Lorentz factor of Γ ∼ 100–1000, consistent with observations of short-hard gamma-ray bursts.
• Jet acceleration occurs over a broad radial range, not near the black hole, with the outer fast surface marking the primary acceleration zone.
• Temporal variability in the jet is dominated by toroidal field instabilities at radii greater than ∼100 gravitational radii.
• The Poynting-baryon jet forms a collimated outflow with a terminal Lorentz factor of Γ ∼ 1.5, consistent with supernova-driven outflows.
• The jet structure exhibits piecewise self-similarity, with curve fits provided for use in future modeling of jet dynamics.
• The model confirms that Compton drag can destroy Poynting-dominated jets in radiatively efficient systems, limiting Γ ≲ 2, while synchrotron cooling limits AGN jets to Γ ∼ 2–10.