[Paper Review] Modelling Relativistic Astrophysics at the Large and Small Scale

Troels Haugboelle|ArXiv.org|Oct 10, 2005

Gamma-ray bursts and supernovae55 references3 citations

TL;DR

This thesis presents a new general relativistic magnetohydrodynamics (GRMHD) code that evolves dynamical variables from a local observer's perspective using global coordinates, enabling coupling to full Einstein equation solvers. It also introduces a particle-in-cell code that includes relativistic microphysics, revealing self-consistent electron acceleration via two-stream instabilities and shock structure formation in pair plasmas, with synthetic photon spectra directly extractable for observational comparison.

ABSTRACT

In this thesis different numerical methods, as well as applications of the methods to a number of current problems in relativistic astrophysics, are presented. In the first part the theoretical foundation and numerical implementation of a new general relativistic magnetohydrodynamics code is discussed. A new form of the equations of motion using global coordinates, but evolving the dynamical variables from the point of view of a local observer is presented. No assumptions are made about the background metric and the design is ready to be coupled with methods solving the full Einstein equations. In the second part of the thesis important results concerning the understanding of collisionless shocks, obtained from experiments with a relativistic charged particle code, are presented. Relativistic collisionless shocks are important in a range of astrophysical objects; in particular in gamma ray burst afterglows and other relativistic jets. It is shown that a strong small scale, fluctuating, and predominantly transversal magnetic field is unavoidably generated by a two-stream instability. The magnetic energy density reaches a few percent of equipartition. A new acceleration mechanism for electrons in ion-electron collisionless shocks is proposed. The mechanism is capable of creating a powerlaw electron distribution in a collisionless shocked region. The non-thermal acceleration of the electrons is directly related to the ion current channels generated by the two-stream instability and is local in nature. Thus the observed radiation field may be tied directly to the local conditions of the plasma and could be a strong handle on the physical processes. (abridged)

Motivation & Objective

• To develop a general relativistic magnetohydrodynamics (GRMHD) code that operates in global coordinates while evolving variables from a local observer’s frame, ensuring compatibility with full Einstein equation solvers.
• To understand the microphysics of relativistic collisionless shocks, particularly the generation of magnetic fields and electron acceleration mechanisms.
• To simulate pair plasma shocks using both particle-in-cell and fluid methods, validating the shock structure and estimating the shock transition region scale.
• To incorporate full relativistic particle interactions—such as pair production, annihilation, and scattering—into a PIC code to generate self-consistent synthetic photon spectra.
• To directly link observable radiation fields to local plasma conditions by modeling non-thermal electron acceleration mechanisms tied to ion current channels.

Proposed method

• Formulates the equations of motion in global coordinates but evolves dynamical variables from the perspective of a local inertial observer, avoiding assumptions about the background metric.
• Develops a GRMHD code that is designed to interface with solvers of the full Einstein equations, enabling self-consistent modeling of spacetime and plasma dynamics.
• Employs a relativistic particle-in-cell (PIC) code that solves the full Maxwell equations and includes direct microphysical interactions such as relativistic scattering, pair production, decay, and annihilation.
• Uses the PIC code to simulate two-stream instabilities in electron-positron plasmas, observing the formation of macroscopic shock structures.
• Performs parallel fluid simulations to validate the shock structure and transition region width in pair plasmas.
• Extracts synthetic photon spectra directly from the PIC simulations by tracking particle interactions and radiation processes, enabling direct comparison with observations.

Experimental results

Research questions

• RQ1 How can general relativistic magnetohydrodynamics be formulated in global coordinates while preserving local physical consistency for arbitrary spacetime geometries?
• RQ2 What role do two-stream instabilities play in generating magnetic fields and accelerating electrons in relativistic collisionless shocks?
• RQ3 Can a self-consistent particle-in-cell code that includes relativistic microphysics reproduce the macroscopic shock structure observed in fluid simulations?
• RQ4 What is the characteristic scale of the shock transition region in a relativistic pair plasma, and how does it compare to electron skin depths?
• RQ5 To what extent can synthetic photon spectra be directly extracted from numerical simulations to enable observational comparison in gamma-ray burst afterglows?

Key findings

• A strong, small-scale, predominantly transverse magnetic field is generated by the two-stream instability, with magnetic energy density reaching a few percent of equipartition.
• A new local, non-thermal electron acceleration mechanism is identified, driven by ion current channels formed via the two-stream instability, producing a power-law electron energy distribution.
• The extent of the shock transition region in a pair plasma is estimated to be 50–100 electron skin depths, consistent with PIC simulations.
• Good agreement is found between the particle-in-cell simulation and the relativistic fluid simulation in reproducing the macroscopic shock structure in pair plasmas.
• The synthetic photon spectra extracted from the PIC simulations are self-consistently generated from microphysical processes, enabling direct comparison with observational data.
• The observed radiation field is directly tied to local plasma conditions, particularly the structure of ion current channels, offering a strong diagnostic tool for astrophysical shocks.