Numerical magneto-hydrodynamics for relativistic nuclear collisions

TL;DR

This paper introduces an enhanced numerical code for relativistic magnetohydrodynamics that models electromagnetic effects in nuclear collisions, providing new insights into magnetic field evolution and its impact on quark-gluon plasma dynamics.

Contribution

The paper presents the first implementation of electromagnetic fields in the ECHO-QGP code for relativistic heavy-ion collisions, enabling self-consistent RMHD simulations of the quark-gluon plasma.

Findings

Magnetic fields in non-central collisions are estimated to be significant.

In ideal RMHD, magnetic fields do not substantially alter elliptic flow.

Further studies are needed to include dissipative effects and initial condition variations.

Abstract

We present an improved version of the ECHO-QGP numerical code, which self-consistently includes for the first time the effects of electromagnetic fields within the framework of relativistic magnetohydrodynamics (RMHD). We discuss results of its application in relativistic heavy-ion collisions in the limit of infinite electrical conductivity of the plasma. After reviewing the relevant covariant $3\!+\!1$ formalisms, we illustrate the implementation of the evolution equations in the code and show the results of several tests aimed at assessing the accuracy and robustness of the implementation. After providing some estimates of the magnetic fields arising in non-central high-energy nuclear collisions, we perform full RMHD simulations of the evolution of the Quark-Gluon Plasma in the presence of electromagnetic fields and discuss the results. In our ideal RMHD setup we find that the magnetic field developing in non-central collisions does not significantly modify the elliptic-flow of the final hadrons. However, since there are uncertainties in the description of the pre-equilibrium phase and also in the properties of the medium, a more extensive survey of the possible initial conditions as well as the inclusion of dissipative effects are indeed necessary to validate this preliminary result.