We present bhac-qgp, a new numerical code to simulate the evolution of matter created in heavy-ion collisions in the presence of electromagnetic fields. It is derived from the Black Hole Accretion Code ( bhac), which has been designed to model astrophysical processes in a general-relativistic magnetohydrodynamical description. As the original Black Hole Accretion Code, bhac-qgp benefits from the use of adaptive mesh refinement, which allows us to dynamically adjust the resolution where necessary and makes use of time-dependent Milne coordinates and the ultrarelativistic equation of state, <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>P</mi><mo>=</mo><mi>e</mi><mo>/</mo><mn>3</mn></mrow></math>. We demonstrate that bhac-qgp accurately passes a number of systematic and rigorous tests.

Markus Mayer

Ashutosh Dash

Gabriele Inghirami

Germany

Hannah Elfner

Ireland

Luciano Rezzolla

Dirk H. Rischke

Three-dimensional magnetohydrodynamics simulations of relativistic heavy-ion collisions with a black-hole accretion code adapted for quark-gluon plasma (BHAC-QGP). I. Methods and tests

We present bhac-qgp, a numerical code to simulate the evolution of matter created in heavy-ion collisions. bhac-qgp is based on the Black Hole Accretion Code ( bhac), which has been designed to model astrophysical processes through the solution of the equations of general-relativistic magnetohydrodynamics. Like the mother code, bhac-qgp uses adaptive mesh refinement, which allows for a dynamic adjustment of the resolution in regions of the computational domain where a particularly high accuracy is needed. We here discuss a number of applications of bhac-qgp to Au-Au collisions at the BNL Relativistic Heavy-Ion Collider energies and show that the code is able to reproduce results of other simulations of these scenarios, but with much higher accuracy.

Three-dimensional magnetohydrodynamics simulations of relativistic heavy-ion collisions with a black-hole accretion code adapted for quark-gluon plasma (BHAC-QGP). II. Application to Au-Au collisions

To assess the degree of equilibration of the matter created in heavy-ion reactions at low to intermediate beam energies, a hadronic transport approach (SMASH) is employed. By using a coarse-graining method, we compute the energy momentum tensor of the system at fixed time steps and evaluate the degree of isotropy of the diagonal terms and the relative magnitude of the off-diagonal terms. This study focuses mostly on Au+Au collisions in the energy range $${\sqrt{s}_\mathrm{NN}}$$ <math> <msub> <msqrt> <mi>s</mi> </msqrt> <mi>NN</mi> </msub> </math> = 2.4–7.7 GeV, but central collisions of lighter ions like C+C, Ar+KCl and Ag+Ag are considered as well. We find that the conditions concerning local equilibration for a hydrodynamic description are reasonably satisfied in a large portion of the system for a significant amount of time (several fm/c) when considering the average evolution of many events, yet they are rarely fulfilled on an event by event basis. This is relevant for the application of hybrid approaches at low beam energies as they are or will be reached by the HADES experiment at GSI, the future CBM experiment at FAIR as well as the beam energy scan program at RHIC.

The applicability of hydrodynamics in heavy ion collisions at $$\sqrt{s_\mathrm{NN}}$$ <math> <msqrt> <msub> <mi>s</mi> <mi>NN</mi> </msub> </msqrt> </math> = 2.4–7.7 GeV

The HADES experiment at GSI has recently provided data on the flow coefficients <math><msub><mrow><mi>v</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>4</mn></mrow></msub></math> for protons in Au+Au reactions at <math><msub><mrow><mi>E</mi></mrow><mrow><mi>lab</mi></mrow></msub><mo>=</mo><mn>1.23</mn><mspace width="0.25em"></mspace><mi>A</mi><mtext>GeV</mtext></math> (or <math><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>NN</mi></mrow></msub></mrow></msqrt><mo>=</mo><mn>2.4</mn><mspace width="0.25em"></mspace><mtext>GeV</mtext></math>). This data allows to estimate the shear viscosity over entropy density ratio, <math><mi>η</mi><mo>/</mo><mi>s</mi></math> at low energies via a coarse graining analysis of the UrQMD transport simulations of the flow harmonics in comparison to the experimental data. By this we can provide for the first time an estimate of <math><mi>η</mi><mo>/</mo><mi>s</mi><mo>≈</mo><mn>0.65</mn><mo>±</mo><mn>0.15</mn></math> (or <math><mo>(</mo><mn>8</mn><mo>±</mo><mn>2</mn><mo>)</mo><mspace width="0.2em"></mspace><msup><mrow><mo>(</mo><mn>4</mn><mi>π</mi><mo>)</mo></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>) at such low energies.

Tom Reichert

Finland

Marcus Bleicher

A first estimate of / in Au+Au reactions at E = 1.23 GeV

At the earliest times after a heavy-ion collision, the magnetic field created by the spectator nucleons will generate an extremely strong, albeit rapidly decreasing in time, magnetic field. The impact of this magnetic field may have detectable consequences, and is believed to drive anomalous transport effects like the Chiral Magnetic Effect (CME). We detail an exploratory study on the effects of a dynamical magnetic field on the hydrodynamic medium created in the collisions of two ultrarelativistic heavy-ions, using the framework of numerical ideal MagnetoHydroDynamics (MHD) with the ECHO-QGP code. In this study, we consider a magnetic field captured in a conducting medium, where the conductivity can receive contributions from the electromagnetic conductivity $$\sigma $$ <math><mi>σ</mi></math> and the chiral magnetic conductivity $$\sigma _{\chi }$$ <math><msub><mi>σ</mi><mi>χ</mi></msub></math> . We first study the elliptic flow of pions, which we show is relatively unchanged by the introduction of a magnetic field. However, by increasing the magnitude of the magnetic field, we find evidence for an enhancement of the elliptic flow in peripheral collisions. This effect is stronger at RHIC than the LHC, and it is evident already at intermediate collision centralities. Next, we explore the impact of the chiral magnetic conductivity on electric charges produced at the edges of the fireball. This initial $$\sigma _\chi $$ <math><msub><mi>σ</mi><mi>χ</mi></msub></math> can be understood as a long-wavelength effective description of chiral fermion production. We then demonstrate that this chiral charge, when transported by the MHD medium, produces a charge dipole perpendicular to the reaction plane which extends a few units in rapidity. Assuming charge conservation at the freeze-out surface, we show that the produced charge imbalance can have measurable effects on some experimental observables, like $$v_1$$ <math><msub><mi>v</mi><mn>1</mn></msub></math> or $$\langle \sin \phi \rangle $$ <math><mrow><mo>⟨</mo><mo>sin</mo><mi>ϕ</mi><mo>⟩</mo></mrow></math> . This demonstrates the ability of a MHD fluid to transport the signature of the initial chiral magnetic fields to late times. We also comment on the limitations of the ideal MHD approximation and detail how further development of a dissipative-resistive model can provide a more realistic description of the QGP.

Mark Mace

South Korea

Yuji Hirono

Italy

Luca Del Zanna

United States

Dmitri Kharzeev

Magnetic fields in heavy ion collisions: flow and charge transport

We present a study of the elliptic flow and $$R_{AA}$$ <math><msub><mi>R</mi><mrow><mi>AA</mi></mrow></msub></math> of $$\text {D}$$ <math><mtext>D</mtext></math> and $$\bar{\text {D}}$$ <math><mover><mrow><mtext>D</mtext></mrow><mrow><mo>¯</mo></mrow></mover></math> mesons in Au+Au collisions at FAIR energies. We propagate the charm quarks and the $$\text {D}$$ <math><mtext>D</mtext></math> mesons following a previously applied Langevin dynamics. The evolution of the background medium is modeled in two different ways: (I) we use the UrQMD hydrodynamics + Boltzmann transport hybrid approach including a phase transition to QGP and (II) with the coarse-graining approach employing also an equation of state with QGP. The latter approach has previously been used to describe di-lepton data at various energies very successfully. This comparison allows us to explore the effects of partial thermalization and viscous effects on the charm propagation. We explore the centrality dependencies of the collisions, the variation of the decoupling temperature and various hadronization parameters. We find that the initial partonic phase is responsible for the creation of most of the $$\text {D}/\bar{\text {D}}$$ <math><mrow><mtext>D</mtext><mo>/</mo><mover><mrow><mtext>D</mtext></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> mesons elliptic flow and that the subsequent hadronic interactions seem to play only a minor role. This indicates that $$\text {D}/\bar{\text {D}}$$ <math><mrow><mtext>D</mtext><mo>/</mo><mover><mrow><mtext>D</mtext></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> mesons elliptic flow is a smoking gun for a partonic phase at FAIR energies. However, the results suggest that the magnitude and the details of the elliptic flow strongly depend on the dynamics of the medium and on the hadronization procedure, which is related to the medium properties as well. Therefore, even at FAIR energies the charm quark might constitute a very useful tool to probe the quark–gluon plasma and investigate its physics.

Hendrik Hees

Stephan Endres

Juan Torres-Rincon

Elliptic flow and $$R_{AA}$$ <math><msub><mi>R</mi><mrow><mi>AA</mi></mrow></msub></math> of $$\text {D}$$ <math><mtext>D</mtext></math> mesons at FAIR comparing the UrQMD hybrid model and the coarse-graining approach

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 magneto-hydrodynamics (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.

Andrea Beraudo

Iran

Mohsen Haddadi Moghaddam

Francesco Becattini

Numerical magneto-hydrodynamics for relativistic nuclear collisions

We provide evidence from full numerical solutions that the hydrodynamical evolution of initial density fluctuations in heavy ion collisions can be understood order-by-order in a perturbative series in deviations from a smooth and azimuthally symmetric background solution. To leading linear order, modes with different azimuthal wave numbers do not mix. When quadratic and higher order corrections are numerically sizable, they can be understood as overtones with corresponding wave numbers in a perturbative series. Several findings reported in the recent literature result naturally from the general perturbative series formulated here.