Abstract
In the initial stage of relativistic heavy-ion collisions, strong magnetic fields appear due to the large velocity of the colliding charges. The evolution of these fields appears as a novel and intriguing feature in the fluid-dynamical description of heavy-ion collisions. In this work, we study analytically the one-dimensional, longitudinally boost-invariant motion of an ideal fluid in the presence of a transverse magnetic field. Interestingly, we find that, in the limit of ideal magnetohydrodynamics, i.e., for infinite conductivity, and irrespective of the strength of the initial magnetization, the decay of the fluid energy density e with proper time τ is the same as for the time-honoured “Bjorken flow” without magnetic field. Furthermore, when the magnetic field is assumed to decay ∼τ−a, where a is an arbitrary number, two classes of analytic solutions can be found depending on whether a is larger or smaller than one. In summary, the analytic solutions presented here highlight that the Bjorken flow is far more general than formerly thought. These solutions can serve both to gain insight on the dynamics of heavy-ion collisions in the presence of strong magnetic fields and as testbeds for numerical codes.
Highlights
Very intense magnetic fields of the order of B ∼ 1018 − 1019 G are produced orthogonal to the direction of motion in a typical non-central Au-Au collision at top RHIC energy (√i.e., with a centre-of-momentum energy per nucleon pair of sNN 200 GeV)
In the presence of a strong magnetic field as created in heavy-ion collisions, a charge current will be induced in the quark-gluon plasma (QGP), leading to what is known as the “chiral magnetic effect” (CME) [3]
Driven by the interest in exploring the effects of strong magnetic fields in the hydrodynamical description of relativistic heavy-ion collisions, we have studied the evolution of the fluid energy density following the instant of the collision and considering an ultrarelativistic fluid with equation of state (EOS) p = c2s e
Summary
Very intense magnetic fields of the order of B ∼ 1018 − 1019 G are produced orthogonal to the direction of motion in a typical non-central Au-Au collision at top RHIC energy (√i.e., with a centre-of-momentum energy per nucleon pair of sNN 200 GeV). The produced magnetic fields show large variations and can be very large in some places where the corresponding fluid energy-density is small In these cases, even for a quickly decaying initial magnetic field we may locally have σ > 1 up to the time when the hydrodynamical expansion starts. Even for a quickly decaying initial magnetic field we may locally have σ > 1 up to the time when the hydrodynamical expansion starts It is not the goal of this work to investigate the temporal evolution of the magnetic field produced in heavy-ion collisions. We indicate three-vectors as bold face letter with an arrow and use bold letters without an arrow to denote four-vectors and tensors
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