Estimate magnetic field strength in heavy-ion collisions via the direct photon elliptic flow

There must be electromagnetic fields created during high-energy heavy-ion collisions. As the quark-gluon plasma (QGP) starts to evolve hydrodynamically, although these fields may become weak comparing to the energy scales of the strong interaction, they are potentially important to some electromagnetic probes. In this work, we focus on the dissipative corrections in QGP due to the presence of a weak external magnetic field, and calculate accordingly the induced photon radiation in the framework of viscous hydrodynamics. By event-by-event hydrodynamical simulations, the experimentally measured direct photon elliptic flow can be well reproduced. Correspondingly, the direct photon elliptic flow implies a magnetic field strength around 0.1$m_\pi^2 \sim 10^{16}$ G. This is indeed a weak field in heavy-ion physics that is compatible to the theoretical predictions, however, it is still an ultra-strong magnetic field in nature.