Event-by-event distribution of the ratio of magnetic field energy to initial fluid energy density insNN=200GeV Au-Au collisions

Abstract

We estimate the event-by-event (e-by-e) distribution of the ratio $(\ensuremath{\sigma})$ of the magnetic and electric field energy density to the fluid energy density in the transverse plane of Au-Au collisions at $\sqrt{{s}_{NN}}=200$ GeV. A Monte Carlo (MC) Glauber model is used to calculate $\ensuremath{\sigma}$ in the transverse plane for impact parameter $b=0$, 12 fm at time ${\ensuremath{\tau}}_{i}\ensuremath{\sim}0.5$ fm. The fluid energy density is obtained by using Gaussian smoothing with two different smoothing parameter ${\ensuremath{\sigma}}_{g}=0.25$, 0.5 fm. For $b=0\phantom{\rule{0.28em}{0ex}}\mathrm{fm}$ collisions $\ensuremath{\sigma}$ is found to be $\ensuremath{\ll}1$ in the central region of the fireball and $\ensuremath{\sigma}\ensuremath{\gtrsim}1$ at the periphery. For $b=12$ fm collisions $\ensuremath{\sigma}\ensuremath{\gtrsim}1$ is observed for some events. The e-by-e correlation between $\ensuremath{\sigma}$ and the fluid energy density $(\ensuremath{\varepsilon})$ is studied. We did not find strong correlation between $\ensuremath{\sigma}$ and $\ensuremath{\varepsilon}$ at the center of the fireball, whereas they are mostly anticorrelated at the periphery of the fireball.