Event-by-event distribution of magnetic field energy over initial fluid energy density in $\sqrt{s_{\rm NN}}$= 200 GeV Au-Au collisions

Abstract

We estimate the event-by-event (e-by-e) distribution of the ratio ($\sigma$) of the magnetic field energy to the fluid energy density in the transverse plane of Au-Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV. A Monte-Carlo (MC) Glauber model is used to calculate the $\sigma$ in the transverse plane for impact parameter b=0, 12 fm at time $\tau_i\sim$0.5 fm. The fluid energy density is obtained by using Gaussian smoothing with two different smoothing parameter $\sigma_g$=0.25 , 0.5 fm. For $b=0~\rm fm$ collisions $\sigma$ is found to be $\ll$ 1 in the central region of the fireball and $\sigma\gtrsim$ 1 at the periphery. For b=12 fm collisions $\sigma\gtrsim$ 1. The e-by-e correlation between $\sigma$ and the fluid energy density ($\varepsilon$) is studied. We did not find strong correlation between $\sigma$ and $\varepsilon$ at the centre of the fireball, whereas they are mostly anti-correlated at the periphery of the fireball.