Correlation between event multiplicity and elliptic flow parameter

The elliptic flow parameter (component), $v_2$, in the Fourier expansion of event-by-event charged particle multiplicity azimuthal distribution in the momentum space is studied by taking into account the multiplicity fluctuations. The correlations between charge multiplicity and impact parameter as well as between elliptic flow parameter and impact parameter (multiplicity) are investigated by both the parton and hadron cascade model PACIAE and a multiple phase transport model AMPT. A discussion is given for the event-wise average and particle-wise average in the definition of elliptic flow parameter.