Hydrodynamical model for $J/\psi$ suppression and elliptic flow

In a hydrodynamic model, we have studied $J/\psi$ suppression and elliptic flow in Au+Au collisions at RHIC energy $\sqrt{s}$=200 GeV. At the initial time, $J/\psi$'s are randomly distributed in the fluid. As the fluid evolve in time, the free streaming $J/\psi$'s are dissolved if the local fluid temperature exceeds a melting temperature $T_{J/\psi}$. Sequential melting of charmonium states ($\chi_c$, $\psi\prime$ and $J/\psi$), with melting temperatures $T_{\chi_c}=T_{\psi\prime} \approx 1.2T_c$, $T_{J/\psi} \approx2T_c$ and feed-down fraction $F\approx 0.3$, is consistent with the PHENIX data on $J/\psi$ suppression and near zero elliptic flow for $J/\psi$'s. It is also shown that the model will require substantial regeneration of charmoniums, if the charmonium states dissolve at temperature close to the critical temperature, $T_{\chi_c}=T_{\psi\prime} \leq T_c$, $T_{J/\psi}\approx1.2T_c$. The regenerated charmoniums will have positive elliptic flow.