Onset of $J/ψ$ Melting in Quark-Gluon Fluid at RHIC

A strong $J/ψ$ suppression in central Au+Au collisions has been observed by the PHENIX experiment at the Relativistic Heavy Ion Collider (RHIC). We develop a hydro+$J/ψ$ model in which hot quark-gluon matter is described by the full (3+1)-dimensional relativistic hydrodynamics and $J/ψ$ is treated as an impurity traversing through the matter. The experimental $J/ψ$ suppression pattern in mid-rapidity is reproduced well by the sequential melting of $χ_{\rm c}$, $ψ'$, and $J/ψ$ in dynamically expanding fluid. The melting temperature of directly produced $J/ψ$ is well constrained by the participant-number dependence of the $J/ψ$ suppression and is found to be about $2.T_{\rm c}$ with $T_{\rm c}$ being the pseudo-critical temperature.