System-size and shape dependencies of collective-flow fluctuations in relativistic nuclear collisions

Quantum fluctuations plays an essential role in forming the collective flow of hadrons observed in relativistic heavy-ion collisions. Event-by-event fluctuations of the collective flow can arise from various sources, such as the fluctuations in the initial geometry, hydrodynamic expansion, hadronization, and hadronic evolution of the nuclear matter, while the exact contribution from each source is still an open question. Using a (3+1)-dimensional relativistic hydrodynamic model coupled to a Monte Carlo Glauber initial condition, Cooper-Frye particlization and a hadronic transport model, we explore the system-size and shape dependencies of the collective-flow fluctuations in Au+Au, Cu+Au, and O+O collisions at √sNN=200 GeV. The particle yields, mean transverse momenta, two-particle and four-particle cumulant elliptic flows (v₂2 and v₂4) from our calculation agree with the currently existing data from RHIC. Different centrality dependencies of the flow fluctuations, quantified by the v₂4/v₂2 ratio, are found for different collision systems due to their different sizes and shapes. By comparing v₂4/v₂2 between different hadron species, and comparing v₂4/v₂2 to the initial state geometric fluctuations quantified by the cumulant eccentricity ratio ε₂4/ε₂2, we find that while the initial state fluctuations are the main source of the v₂ fluctuations in large collision systems, other sources like nonlinear hydrodynamic response, hadronization, and hadronic afterburner can significantly affect the v₂ fluctuations in small systems.