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 $\mathrm{Au}+\mathrm{Au}, \mathrm{Cu}+\mathrm{Au}$, and $O+O$ collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV. The particle yields, mean transverse momenta, two-particle and four-particle cumulant elliptic flows ($v_2\left\{2\right\}$ and $v_2\left\{4\right\}$) from our calculation agree with the currently existing data from RHIC. Different centrality dependencies of the flow fluctuations, quantified by the $v_2\left\{4\right\}/v_2\left\{2\right\}$ ratio, are found for different collision systems due to their different sizes and shapes. By comparing $v_2\left\{4\right\}/v_2\left\{2\right\}$ between different hadron species, and comparing $v_2\left\{4\right\}/v_2\left\{2\right\}$ to the initial state geometric fluctuations quantified by the cumulant eccentricity ratio ${\varepsilon }_2\left\{4\right\}/{\varepsilon }_2\left\{2\right\}$, we find that while the initial state fluctuations are the main source of the $v_2$ fluctuations in large collision systems, other sources like nonlinear hydrodynamic response, hadronization, and hadronic afterburner can significantly affect the $v_2$ fluctuations in small systems.