Probing the $\alpha$ cluster of ${}^{16}\mathrm{O}$ with the relativistic ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ collisions has raised great interest in the heavy ion community. However, the effects of the $\alpha$ cluster on the soft hadron observables vary largely among different studies. In this paper, we explain the differences by the compactness of the $\alpha$ cluster in oxygen, using iEBE-VISHNU hydrodynamic simulations with different initial state $\alpha$ cluster configurations. We also find several observables, such as the intensive skewness of the $\left[p_{\mathrm{T}}\right]$ correlator ${\mathrm{\Gamma }}_{p_{\mathrm{T}}}$, the harmonic flows $v_2\left\{2\right\}, v_2\left\{4\right\}, v_3\left\{2\right\}$, and the $v_n^2-\delta \left[p_{\mathrm{T}}\right]$ correlations $\rho (v_2^2,\left[p_{\mathrm{T}}\right]), \rho (v_3^2,\left[p_{\mathrm{T}}\right])$ in ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ collisions are sensitive to the compactness of the $\alpha$ cluster in the colliding nuclei, which can be used to constrain the configurations of ${}^{16}\mathrm{O}$ in the future. Our study serves as an important step toward the quantitative exploration of the $\alpha$ cluster configuration in the light nuclei with relativistic heavy ion collisions.

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• Collective flow
• Particle correlations & fluctuations
• Quark-gluon plasma
• 6 ≤ A ≤ 19