An open question in the field of heavy-ion collisions is to what extent the size of initial inhomogeneities in the system affects measured observables. Here we present a method to smooth out these inhomogeneities with minimal effect on global properties, in order to quantify the effect of shortrange features of the initial state. We show a comparison of hydrodynamic predictions with original and smoothened initial conditions for four models of initial conditions and various observables. Integrated observables (integrated vn, scaled vn distributions, normalized symmetric cumulants, event-plane correlations) as well as most differential observables (vn(pT )) show little dependence on the inhomogeneity sizes, and instead are sensitive only to the largest-scale geometric structure. However other differential observables such as the flow factorization ratio and sub-leading principal components are more sensitive to the granularity and could be a good tool to probe the short-scale dynamics of the initial stages of a heavy-ion collision, which are not currently well understood.

We carry out a principal component analysis of fluctuations in a hydrodynamic simulation of heavy-ion collisions, and compare with experimental data from the CMS collaboration. The leading and subleading principal components of elliptic and triangular flow reproduce the trends seen in data. By contrast, the principal components of multiplicity fluctuations show an interesting difference in their pT dependence for simulations compared to experimental data. Specifically, the leading component increases with pT in hydrodynamics, while it is constant in experiment. In order to understand how the leading and subleading modes arise, we construct a toy model where the principal components have a simple analytic form. We show how the PCA components depend on fluctuations of the average transverse momentum and of the total multiplicity, as well as correlations between the two, and we verify that hydrodynamic simulations agree with the predictions of the toy model. The difference in the momentum trend is likely due to the fact that hydrodynamic models typically have transverse momentum fluctuations that are larger than seen experimentally.

Disentangling the effect of initial conditions and medium properties is an open question in the field of relativistic heavyion collisions. We argue that, while one can study the impact of initial inhomogeneities by varying their size, it is important to maintain the global properties fixed. We present a method to do this. We show that many observables are insensitive to the the hot spot sizes, including integrated v n , scaled distributions of v n , symmetric cumulants, eventplane correlations, and differential v n (p T ). We find however that the factorization breaking ratio r n and sub-leading component in a Principal Component Analysis are more sensitive to the initial granularity and can be used to probe short-scale features of the initial density.

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