Fluid velocity from transverse momentum spectra

We show that the momentum distributions calculated in ideal hydrodynamic simulations of nucleus-nucleus collisions are determined, to a good approximation, by the distribution of the transverse velocity of the fluid. We compute the fluid velocity distribution that gives the best fit to experimental data on Pb+Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV. We obtain reasonable fits up to $p_t\sim 6$ GeV, much beyond the range where hydrodynamics is usually applied. However, the fit is not perfect, even at low $p_t$. We actually argue that an ideal hydrodynamic calculation cannot fit simultaneously all identified particle spectra, irrespective of the specific implementation. In particular, data display a significant excess of pions at low $p_t$, whose physical interpretation is discussed. Data also show that the distribution of the fluid velocity becomes broader as the collision becomes less central. This broadening is explained by event-by-event hydrodynamic calculations, where it results from the centrality dependence of initial state fluctuations.