Analytical insights into the interplay of momentum, multiplicity and the speed of sound in heavy-ion collisions

We introduce a minimal model of ultracentral heavy-ion collisions to study the relation between the speed of sound of the produced plasma and the final particles' energy and multiplicity. We discuss how the particles' multiplicity Nₜₒₜ and average energy Eₜₒₜ/Nₜₒₜ is related to the speed of sound cₛ by cₛ²=d ln (Eₜₒₜ/Nₜₒₜ)/dln Nₜₒₜ if the fluid is inviscid, its speed of sound is constant and all final particles can be measured. We show that finite rapidity cuts on the particles' multiplicity N and energy E introduce corrections between cₛ² and d ln (E/N)/dln N that depend on the system's lifetime. We study analytically these deviations with the Gubser hydrodynamic solution, finding that, for ultrarelativistic bosons, they scale as the ratio of the freezeout temperature TFO over the maximum initial temperature of the fluid T₀; the non-thermodynamic aspect of these corrections is highlighted through their dependence on the system's initial conditions.