One the many surprises to have emerged from studies of heavy-ion collisions at Brookhaven’s Relativistic Heavy Ion Collider (RHIC) and now at CERN’s LHC concerns the extreme fluidity of the dense matter of the nuclear fireball produced. This has traditionally been studied experimentally by measuring the second harmonic of the azimuthal distribution of emitted particles with respect to the plane of nuclear impact. Known as v2, this observable is remarkably large, saturating expectations from hydrodynamic models, suggesting that the so-called quark-gluon plasma is one of the most perfect fluids in nature. Many assumed that the matter in the elliptical nuclear overlap region becomes smooth upon thermalization, rendering the Fourier coefficients other than v2 negligible in comparison.
However, recently it was proposed that collective flow also responds to pressure gradients from the “chunkiness” of matter distributed within the initial fireball in random event-by-event fluctuations. These nonuniformities lead to anisotropy patterns beyond smooth ellipses: triangular, quadrangular, and pentangular flow are now being studied by measurements of v3, v4, v5 and beyond at RHIC and the LHC.
The new measurements evoke comparisons with the vestigial cosmic microwave background (CMB) radiation, whose nonuniformities offer hints about the conditions at the universe’s earliest moments. Just as the CMB anisotropy is expressed by multipole moments, the azimuthal anisotropy of correlated hadron pairs from heavy-ion collisions can be represented by a spectrum of Fourier coefficients VnΔ. In pair-correlation measurements, a “trigger” particle is paired with associated particles in the event to form a distribution in relative azimuth Δφ. Over many events, a correlation function is produced, whose peaks and valleys describe the relative probability of pair coincidence.
The left side of the figure shows a correlation function measured by ALICE for the 2% most central (i.e. head-on) lead–lead collisions at the LHC, where the particle pairs are separated in pseudorapidity to suppress “near-side” jet correlations near Δφ = 0. Even when this gap is imposed, a curious longitudinally-extended near-side “ridge” feature remains. Considerable theoretical effort has been devoted to explaining the source of this feature since its discovery at RHIC. In the correlation function in the figure, the first five VnΔ harmonics are superimposed. The right side of the figure shows the spectrum of the Fourier amplitudes. Evidently in the most head-on collisions, the dominant harmonic is not the second elliptical term, but the triangular one, V3Δ; moreover, the Fourier coefficients here are significant up to n = 5. These results corroborate the idea that initial density fluctuations are non-negligible.
The intriguing double-peak structure evident on the “away side” (i.e. opposite to the trigger particle, at Δφ = π) was not observed in inclusive (i.e. not background-subtracted) correlation functions prior to the LHC. However, in the hope of isolating jet-like correlations, the v2 component was often subtracted as a non-jet background, leaving a residual double peak when the initial away-side peak was broad. This led to interpretation of the structure as a coherent shock-wave response of the nuclear matter to energetic recoil partons, akin to a Mach cone in acoustics. However, the concepts of higher-order anisotropic flow are now gaining favour over theories that depend on conceptually independent Mach-cone and ridge explanations.
These measurements at the LHC are significant because they suggest a single consistent physical picture, vindicating relativistic viscous hydrodynamics as the most plausible explanation for the observed anisotropy. The same collective response to initial spatial anisotropy that causes elliptic flow also economically explains the puzzling “ridge” and “Mach cone” features, once event-by-event initial-state density fluctuations are considered. Moreover, measuring the higher Fourier harmonics offers tantalizing possibilities to improve understanding of the nuclear initial state and the transport properties of the nuclear matter. For example, the high-harmonic features at small angular scales are suppressed by the smoothing effects of shear viscosity. This constrains models incorporating a realistic initial state and hydrodynamic evolution, improving understanding of the deconfined phase of nuclear matter.
