Azimuthal Anisotropy at the Relativistic Heavy Ion Collider: The First and Fourth Harmonics

We report the first observations of the first harmonic (directed flow, $v_1$) and the fourth harmonic ($v_4$), in the azimuthal distribution of particles with respect to the reaction plane in $\mathrm{A}\mathrm{u}+\mathrm{A}\mathrm{u}$ collisions at the BNL Relativistic Heavy Ion Collider (RHIC). Both measurements were done taking advantage of the large elliptic flow ($v_2$) generated at RHIC. From the correlation of $v_2$ with $v_1$ it is determined that $v_2$ is positive, or in-plane. The integrated $v_4$ is about a factor of 10 smaller than $v_2$. For the sixth ($v_6$) and eighth ($v_8$) harmonics upper limits on the magnitudes are reported.

Figure 1

The values of $v_1$ (stars) for charged particles for 10% to 70% centrality plotted as a function of pseudorapidity. Also shown are the results from NA49 (triangles) for pions from $158A\mathrm{G}\mathrm{e}\mathrm{V}$ $\mathrm{P}\mathrm{b}+\mathrm{P}\mathrm{b}$ midcentral (12.5% to 33.5%) collisions plotted as a function of rapidity. The open points have been reflected about midrapidity. The NA49 points have also been shifted (circles) plus or minus by the difference in the beam rapidities of the two accelerators. The dashed lines indicate midrapidity and RHIC beam rapidity. Both results are from analyses involving three-particle cumulants, $v_1\{3\}$.

Figure 2

The minimum bias values of $v_2$, $v_4$, and $v_6$ with respect to the second harmonic event plane as a function of $p_t$ for $|\eta |\mathrm{<}1.2$. The $v_2$ values have been divided by a factor of 2 to fit on scale. Also shown are the three particle cumulant values (triangles) for $v_4$ ($v_4\{3\}$). The dashed curves are $1.2v_2^2$ and $1.2v_2^3$.

Figure 3

The $p_t$- and $\eta$-integrated values of $v_2$, $v_4$, and $v_6$ as a function of centrality. The $v_2$ values have been divided by a factor of 4 to fit on scale. Also shown are the three particle cumulant values for $v_4$ ($v_4\{3\}$). The dotted histograms are $1.4v_2^2$ and $1.4v_2^3$.