System-Size Independence of Directed Flow Measured at the BNL Relativistic Heavy-Ion Collider

We measure directed flow ($v_1$) for charged particles in $\mathrm{Au}+\mathrm{Au}$ and $\mathrm{Cu}+\mathrm{Cu}$ collisions at $\sqrt{s_{NN}}=200$ and 62.4 GeV, as a function of pseudorapidity ($\eta$), transverse momentum ($p_t$), and collision centrality, based on data from the STAR experiment. We find that the directed flow depends on the incident energy but, contrary to all available model implementations, not on the size of the colliding system at a given centrality. We extend the validity of the limiting fragmentation concept to $v_1$ in different collision systems, and investigate possible explanations for the observed sign change in $v_1(p_t)$.

Figure 1

Charged particle $v_1(\eta )$ for three centralities in $\mathrm{Au}+\mathrm{Au}$ collisions at 200 GeV. The arrows indicate the algebraic sign of $v_1$ for spectator neutrons, and their positions on the $\eta$ axis correspond to beam rapidity. The inset shows the mid-$\eta$ region in more detail. The error bars are statistical, and the shaded bands show systematic errors. PHOBOS results [18] are also shown for midcentral collisions.

Figure 2

Charged particle $v_1(p_t)$ in 200 GeV $\mathrm{Au}+\mathrm{Au}$ for three centralities. The dashed curve and dotted curve are hydrodynamic calculations for the labeled rapidities at impact parameter 6.8 fm (15%–25% most central collisions). See the text for an explanation of the solid curve. The plotted error bars are statistical, and systematic errors (see Fig. 1) are within 10%.

Figure 3

Charged particle $v_1(\eta )$ for midcentral (30%–60%) $\mathrm{Au}+\mathrm{Au}$ and $\mathrm{Cu}+\mathrm{Cu}$ at 200 and 62.4 GeV. The solid curves and dashed curves are odd-order polynomial fits to guide the eye and demonstrate the forward-backward symmetry of the data. The wider shaded bands are from AMPT for the same conditions as the data. For clarity, 200 (62.4) GeV calculations are shown only at negative (positive) $\eta$. The plotted error bars are statistical, and systematic errors (see Figs. 1 and 5) are within 10%.

Figure 4

Charged particle $v_1$ versus centrality, for $\mathrm{Au}+\mathrm{Au}$ and $\mathrm{Cu}+\mathrm{Cu}$ at 200 and 62.4 GeV. The upper (lower) panels show results from the main TPC (FTPC). The plotted error bars are statistical, and systematic errors (see Figs. 1 and 5) are within 10%.

Figure 5

Charged particle $v_1$ versus $\eta -y_{\mathrm{beam}}$, for 30%–60% $\mathrm{Au}+\mathrm{Au}$ and $\mathrm{Cu}+\mathrm{Cu}$ at 200 and 62.4 GeV. The plotted error bars are statistical, and the shaded bars show systematic errors.