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 Au+Au collisions at the 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 {\it 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.
$v_1$ of charged particles as a function of pseudorapidity for 10-70% centrality. Non-flow systematic uncertainties are approximately 20%.
$v_2$ with respect to the second harmonic event plane as a function of $p_T$ for the minimum bias Au+Au collisions. Background from secondary particles is expected to be less than 15%. Non-flow systematic uncertainties are approximately 20%. Fluctuations in initial geometry can lead to an effect of about a factor of 1.2 to 1.5.
$v_4$ with respect to the second harmonic event plane as a function of $p_T$ for the minimum bias Au+Au collisions. Background from secondary particles is expected to be less than 15%. Non-flow systematic uncertainties are approximately 20%. Fluctuations in initial geometry can lead to an effect of about a factor of 1.2 to 1.5.
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