  Directed flow ($v_1$) is a good probe of the early-stage dynamics of
collision systems, and the $v_1$ slope at midrapidity ($dv_1/dy|_{y=0}$) is
sensitive to the system's equation of state. STAR has published $v_1(y)$
measurements for ten particle species ($\pi^\pm$, $p$, $\bar{p}$, $\Lambda$,
$\bar{\Lambda}$, $\phi$, $K^\pm$ and $K^0_{S}$) in Au+Au collisions at eight
beam energies from $\sqrt{s_{NN}} = 7.7$ GeV to 200 GeV. In this study, we
employ a simple coalescence idea to decompose $v_1$ of hadrons into $v_1$ of
constituent quarks. The $dv_1/dy$ values of $\bar{p}$, $K^-$ and
$\bar{\Lambda}$ are used to test the coalescence sum rule for produced quarks.
Data involving produced quarks support the coalescence picture at
$\sqrt{s_{NN}} = 11.5$ GeV to 200 GeV, and a sharp deviation from this picture
is observed at 7.7 GeV. The $dv_1/dy$ of transported quarks is studied via net
particles (net $p$ and net $\Lambda$). In these proceedings, we further extract
the $v_1$ slopes of produced and transported quarks, assuming that the
coalescence sum rule is valid.
