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We report the first measurement of the elliptic anisotropy ($v_2$) of thecharm meson $D^0$ at mid-rapidity ($|y|$\,$<$\,1) in Au+Au collisions at \sNN =200\,GeV. The measurement was conducted by the STAR experiment at RHICutilizing a new high-resolution silicon tracker. The measured $D^0$ $v_2$ in0--80\% centrality Au+Au collisions can be described by a viscous hydrodynamiccalculation for transverse momentum ($p_{\rm T}$) less than 4\,GeV/$c$. The$D^0$ $v_2$ as a function of transverse kinetic energy ($m_{\rm T} - m_0$,where $m_{\rm T} = \sqrt{p_{\rm T}^2 + m_0^2}$) is consistent with that oflight mesons in 10--40\% centrality Au+Au collisions. These results suggestthat charm quarks have achieved local thermal equilibrium with the mediumcreated in such collisions. Several theoretical models, with thetemperature--dependent, dimensionless charm spatial diffusion coefficient($2{\pi}TD_s$) in the range of $\sim$2--12, are able to simultaneouslyreproduce our $D^0$ $v_2$ result and our previously published results for the$D^0$ nuclear modification factor.

Measurement of $D^0$ azimuthal anisotropy at mid-rapidity in Au+Au collisions at \sNN = 200\,GeV