Azimuthal-angle dependence of charged-pion-interferometry measurements with respect to 2${}^{\mathrm{n}\mathrm{d}}$- and $3^{\mathrm{r}\mathrm{d}}$-order event planes in Au$+$Au collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV

Charged-pion-interferometry measurements were made with respect to the 2${}^{\mathrm{n}\mathrm{d}}$- and 3${}^{\mathrm{r}\mathrm{d}}$-order event plane for Au$+$Au collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV. A strong azimuthal-angle dependence of the extracted Gaussian-source radii was observed with respect to both the 2$^{\rm nd}$-and3$^{\rm rd}$-ordereventplanes\mathrm{.}Theresultsforthe2$^{\rm nd}$-order dependence indicate that the initial eccentricity is reduced during the medium evolution, but not reversed in the final state, which is consistent with previous results. In contrast, the results for the 3${}^{\mathrm{r}\mathrm{d}}$-order dependence indicate that the initial triangular shape is significantly reduced and potentially reversed by the end of the medium evolution, and that the 3${}^{\mathrm{r}\mathrm{d}}$-order oscillations are largely dominated by the dynamical effects from triangular flow.