  We predict the transverse momentum (pT) dependence of elliptic flow of
thermal photons for Au+Au collisions at the Relativistic Heavy Ion Collider. We
model the system hydrodynamically, assuming formation of a thermalized
quark-gluon plasma at some early time, followed by cooling through expansion,
hadronization and decoupling. Photons are emitted throughout the expansion
history. Contrary to hadron elliptic flow, which hydrodynamics predicts to
increase monotonically with pT, the elliptic flow of thermal photons is
predicted to first rise and then fall again as pT increases. Photon elliptic
flow at high pT is shown to reflect the quark momentum anisotropy at early
times when it is small, whereas at low pT it is controlled by the much larger
pion momentum anisotropy during the late hadronic emission stage. An
interesting structure is predicted at intermediate pT ~ 0.4 GeV/c where photon
elliptic flow reflects the momenta and the (compared to pions) reduced v2 of
heavy vector mesons in the late hadronic phase.
