  Direct photon production in minimum bias d+Cu and d+Au and central Cu+Cu and
Au+Au collisions at center of mass energies $\sqrt{s}=62.4$ GeV and 200GeV at
RHIC is systematically investigated. We study the jet quenching effect, the
medium-induced photon bremsstrahlung and jet-photon conversion in the hot QGP.
We account for known cold nuclear matter effects, such as the isospin effect,
the Cronin effect, shadowing and cold nuclear matter energy loss. It is shown
that at high $p_T$ the nuclear modification factor for direct photons
$R_{AA}^{\gamma} (p_T) < 1$ is dominated by cold nuclear matter effects and
there is no evidence for large cross section amplification due to
medium-induced photon bremsstrahlung and jet-photon conversion in the medium.
Comparison of numerical simulations to experimental data also rules out large
Cronin enhancement and incoherent photon emission in the QGP but the error bars
in the current experimental data cannot provide further constraints on the
magnitudes of other nuclear matter effects.
