  A recent analysis from the PHENIX collaboration of available direct photon
measurement results in collisions of various systems such as Au+Au, Cu+Cu, and
Pb+Pb, at different beam energies ranging from 39 to 2760 GeV, has shown a
universal, within experimental uncertainties, $multiplicity$ scaling, in which
direct photon $p_{T}$-spectra for transverse momenta up to 2 GeV/$c$ are scaled
with charged hadron pseudorapidity density at midrapidity raised to power
$\alpha=1.25$. On the other hand, those direct photon $p_{T}$-spectra also
exhibit $geometrical$ scaling in the similar $p_{T}$ range. Assuming power-law
dependence of the scaled photon spectra for both scaling laws, we formulate two
independent conditions for the power $\alpha$, which overshoot experimental
data by $\sim 10\%$ on average. We discuss possible sources that might improve
this estimate.
