The PHENIX collaboration presents first measurements of low-momentum (0.41 GeV/c) direct-photon yield dNγdir/dη is a smooth function of dNch/dη and can be well described as proportional to (dNch/dη)α with α≈1.25. This scaling behavior holds for a wide range of beam energies at the Relativistic Heavy Ion Collider and the Large Hadron Collider, for centrality selected samples, as well as for different A+A collision systems. At a given beam energy, the scaling also holds for high pT (>5 GeV/c), but when results from different collision energies are compared, an additional sNN-dependent multiplicative factor is needed to describe the integrated-direct-photon yield. © 2019 authors. Published by the American Physical Society.