  Electromagnetic (EM) radiation off strongly interacting matter created in
high-energy heavy-ion collisions (HICs) encodes information on the
high-temperature phases of nuclear matter. Microscopic calculations of thermal
EM emission rates are usually rather involved and not readily accessible to
broad applications in models of the fireball evolution which are required to
compare to experimental data. An accurate and universal parametrization of the
microscopic calculations is thus key to honing the theory behind the EM
spectra. Here we provide such a parametrization for photon emission rates from
hadronic matter, including the contributions from in-medium rho mesons (which
incorporate effects from anti-/baryons), as well as Bremsstrahlung from pi-pi
scattering. Individual parametrizations for each contribution are numerically
determined through nested fitting functions for photon energies from 0.2 to 5
GeV in chemically equilibrated matter of temperatures 100-180 MeV and baryon
chemical potentials 0-400 MeV. Special care is taken to extent the
parameterizations to chemical off-equilibrium as encountered in HICs after
chemical freezeout. This provides a functional description of thermal photon
rates within a 20% variation of the microscopically calculated values.
