  Future gamma-ray experiments, such as the e-ASTROGAM and AMEGO telescopes,
can detect the Hawking radiation of photons from primordial black holes (PBHs)
if they make up a fraction or all of dark matter. PBHs can analogously also
Hawking radiate new particles, which is especially interesting if these
particles are mostly secluded from the Standard Model (SM) sector, since they
might therefore be less accessible otherwise. A well-motivated example of this
type is axion-like particles (ALPs) with a tiny coupling to photons. We assume
that the ALPs produced by PBHs decay into photons well before reaching the
earth, so these will augment the photons directly radiated by the PBHs.
Remarkably, we find that the peaks in the energy distributions of ALPs produced
from PBHs are different than the corresponding ones for Hawking radiated
photons due to the spin-dependent greybody factor. Therefore, we demonstrate
that this process will in fact distinctively modify the PBHs' gamma-ray
spectrum relative to the SM prediction. We use monochromatic asteroid-mass PBHs
as an example to show that e-ASTROGAM can observe the PBH-produced ALP
gamma-ray signal (for masses up to ~60 MeV) and further distinguish it from
Hawking radiation without ALPs. By measuring the gamma-ray signals, e-ASTROGAM
can thereby probe yet unexplored parameters in the ALP mass and photon
coupling.
