  Axion-like particles (ALPs) belong to a class of new pseudoscalar particles
that generically couple to photons, opening the possibility of oscillations
from photons into ALPs in an external magnetic field. Having witnessed the
turbulence of their magnetic fields, these oscillations are expected to imprint
irregularities in a limited energy range of the spectrum of astrophysical
sources. In this study, Chandra observations of the Hydra galaxy cluster are
used to constrain the value of the coupling of ALPs to photons. We consider the
conversion of X-ray photons from the central source Hydra A in the magnetic
field of the cluster. The magnetic field strength and structure are well
determined observationally, which adds to the robustness of the analysis. The
absence of anomalous irregularities in the X-ray spectrum of Hydra A
conservatively provides the most competitive constraints on the coupling
constant for ALP masses below 7e-12 eV at the level of g < 8.3e-12 GeV-1 at the
95% confidence level. Because of the specific phenomenology involved, these
constraints actually hold more generally for very light pseudo-Nambu-Goldstone
bosons.
