  Conversion of photons into axions under the presence of a strong magnetic
field can dim the radiation from magnetized astrophysical objects. Here we
perform a detailed calculation aimed at quantifying the signatures of
photon-axion conversion in the spectra, light curves, and polarization of
neutron stars (NSs). We take into account the energy and angle-dependence of
the conversion probability and the surface thermal emission from NSs. The
latter is computed from magnetized atmosphere models that include the effect of
photon polarization mode conversion due to vacuum polarization. The resulting
spectral models, inclusive of the general-relativistic effects of gravitational
redshift and light deflection, allow us to make realistic predictions for the
effects of photon to axion conversion on observed NS spectra, light curves, and
polarization signals. We identify unique signatures of the conversion, such as
an increase of the effective area of a hot spot as it rotates away from the
observer line of sight. For a star emitting from the entire surface, the
conversion produces apparent radii that are either larger or smaller (depending
on axion mass and coupling strength) than the limits set by NS equations of
state. For an emission region that is observed phase-on, photon-axion
conversion results in an inversion of the plane of polarization with respect to
the no-conversion case. While the quantitative details of the features that we
identify depend on NS properties (magnetic field strength, temperature) and
axion parameters, the spectral and polarization signatures induced by
photon-axion conversion are distinctive enough to make NSs very interesting and
promising probes of axion physics.
