  The directly detected planetary mass companion candidate close to the young,
nearby star Fomalhaut is a subject of intense discussion. While the detection
of common proper motion led to the interpretation as Jovian-mass companion,
later non-detections in the infrared raised doubts. Recent astrometric
measurements indicate a belt crossing or highly eccentric orbit for the object,
if a companion, making the planetary interpretation potentially even more
problematic. In this study we discuss the possibility of Fomalhaut\,b being a
background object with a high proper motion. By analysing the available
photometric and astrometric data of the object, we show that they are fully
consistent with a neutron star: Neutron stars are faint, hot (blue), and fast
moving. Neutron stars with an effective temperature of the whole surface area
being 112,000 K to 126,500 K (with small to negligible extinction) at a
distance of roughly 11 pc (best fit) would be consistent with all observables,
namely with the photometric detections in the optical, with the upper limits in
the infrared and X-rays, as well as with the astrometry (consistent with a
distances of 11 pc or more and high proper motion as typical for neutron stars)
as well as with non-detection of pulsation (not beamed). We consider the
probability of finding an unrelated object or even a neutron star nearby and
mostly co-aligned in proper motion with Fomalhaut A and come to the conclusion
that this is definitely well possible.
