  We show that ultraluminous X-ray sources (ULXs) with coherent X-ray pulsing
(PULXs) probably have neutron-star spin axes significantly misaligned from
their central accretion discs. Scattering in the funnels collimating their
emission and producing their apparent super-Eddington luminosities is the most
likely origin of the observed correlation between pulse fraction and X-ray
photon energy. Pulsing is suppressed in systems with the neutron-star spin
closely aligned to the inner disc, explaining why some ULXs show cyclotron
features indicating strong magnetic fields, but do not pulse. We suggest that
alignment (or conceivably, field suppression through accretion) generally
occurs within a fairly short fraction of the ULX lifetime, so that most
neutron-star ULXs become unpulsed. As a result we further suggest that almost
all ULXs actually have neutron-star accretors, rather than black holes or white
dwarfs, reflecting their progenitor high-mass X-ray binary and supersoft X-ray
source populations.
