  Pulsating ultraluminous X-ray sources (PULXs) are accreting pulsars with
apparent X-ray luminosity exceeding $10^{39}\, \rm erg\ s^{-1}$. We perform
Monte-Carlo simulations to investigate whether high collimation effect (or
strong beaming effect) is dominant in the presence of accretion outflows, for
the fan beam emission of the accretion column of the neutron stars in PULXs. We
show that the three nearby PULXs (RX J0209.6$-$7427, Swift J0243.6+6124 and SMC
X-3), namely the three musketeers here, have their main pulsed emission not
strongly collimated even if strong outflows exist. This conclusion can be
extended to the current sample of extragalactic PULXs, if accretion outflows
are commonly produced from them. This means that the observed high luminosity
of PULXs is indeed intrinsic, which can be used to infer the existence of very
strong surface magnetic fields of $\sim10^{13-14}$ G, possibly multipole
fields. However, if strong outflows are launched from the accretion disks in
PULXs as a consequence of disk spherization by radiation pressure, regular
dipole magnetic fields of $\sim10^{12}$ G may be required, comparable to that
of the three musketeers, which have experienced large luminosity changes from
well below their Eddington limit ($2\times10^{38}\, \rm erg\ s^{-1}$ for a NS)
to super-Eddington and their maximum luminosity fills the luminosity gap
between Galactic pulsars and extragalactic PULXs.

High Energy Astrophysical Phenomena