How do ultraluminous X-ray pulsars exceed the Eddington limit?
In plain words
Some neutron stars shine hundreds of times brighter than the Eddington limit (the brightness at which the push of light on infalling gas balances gravity), and it is unclear whether they truly do or only beam their light toward us.
Precise statement
Pulsating ultraluminous X-ray sources (M82 X-2, NGC 7793 P13, NGC 5907 ULX-1 with peak $L_X \sim 1e41\,\mathrm{erg}/\mathrm{s}$, several hundred times $L_{\mathrm{Edd}}$ for $1.4\,M_{\mathrm{sun}}$) are accreting neutron stars. Decide among geometric beaming by optically thick wind funnels, magnetar-strength fields ($B > 1e14\,\mathrm{G}$) that suppress the electron-scattering cross section, and accretion columns with strong multipole fields. Answer: the beaming factor and surface field for each pulsating ULX, consistent with spin-up rate, pulsed fraction and isotropic calorimetry from surrounding nebulae.
What would settle it
Cyclotron-line field measurements combined with isotropic luminosity estimates from photoionized nebulae for several pulsating ULXs.
Status in the literature
2018: an absorption feature in M51 ULX-8 was interpreted as a proton cyclotron line implying a magnetar-strength field; this has not been established for other sources.