Abstract
Ultraluminous X-ray sources (ULXs) with neutron star (NS) accretors pose a challenge to traditional accretion models, sparking a debate regarding the role of geometrical beaming and strong magnetic fields (B). The reduction of the Thomson cross-section in the presence of strong B leads to a modification of the Eddington limit; therefore, it is expected to affect significantly the observational appearance of NS-ULXs. We investigate the role of this modification using population synthesis models and explore its effects on the X-ray luminosity functions, spin-up rates, and outflow energetics of the observed NS-ULXs. Our results show that the new prescription allows NS-ULXs to achieve super-Eddington luminosities with a milder beaming compared to before, improving the agreement with observations. In addition, it broadens the range of spin-up rates, allowing for more diverse conditions in NS-ULXs in terms of accretion rates and magnetic fields. More importantly, the reduced beaming increases the likelihood of observing the NS-ULXs within wind-powered nebulae, such as NGC,5907,ULX-1. Our findings highlight the need to take B effects into account, independently of the usual approach based on geometrical beaming or strong B. Finally, we call for magnetospheric accretion prescriptions that can be integrated in population synthesis codes.
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