Exploring the magnetic field of the ultraluminous X-ray pulsar NGC 4631 X-8

Abstract

NGC 4631 X-8 is an ultraluminous X-ray pulsar (ULXP) having a spin period of about 9.7 s, discovered using XMM-Newton observations in 2025. The pulsar is known to show one of the largest spin-up rates ($\sim -9.6 \times 10^{-8}$ s s$^{-1}$) among the ULXP population. We explore the surface magnetic field of the neutron star in this source using different models, and find that the inferred magnetic field lies in the range of about $0.3-7 \times 10^{14}$G. We study the long-term magnetic field and spin period evolution of the pulsar assuming steady accretion using prevalent theoretical mechanisms and find that the pulsar will likely evolve to become a millisecond pulsar having decayed magnetic field of about $\sim 10^{9}$G in about a million years. The scenario of the formation of a millisecond pulsar is also probed using an estimate of the super-Eddington duty cycle of about 14% from the literature, which suggests that the neutron star would accrete sufficient matter to likely become a recycled millisecond pulsar. Exploring the magnetic field as well as the spin period evolution properties of ULXPs may enable us to understand the poorly understood evolutionary features of ULXPs, shed light on one of the pathways of millisecond pulsar formation and also help us to understand the possibility of transient super-Eddington accretion phases in newborn magnetars, which are believed to power energetic events such as long gamma-ray bursts and Type I superluminous supernovae.