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

TL;DR

This work investigates the surface dipole magnetic field and long-term spin evolution of the ultraluminous X-ray pulsar NGC 4631 X-8, a recently identified ULXP with $P \approx 9.665$ s and a large spin-up rate. By applying multiple magnetic-field estimation methods, including magnetospheric-torque constraints, torque balance, and propeller-line limits, the authors infer $B_s$ in the range $0.3-2\times10^{14}$ G, with independent estimates clustering around $\sim(6-7)\times10^{13}$ G and $\sim3\times10^{13}$ G. They then model accretion-induced magnetic-field decay using the ZK framework, showing rapid ($\sim5\times10^{3}$ yr) decay from an initial $B_0\approx4\times10^{14}$ G to $B\sim(0.3-2)\times10^{14}$ G, followed by a gradual decline to $\sim(0.7-2.8)\times10^{9}$ G over $10^{6-7}$ years as $\sim0.3-0.5\,M_\odot$ is accreted. The inferred accretion history and ensuing $B$–$P$ evolution suggest NGC 4631 X-8 can evolve into a recycled millisecond pulsar with $P$ of tens of milliseconds and $B$ near $10^{9}$ G, illustrating a potential ULXP-to-MSP pathway and informing magnetar evolution during transient super-Eddington phases. The work highlights the importance of duty-cycle constraints and companion mass in shaping the end state, and it motivates further multiwavelength observations to refine these evolutionary links.

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 $0.3-2 \times 10^{14}$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 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 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 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.

Figures (4)

• Figure 1: Variation of the surface dipole magnetic field of the neutron star ($B_S$) and the accretion rate at the magnetospheric radius ($\dot{M}$). The vertical dotted line marks the accretion rate of $3.3\times 10^{19}~{\rm g\,s^{-1}}$ estimated in section 2.
• Figure 2: Accretion-induced decay of the magnetic field of NGC 4631 X-8. The magnetic field evolution is assumed to begin at $T_{ac}=0$ with initial $B_{0}=4 \times 10^{14}\,G$. The curves plotted with dotted, dashed, dashed-dotted, and solid lines show the magnetic field evolution for $\dot{M_{min}}\sim 3.3\times 10^{19}~{\rm g\,s^{-1}}$, $\dot{M}\sim 7\times 10^{18}~{\rm g\,s^{-1}}$, $\dot{M}\sim 4.5\times 10^{18}~{\rm g\,s^{-1}}$, and $\dot{M}\sim 1\times 10^{18}~{\rm g\,s^{-1}}$, respectively. The magnetic field decays to the bottom value of $\sim 0.7-1.5 \times 10^{9}\,G$ in about $10^{6-7}$ years. The $B-T_{ac}$ positions are plotted for the minimum and the maximum estimated values of the magnetic field.
• Figure 3: Accretion time ($T_{\rm ac}$) variation with mass of the companion star. The dotted and dashed lines show the estimated accretion time and the companion mass for $\dot{M}\sim 3.3\times 10^{19}~{\rm g\,s^{-1}}$, and $\dot{M}\sim 1.8\times 10^{18}~{\rm g\,s^{-1}}$, respectively.
• Figure 4: Diagram showing magnetic field vs spin period. The red and blue stars in the figure show the B-P position of NGC 4631 X-8 for $B_{min} \sim 3 \times 10^{13}\,G$ and $B_{max} \sim 2 \times 10^{14}\,G$, respectively, having spin period of about 9.67 s. The dotted, dashed and solid lines exhibit the spin-up line having accretion rate $\dot{M}\sim 3.3\times 10^{19}\rm g\,s^{-1}$, $\dot{M}\sim 1.8\times 10^{18}~{\rm g\,s^{-1}}$, and the Eddington accretion rate, respectively. The B-P positions of binary pulsars obtained from the ATNF pulsar catalogue (https://www.atnf.csiro.au/research/pulsar/psrcat/, manchester2005australia) are marked by solid dots while those of magnetars are marked by plus signs. The B-P positions of other confirmed ultraluminous X-ray pulsars M82 X-2, NGC 7793 P13, NGC 5907 ULX, NGC 300 ULX-1, M51 ULX-7, NGC 1313 X-2, Swift J0243.6+6124, RX J0209.6-7427, and SMC X-3 obtained from literature are plotted with black stars.