The role of equation of state on the spin-up of millisecond pulsars

TL;DR

The paper addresses how the pulsar equation of state (EoS) influences millisecond pulsar spin-up during accretion by comparing gravity-bound neutron stars and self-bound strangeon stars using four representative EoS models. It derives EoS-dependent spin-up lines and tracks spin evolution under accretion with evolving magnetic fields, showing that low-mass self-bound SSs can reach shorter spin periods than NSs for the same accreted mass. The work highlights that MSPs with $M\lesssim1.2\,M_\odot$ are particularly informative for constraining the EoS, as differences between SS and NS populations are most pronounced there. It suggests that precise mass measurements and estimates of the accreted mass $\Delta M$ for fast-spinning, low-mass MSPs could help distinguish between gravity-bound and self-bound models, with future surveys (e.g., SKA, FAST) poised to tighten these constraints.

Abstract

Millisecond pulsars (MSPs) are recycled pulsars which have been spun-up due to mass accretion during the phase of mass exchange in binaries. Although the interactions with companion stars play important roles on the spin-up process, the global properties of pulsars determined by the equation of state (EoS), such as mass, radius and the moment of inertia, should also play a role. We investigate the spin-up of MSPs in neutron star (NS) and strangeon star (SS) models, both of which have passed the tests by the existence of high-mass pulsars and the tidal deformability of GW~170817. Combining the spin-up condition and the transferred angular momentum, and taking into account the evolution of magnetic field strength during accretion, we can constrain the spin-period and mass of an MSP. Our results show that the impeding effect of magnetic field on the spin-up of MSPs would be more significant for NSs than for SSs, especially for the ones with low masses. In the low-mass ($M$ below or around about $1.2 M_\odot$) case, an SS can spin faster than an NS of the same mass by accreting the same amount of mass. Finding more low-mass and fully recycled MSPs, with accurate mass-measurement and better constraints on the amount of accreted mass, could help to put more strict constraints on the EoS of pulsars.

Figures (5)

• Figure 1: $M$-$R$ curves for SSs in LX3630 (red solid lines), hybrid SSs in Z-2023 (red dashed line), NSs in AP4 (blue solid line), and hybrid NSs in X-2024 (blue dashed line). In this paper we use the former two models to describe SSs and the latter two models to describe NSs
• Figure 2: Spin-up lines of $B=5\times 10^8$ G for SSs in LX3630 (red solid line) and Z-2023 (red dashed line), and for NSs in AP4 (blue solid line) and X-2024 (blue dashed line).
• Figure 3: The curves of $P$ after accretion of the amount of mass $\Delta M=0.1 M_\odot$, as the function of the final mass $M$. The results of SSs in LX3630 and Z-2023 models are shown respectively by red solid line and red dashed line, and the results of NSs in AP4 and X-2024 models are shown respectively by blue solid line and blue dashed line.
• Figure 4: The allowed regions of SSs (upper) and NSs (lower) in $MP$ diagram. The upper panel shows the spin-periods of SSs with mass $M$ after accretion of $\Delta M=0.1 M_\odot$ in LX3630 (orange solid line) and Z-2023 (red solid line), and the spin-up line of SSs whose magnetic field strength equals to the final $B$ after accretion of $\Delta M=0.1 M_\odot$ in LX3630 (orange dashed line) and Z-2023 (red dashed line). If $\Delta M<0.1 M_\odot$, the allowed region for SSs in LX3630 is covered by both orange and red patches, and that for SSs in Z-2023 is covered by red patch. The lower panel of shows the same results as in the upper one, for NSs in AP4 model (blue solid line, blue dashed line, and blue patch) and in X-2024 model (green solid line, green dashed line, and patches in both blue and green).
• Figure 5: $M$-$P$ curves after accretion of $\Delta M$, for SSs in LX3630 (red solid line in upper panel), SSs in Z-2023 (red dashed line in the upper panel), NSs in AP4 (blue solid line in lower panel), and NSs in X-2024 (blue dashed line in lower panel). For each model, we show the results for $\Delta M/M_\odot=0.04, 0.06, 0.1, 0.2$, increasing downwards. Data points with 1-$\sigma$ uncertainties are from Ozel2016.