Formation of millisecond pulsar-helium star binaries

TL;DR

This study shows that pre-CE Roche-lobe overflow can spin up neutron stars to millisecond periods through super-Eddington accretion, forming NS + He-star binaries with properties matching PSR J1928+1815. By combining MESA with binary population synthesis, it predicts distributions of orbital periods, He-star masses, NS spin periods, magnetic fields, and accreted mass, and finds that the CE ejection efficiency mainly shifts the orbital period distribution and the overall birthrate. An intermediate initial NS magnetic field (around 10¹² G) best reproduces the observed spin and magnetic-field pair, while variations in other initial conditions largely affect only selected parameters. The estimated Galactic birthrates range from about 5×10⁻⁵ to 2×10⁻⁴ per year, corresponding to roughly 626–2684 NS + He binaries, demonstrating that pre-CE RLO accretion is a viable MSP formation channel albeit with significant CE-physics uncertainties.

Abstract

PSR J1928+1815, the first recycled pulsar-helium (He) star binary discovered by the Five-hundred-meter Aperture Spherical radio Telescope, consists of a 10.55 ms pulsar and a companion star with mass $1-1.6\,M_{\sun}$ in a 0.15-day orbit. Theoretical studies suggest that this system originated from a neutron star (NS) intermediate-mass or high-mass X-ray binary that underwent common envelope (CE) evolution, leading to the successful ejection of the giant envelope. The traditional view is that hypercritical accretion during the CE phase may have recycled the NS. However, the specific mechanism responsible for accelerating its spin period remains uncertain due to the complex processes involved in CE evolution.In this study, we investigate the influence of Roche lobe overflow (RLO) accretion that takes place prior to the CE phase on the spin evolution of NSs. Our primary objective is to clarify how this process affects the spin characteristics of pulsars. We utilized the stellar evolution code \texttt{MESA} and the binary population synthesis code \texttt{BSE} to model the formation and evolution of NS-He star binaries. We calculated the distributions of the orbital period, He star mass, NS spin period, and magnetic field for NS + He star systems in the Galaxy. Our results indicate that RLO accretion preceding the CE phase could spin up NSs to millisecond periods through super-Eddington accretion. Considering a range of CE efficiencies $α_{\rm CE}$ from 0.3 to 3, we estimate the birthrate (total number) of NS + He star systems in our Galaxy to be 5.2$\times 10^{-5}$ yr$^{-1}$ (626 systems) to 1.9$\times 10^{-4}$ yr$^{-1}$ (2684 systems).

Figures (6)

• Figure 1: Evolution of a 1.4 $M_{\odot}$ NS and a 9.5 $M_{\odot}$ MS donor, commencing with an orbital period $P_{\rm orb,i}$ = 891 days. Panel (a) depicts the evolution of the accretion rate as a function of time. The blue dashed line represents the RLO MT rate for a system containing a NS with an initial magnetic field of $B=10^{13}$ G. Panels (b-f) illustrate the evolution of binary orbital period, donor star's He core mass, NS accreted mass, magnetic field and spin period as a function of the donor mass. The yellow, green, and blue solid lines correspond to initial NS magnetic fields of $10^{11}$, $10^{12}$, and $10^{13}$ G, respectively. The red dashed line denotes the observed values of J1928+1815. Note that the required accreted mass of 0.01 $M_{\odot}$ for accelerating J1928+1815 was derived by applying Eq. (9).
• Figure 2: Distinct evolutionary pathways for NS X-ray binaries in the $M_{\rm d,i}-P_{\rm orb,i}$ plane. Stars denote binary systems capable of stable MT, triangles indicate systems without RLO MT, circles represent systems undergoing unstable MT and entering a CE phase and merging, squares and diamonds signify systems experiencing instable Case B and Case C MT and entering a CE phase but successfully ejecting the envelope, respectively. Red, orange, green, blue, and gray colors correspond to NS spin periods of less than 10 ms, 10-30 ms, 30-100 ms, 100-1000 ms, and greater than 1000 ms, respectively, following the RLO MT phase. The black dotted line marks the orbital period at which the companion star fills its RL at the zero-age main sequence.
• Figure 3: Distributions of NS + He systems in terms of companion star mass vs. orbital period, NS magnetic field vs. NS spin period, and accreted mass onto the NS vs. NS spin period (from top left to bottom right). Color intensity represents the birthrate. Here, $\alpha_{\rm CE}$=1, $B_0=10^{12}$ G, and $P_{\rm s,0}=$1 s. In the bottom right plot, the blue line corresponds to Eq. (9). The black star indicates the observational parameters of J1928+1815.
• Figure 4: Similar to Figure 3 but initial NS magnetic field $B_0=10^{11}$ G (upper panels) and $B_0=10^{13}$ G (lower panels).
• Figure 5: Similar to Figure 3 but for initial NS spin period $P_{s,0}=0.01$ s.