Formation of Recycled Pulsars in Common Envelope Binaries

TL;DR

The paper tackles how recycled pulsars form in low- and intermediate-mass X-ray binaries by simulating $1.4\,M_{\odot}$ NS binaries with donors from $1-8\,M_{\odot}$ using grids of MESA models. It highlights the importance of CE evolution and a recently characterized common-envelope decoupling phase (CEDP), exploring CE ejection efficiencies $α_{\rm CE}=3.0,1.0,0.3$ to connect initial conditions with observed binary pulsars. Key findings show that CE survivors and the CEDP significantly influence the final WD/NS demographics, with NS–COWD systems dominating post-CE outcomes at higher donor masses, while SMT paths favor NS–HeWD/HyWD. The work identifies two formation channels for PSR J1928+1815 and finds that a higher CE efficiency ($α_{\rm CE}=3.0$) yields better agreement with the observed NS–WD population; it also demonstrates that NSs can accrete enough mass during CE and subsequent MT phases to become millisecond pulsars, providing constraints on CE physics and informing pulsar population models.

Abstract

We present a systematic study of the evolution of low- and intermediate-mass X-ray binaries (L/IMXBs) consisting of a $1.4\,M_{\odot}$ neutron star (NS) and a donor star of mass $1-8\,M_{\odot}$. Using grids of detailed MESA simulations, we show that for donor masses of $2-8\,M_{\odot}$, mass transfer may be dynamically unstable, leading to a common envelope (CE) phase. By adopting CE ejection efficiencies in the range $α_{\rm CE} = 0.3-3.0$, we find that post-CE binaries frequently experience a CE decoupling phase (CEDP), which plays a critical role in determining their final orbital and compositional properties. Systems with initial donor masses $\gtrsim 3.5\,M_{\odot}$ predominantly evolve into NS binaries with carbon-oxygen or oxygen-neon white dwarfs (WDs) with masses between $0.5\,M_{\odot}$ and $1.4\,M_{\odot}$. Comparison with the observed population of binary pulsars with a WD companion shows better agreement with higher CE ejection efficiencies ($α_{\rm CE} = 3.0$). Furthermore, we demonstrate that NSs can accrete a sufficient amount of matter ($\gtrsim 0.01\,M_{\odot}$) during the CEDP and subsequent Case BA/BB/BC mass transfer phases to be effectively recycled into millisecond pulsars. We identify two distinct evolutionary channels capable of reproducing the observed characteristics of the millisecond pulsar PSR J1928+1815 with a helium-star companion. Our results highlight the importance of the CEDP in the formation of recycled pulsars and provide constraints on the CE ejection efficiency during binary evolution.

Figures (8)

• Figure 1: The parameter space of initial donor mass versus orbital period ($M^{\rm i}_{\rm d}- P^{\rm i}_{\rm orb}$), illustrating the evolutionary fates of L/IMXBs with a $1.4\,M_\odot$ NS. The three panels correspond to CE ejection efficiencies of $\alpha_{\rm CE}=3.0$, 1.0 and 0.3. Green, blue, red, and black squares represent SMT binaries, CE mergers, CE survivors, and noninteracting binaries, respectively. Black crosses denote systems that are already Roche-lobe filling at the donor's ZAMS. The gray dashed curves separate the regimes of Case A, Case B, and Case C MT. The parameter space for CE survivors is shown to contract significantly with decreasing $\alpha_{\rm CE}$. Simulations for $\alpha_{\rm CE}=0.1$ (not shown) were attempted but most encountered numerical instabilities during the CE phase.
• Figure 2: Final fates of donor stars across the initial parameter space for $\alpha_{\rm CE}=3.0$, 1.0 and 0.3. The compact remnants are categorized as HeWDs (blue), HyWDs (green), COWDs (red), ONeWDs (azure), NSs (purple), or degenerate hydrogen-rich stars (orange). Black squares denote ZAMS RLOF binaries, CE mergers, and noninteracting binaries. Filled and open squares distinguish CE survivors and SMT binaries, respectively. The gray dashed curves separate the regimes of Case A, Case B, and Case C MT.
• Figure 3: Orbital period versus donor's hydrogen envelope mass ($P^{\rm CE}_{\rm orb}-M^{\rm CE}_{\rm H,env}$) at the termination of CE evolution. The three panels display the distributions for $\alpha_{\rm CE}=3.0$, 1.0 and 0.3. The red dots represent all simulated systems that survived CE evolution. The number annotated next to each data cluster indicates the initial mass of the donor star.
• Figure 4: Orbital period versus donor's He core mass ($\log_{10} P^{\rm CE}_{\rm orb}$, $M^{\rm CE}_{\rm He,core}$) at the termination of CE evolution for $\alpha_{\rm CE}=3.0$, 1.0 and 0.3. Red dots denote all systems that survived CE evolution. The number annotated next to each data cluster indicates the initial donor mass. The blue star and horizontal error bar mark the central value and mass range, respectively, of the He star companion in PSR J1928+1815.
• Figure 5: Evolutionary tracks for a binary system with a $1.4M_{\odot}$ NS and a $6\,M_{\odot}$ donor in an initial 316-day orbit, computed with $\alpha_{\rm CE}=1.0$. Upper left: Hertzsprung-Russell diagram for the donor star. The black square marks the onset of MT. The red and magenta curves correspond to the binary undergoing a CE phase and the subsequent Case BC MT phase, respectively. Upper right: Evolution of the donor star mass (solid curve), He core mass (dashed curve), and CO core mass (dotted curve) after the CE phase. Lower left: MT rate via RLOF as a function of time. The black dashed line indicates the Eddington accretion limit. Lower right: Mass accretion history of the NS, showing the total mass gained over time.