Mass distribution of neutron stars in binary systems

Technical Summary: Mass Distribution of Neutron Stars in Binary Systems

Problem Statement
Observations indicate that the mass distribution of known neutron stars (NSs) in binary systems exhibits a bimodal pattern, with peaks around 1.4 M$_\odot$ and $\sim$1.8 M$_\odot$. While the 1.4 M$_\odot$ peak is often attributed to standard core-collapse supernovae or common envelope evolution, the origin of the $\sim$1.8 M$_\odot$ peak remains debated. Previous theoretical models attempting to explain NS mass growth via accretion have often been limited by the Eddington limit or have not fully accounted for super-Eddington accretion regimes. Furthermore, uncertainties regarding the efficiency of mass transfer, the propeller effect, and magnetic field evolution have hindered accurate predictions of the final mass distribution of accreting NSs. This study aims to investigate whether a super-Eddington accretion model can successfully reproduce the observed bimodal mass distribution of NSs in binary systems.

Methodology
The authors employed a hybrid population synthesis approach combining two distinct codes:

1. Binary Star Evolution (BSE): Used to simulate the formation and initial evolution of $10^7$ primordial binary systems. This code generated a population of NS binaries with main-sequence companions, incorporating initial mass functions, mass ratios, eccentricities, and natal kick velocities. Systems were filtered to identify those capable of stable mass transfer, excluding those prone to unstable common envelope evolution or extreme mass transfer rates ($>10^4 \dot{M}_{Edd}$).
2. Modules for Experiments in Stellar Astrophysics (MESA): Selected NS binaries from the BSE output were subjected to detailed evolutionary calculations using MESA (version r24.08.1). This stage focused on the accretion process under stable Roche lobe overflow conditions.

Key Physical Models and Assumptions:

• Super-Eddington Accretion: Unlike previous models limited by the Eddington limit, this study incorporates the physics of super-Eddington accretion as described by Lipunov (1987). The model distinguishes between sub-critical and super-critical regimes based on the relationship between the Alfvén radius ($R_a$) and the spherization radius ($R_s$).
• Accretion Efficiency: The fraction of transferred mass accreted by the NS ($f_{mt,a}$) is determined by the accretion state. In the super-critical regime, excess material is blown away by radiation pressure near the NS, carrying away specific orbital angular momentum. An accretion efficiency of 0.5 is assumed for the retained mass.
• Magnetic Field Evolution: The NS magnetic field decays as a function of accreted mass ($\Delta M$) following an exponential law, reducing from an initial $5 \times 10^{12}$ G to a minimum of $5 \times 10^8$ G.
• Spin Evolution: The model tracks the NS spin period through three phases: Radio (no accretion), Propeller (ejection of matter), and Accretion (spin-up). The transition between these phases depends on the relative positions of the light cylinder, corotation radius, and magnetospheric radius.
• Angular Momentum Loss: The simulation accounts for gravitational wave radiation, magnetic braking, and angular momentum loss due to ejected mass and circumbinary disk formation.

Key Results

1. Mass Growth Mechanism: The study demonstrates that NS mass growth is heavily dependent on the binary orbital period and the donor star mass. In the super-Eddington model, NSs can remain in an accretion equilibrium state for extended periods, allowing for significant mass accumulation (up to $\sim$1.0 M$_\odot$ growth from a 1.4 M$_\odot$ birth mass). This contrasts with the Li et al. (2021) model (Eddington-limited), where NSs often enter a prolonged propeller phase that limits mass growth.
2. Reproduction of Bimodality: The population synthesis results successfully reproduce the observed bimodal distribution:
   • The $\sim$1.8 M$_\odot$ Peak: This peak primarily arises from NS binaries with donor masses $M_d < \sim$1.6 M$_\odot$ and orbital periods $P_{orb} < 20$ days. In these systems, the mass transfer rate allows for efficient, quasi-equilibrium sub-Eddington accretion over long timescales.
   • The 1.4 M$_\odot$ Peak: This peak is attributed to NS systems that undergo common envelope evolution (often involving more massive donors or specific orbital configurations), where mass growth is minimal.
   • High-Mass Tail: Systems with intermediate-mass donors ($1.6 \le M_d \le 3.0$ M$_\odot$) and short orbital periods can accrete sufficient material to exceed 2.1 M$_\odot$.
3. Spin Period Distribution: The model predicts NS spin periods concentrated between 1 ms and 15 ms for low-mass X-ray binaries (LMXBs). The results are slightly larger than some observational data, which the authors attribute to the assumption of a minimum magnetic field of $5 \times 10^8$ G, preventing the accretion disk from extending too close to the NS surface.

Significance and Claims
The paper claims that the inclusion of super-Eddington accretion physics is crucial for explaining the high-mass peak in the NS mass distribution. By allowing NSs to accrete efficiently even when mass transfer rates exceed the Eddington limit, the model resolves the discrepancy between theoretical predictions of low mass growth and the observed population of massive NSs. The authors assert that their model provides a coherent physical explanation for the bimodal distribution without requiring exotic formation channels for the high-mass peak, attributing it instead to standard binary evolution with super-Eddington accretion.

Limitations and Uncertainties
The authors acknowledge several uncertainties in their model:

• Accretion Efficiency: The assumed efficiency of 0.5 and the treatment of mass loss near the NS are simplified.
• Magnetic Field Decay: The decay rate and minimum field strength are parameters that significantly influence the spin evolution and accretion efficiency.
• Equation of State (EoS): The moment of inertia is fixed at $10^{45}$ g cm$^2$, which is near the lower limit. Variations in the NS EoS could alter the moment of inertia, affecting spin-up timescales and the transition to the propeller regime.
• Excluded Channels: The study does not quantify the contribution of NSs formed via accretion-induced collapse (AIC) or those born with bimodal mass distributions, focusing instead on NSs formed via standard core collapse and subsequent binary evolution.