[Paper Review] Evolution of the Magnetic Field in Accreting Neutron Stars

Sushan Konar|arXiv (Cornell University)|Jan 20, 2000

Scientific Research and Discoveries7 references3 citations

TL;DR

This paper investigates magnetic field evolution in accreting neutron stars, proposing that crustal ohmic decay and accretion-driven heating govern field reduction. It finds that diamagnetic screening is ineffective due to rapid interchange instabilities, while accretion leads to initial rapid field decay followed by freezing; millisecond pulsars require high accretion rates or core flux expulsion with large impurity strengths.

ABSTRACT

There has been sufficient observational indication suggesting a causal connection between the binary history of neutron stars and the evolution of their magnetic field. In particular, it is believed that the generation of the low-field millisecond pulsars is a consequence of the processing of normal high-field neutron stars in binary systems. We try to understand the mechanism of field evolution in neutron stars that are members of binary systems with an aim to understand the problem of millisecond pulsar generation. To this end we have looked at four related problems : i. the effect of diamagnetic screening on the final field of a neutron star accreting material from its binary companion; ii. evolution of magnetic flux located in the crust of an accreting neutron star; iii. application of the above-mentioned model to real systems and a comparison with observations; iv. an investigation into the consequences of magnetic flux being initially located in the core of the star and its observational implications.

Motivation & Objective

• To understand the mechanism of magnetic field evolution in neutron stars with binary histories, particularly in relation to observed low-field systems.
• To assess whether diamagnetic screening in accreting material can significantly reduce the external dipole field.
• To model the evolution of crustal magnetic fields under accretion-induced heating and mass loading.
• To compare theoretical predictions with observations of binary pulsars, millisecond pulsars, and X-ray binaries.
• To evaluate the role of core magnetic flux expulsion during spin-down and its implications for field decay in isolated and accreting systems.

Proposed method

• Modeling the time evolution of magnetic fields in neutron star crusts using ohmic diffusion equations with temperature-dependent conductivity.
• Incorporating accretion-induced crustal heating via the relation $\log T = 0.397\log\dot{M} + 12.35$ to compute changes in electrical resistivity.
• Analyzing time-scale competition between diffusive, screening, and Rayleigh-Taylor instability processes to assess field burial feasibility.
• Simulating field evolution through multiple binary phases: isolated phase, wind accretion, and Roche lobe overflow (Roche-contact phase).
• Using impurity strength $Q$ as a free parameter to control resistivity and decay timescales in both crustal and core flux expulsion models.
• Comparing model outputs with observational data on pulsar magnetic fields, ages, and accretion rates to constrain model parameters.

Experimental results

Research questions

• RQ1 Can diamagnetic screening by accreting material effectively reduce the external magnetic dipole field of a neutron star?
• RQ2 How does accretion-induced heating affect the ohmic decay timescale of crustal magnetic fields?
• RQ3 What determines the final surface magnetic field strength in accreting neutron stars, and how does it depend on accretion rate and initial field configuration?
• RQ4 Can spin-down-induced flux expulsion from the core explain the low magnetic fields observed in millisecond pulsars?
• RQ5 What constraints do observations of binary pulsars and X-ray binaries place on the impurity strength $Q$ in neutron star crusts?

Key findings

• Diamagnetic screening is ineffective in reducing the external magnetic field because the Rayleigh-Taylor instability time-scale is much shorter than both diffusive and screening time-scales, preventing field line dragging or burial.
• Accretion leads to an initial rapid decay of the surface magnetic field due to enhanced ohmic diffusion from crustal heating, followed by a freeze-out phase where decay slows significantly.
• Higher accretion rates lead to faster crustal heating, earlier freezing, and lower final surface field strengths, with a positive correlation between accretion rate and final field strength observed in models.
• For millisecond pulsars to form via the core flux expulsion model, impurity strength $Q$ must exceed unity, which is inconsistent with constraints from isolated pulsars unless $Q \leq 0.05$.
• In the crustal model, final surface fields are lower for lower accretion rates and longer pre-accretion phases, and higher for deeper initial current loops.
• Low-mass X-ray binaries (LMXBs) can produce fields as low as $10^8$ G if impurity strength $Q \geq 0.5$, consistent with millisecond pulsar observations.