[Paper Review] Magnetic Field Decay Makes Neutron Stars Look Older Than They Are

Shuang‐Nan Zhang, Yi Xie|arXiv (Cornell University)|Oct 14, 2011

Pulsars and Gravitational Waves Research1 references3 citations

TL;DR

This paper provides strong observational evidence that magnetic field decay in young neutron stars causes their spin-down ages to significantly overestimate their true ages, making them appear older than they are. Using true ages from supernova remnant associations, the study finds that about half of these neutron stars exhibit rapid magnetic field decay via ambipolar diffusion (α ≈ 0.5), resolving the long-standing puzzle of mismatched neutron star and remnant ages.

ABSTRACT

It is commonly accepted that a neutron star is produced, when a massive star exhausts its nuclear fuel and ends its life in a core-collapse supernova explosion. This scenario is confirmed by the detection of pulsars, which are believed to be rapidly spinning neutron stars, in the central regions of many supernova remnants. Neutron stars and their associated supernova remnants should therefore have the same ages. As expected, the age of the Crab Pulsar, the first to be connected with a supernova remnant (the Crab Nebula), can be inferred from its current spin period and its derivative and indeed has about the same age of the supernova remnant, that was produced from a historically recorded supernova explosion in 1054. However most neutron stars appear to be much older than the ages of their associated supernova remnants, a puzzle not yet understood. Another puzzle is that so far no convincing evidence has been found in favor of magnetic field decay in neutron stars, that is predicted in most models of neutron stars. Here we show convincing evidence of magnetic field decay in some young neutron stars, and that the magnetic field decay can alter their spinning behaviors significantly such that these neutron stars appear much older than they really are.

Motivation & Objective

• To resolve the longstanding puzzle that most neutron stars appear older than their associated supernova remnants.
• To test whether magnetic field decay is responsible for the discrepancy between spin-down ages and true ages of neutron stars.
• To determine the dominant mechanism of magnetic field decay in young neutron stars using observational data.
• To assess the implications of magnetic field decay for neutron star evolution, equation of state, and pulsar population synthesis.

Proposed method

• The study compares spin-down ages (T_s) with true ages (T_SNR) derived from the morphological evolution of supernova remnants.
• It uses the braking index n_b = 2 - P P̈ / Ṗ² to infer whether the spin-down law deviates from n = 3, indicating magnetic field evolution.
• The magnetic field decay is modeled as B(t) ∝ t^(-α), where α quantifies the decay rate, and the best-fit α is derived from T_SNR/T_s vs. B data.
• The model assumes that neutron stars are born with similar properties, and evolutionary tracks are reconstructed from P, Ṗ, and B correlations.
• Statistical fitting is performed on the T_SNR/T_s vs. B distribution in log-log space to determine α and identify bi-modality.
• Theoretical constraints on ambipolar diffusion (α = 0.5) and ohmic/hall diffusion timescales are used to validate the dominant decay mechanism.

Experimental results

Research questions

• RQ1 Why do most neutron stars appear significantly older than their associated supernova remnants?
• RQ2 Is magnetic field decay the primary cause of the discrepancy between spin-down and true ages in neutron stars?
• RQ3 What is the dominant physical mechanism driving magnetic field decay in young neutron stars?
• RQ4 Can the observed distribution of T_SNR/T_s and B be explained by a model of time-dependent magnetic field decay?
• RQ5 What fraction of young neutron stars experience rapid magnetic field decay, and what are the implications for pulsar evolution and neutron star equations of state?

Key findings

• A strong positive correlation is found between the ratio T_SNR/T_s and the dipole magnetic field strength B, indicating that lower B values correlate with larger age discrepancies.
• The distribution of T_SNR/T_s is bi-modal, with a clear division at T_SNR/T_s ≈ 0.5, suggesting two distinct evolutionary populations.
• About 50% of young neutron stars exhibit rapid magnetic field decay with α ≈ 0.5, consistent with ambipolar diffusion being the dominant mechanism.
• The remaining ~50% show little or no magnetic field decay (α ≈ 0), indicating a bimodal evolutionary behavior.
• The model with α = 0.5 successfully reproduces the observed data, and the predicted core temperature (~10^6 K) is consistent with observations of surface temperatures (~6×10^5 K).
• The study concludes that magnetic field decay is necessary to explain the age discrepancy, as alternative models with constant or increasing n (braking index) are physically implausible.