[Paper Review] Sleeping beasts: strong toroidal magnetic field in quiescent magnetars explains their large pulsed fraction

Andrei P. Igoshev, Rainer Hollerbach+2 more|arXiv (Cornell University)|Oct 16, 2020

Pulsars and Gravitational Waves Research28 references4 citations

TL;DR

This study presents the first 3D magneto-thermal MHD simulations of quiescent magnetars with strong toroidal magnetic fields, showing that such fields generate asymmetric surface temperature distributions that explain the high pulsed fractions (16–53%) observed in soft X-ray light curves. The simulations, incorporating relativistic ray propagation, successfully reproduce observed light curves of transient magnetars and constrain their rotational orientation and magnetic geometry.

ABSTRACT

Magnetars are neutron stars (NSs) with extreme magnetic fields of strength $5 imes 10^{13}$ - $10^{15}$ G. They exhibit transient, highly energetic events, such as short X-ray flashes, bursts and giant flares, all of which are powered by their enormous magnetic energy. Quiescent magnetars have X-ray luminosities between $10^{29}$ and $10^{35}$ erg/s, and are further classified as either persistent or transient magnetars. Their X-ray emission is modulated with the rotational period of the NS, with a typical relative amplitude (so-called pulsed fraction) between 10-58 per cent, implying that the surface temperature is significantly non-uniform despite the high thermal conductivity of the star's crust. Here, we present the first 3D magneto-thermal MHD simulations of magnetars with strong toroidal magnetic fields. We show that these models, combined with ray propagation in curved space-time, accurately describe the light-curves of most transient magnetars in quiescence and allow us to further constrain their rotational orientation. We find that the presence of a strong toroidal magnetic field explains the observed asymmetry in the surface temperature, and is the main cause of the strong modulation of thermal X-ray emission in quiescence.

Motivation & Objective

• To explain the origin of high pulsed fractions (10–58%) in quiescent magnetars' soft X-ray emission, which cannot be explained by symmetric models.
• To investigate how strong toroidal magnetic fields in the neutron star crust influence surface temperature distribution and thermal X-ray modulation.
• To constrain the rotational orientation (inclination, phase shift, dipole-axis angle) of transient magnetars using 3D simulations and observed light curves.
• To test whether strong toroidal fields—previously inferred from spectral modeling—can naturally produce the observed thermal asymmetries without ad hoc hot spot placements.
• To determine whether the observed light curves of seven transient magnetars in quiescence are consistent with models featuring strong toroidal fields and relativistic effects.

Proposed method

• Conducted 3D magneto-thermal MHD simulations in a spherical shell using a modified PARODY code to model heat flow and magnetic field evolution in the neutron star crust.
• Simulated two configurations: one with aligned poloidal and toroidal fields (model A), and one with a 45° inclination (model B), both with 90% of total magnetic energy in the toroidal component.
• Used relativistic ray tracing in the Schwarzschild metric to compute light curves, accounting for gravitational lensing and light-bending effects.
• Fitted simulated light curves to folded soft X-ray (0.3–2 keV) observations of seven transient magnetars using C-statistics and the Nelder-Mead optimization algorithm.
• Performed statistical analysis with 95% confidence intervals via Δχ² = 3.84 to determine parameter uncertainties for κ (dipole-axis angle), i (inclination), and ΔΦ (phase shift).
• Used XMM-Newton and Chandra data, applying background filtering, source extraction (20 arcsec radius), and barycentric correction; derived unabsorbed luminosities using N_H from the McGill catalogue and xspec for spectral fitting.

Experimental results

Research questions

• RQ1 Can strong toroidal magnetic fields in the crust naturally produce the observed high pulsed fractions in quiescent magnetars?
• RQ2 How does the geometry of the toroidal field (aligned vs. inclined) affect the resulting surface temperature distribution and light curve shape?
• RQ3 To what extent can 3D magneto-thermal simulations reproduce the folded soft X-ray light curves of transient magnetars in quiescence?
• RQ4 What are the most probable rotational orientations (κ, i, ΔΦ) for individual magnetars based on light curve fitting?
• RQ5 Why do some magnetars (e.g., SGR 0501 and 3XMM J1852) deviate from the model predictions, and what physical mechanisms might explain these discrepancies?

Key findings

• Model A (aligned poloidal-toroidal fields) and model B (45° inclined) both produce surface temperature distributions with filamentary hot and cold regions due to toroidal field instability, matching observed thermal asymmetries.
• The simulations yield soft X-ray luminosities of 0.8–2×10³² erg/s and pulsed fractions between 16% and 53%, consistent with observations of transient magnetars.
• Models with weak toroidal fields produce symmetric temperature distributions and maximum pulsed fractions of ~10%, insufficient to explain the observed modulation.
• The best-fit model for SGR 0418+5729 has κ = 230° ± 26°, i = 274° ± 22°, ΔΦ = 217° ± 9°, and an age of 24.0 Kyr, with a reduced χ²/d.o.f. indicating a good fit.
• SGR 0501 and 3XMM J185246.6+003317 show discrepancies: SGR 0501 has a skewed light curve with a shallow central valley, likely due to a magnetospheric power-law component from inverse Compton scattering.
• The low photon count and uncertain N_H for 3XMM J185246.6+003317 suggest it may be a persistent magnetar, possibly brighter than 2×10³³ erg/s, explaining its poor fit to the model.