Magneto--thermal evolution of neutron stars

Abstract: We study the mutual influence of thermal and magnetic evolution in a neutron star's crust in axial symmetry. Taking into account realistic microphysical inputs, we find the heat released by Joule effect consistent with the circulation of currents in the crust, and we incorporate its effects in 2D cooling calculations. We solve the induction equation numerically using a hybrid method (spectral in angles, but a finite--differences scheme in the radial direction), coupled to the thermal diffusion equation. We present the first long term 2D simulations of the coupled magneto-thermal evolution of neutron stars. This substantially improves previous works in which a very crude approximation in at least one of the parts (thermal or magnetic diffusion) has been adopted. Our results show that the feedback between Joule heating and magnetic diffusion is strong, resulting in a faster dissipation of the stronger fields during the first million years of a NS's life. As a consequence, all neutron stars born with fields larger than a critical value (about 5 10^13 G) reach similar field strengths (approximately 2-3 10^{13} G) at late times. Irrespectively of the initial magnetic field strength, after $10^6$ years the temperature becomes so low that the magnetic diffusion timescale becomes longer than the typical ages of radio--pulsars, thus resulting in apparently no dissipation of the field in old NS. We also confirm the strong correlation between the magnetic field and the surface temperature of relatively young NSs discussed in preliminary works. The effective temperature of models with strong internal toroidal components are systematically higher than those of models with purely poloidal fields, due to the additional energy reservoir stored in the toroidal field that is gradually released as the field dissipates.

• The paper demonstrates that coupling magnetic field and thermal diffusion equations reveals rapid decay of strong fields due to Joule heating.
• The hybrid computational approach models the interaction between realistic microphysics in the NS crust and the evolving magnetic configuration.
• The study finds that initial strong fields converge to about 2–3×10^13 G over 10^5–10^6 years and suggests future 3D simulations to capture additional effects.

Magneto-Thermal Evolution of Neutron Stars

The paper by Pons, Miralles, and Geppert provides an in-depth investigation into the coupled magneto-thermal evolution of neutron stars (NSs). This study comprehensively addresses the interaction between the magnetic field (MF) and thermal processes within the NS crust, emphasizing the importance of considering them as interconnected rather than isolated phenomena.

Methodology and Key Findings

The authors solve the induction equation using a hybrid computational approach, coupling it with the thermal diffusion equation. This methodology facilitates an accurate simulation of the mutual influence between a NS's thermal and magnetic evolution under axial symmetry. The computation incorporates realistic microphysical inputs, ensuring more precise modeling of the NS environment than prior one-dimensional approximations or cruder two-dimensional models.

A significant result from their simulations is the role of Joule heating, driven by electrical currents, in the thermal and magnetic dynamics of NSs. The simulations reveal that the dissipation of magnetic fields is influenced strongly by Joule heating, leading to a rapid decay of strong fields during the early life of NSs. This effect is particularly evident in NSs with fields exceeding a critical value of $5 \times 10^{13} \, \text{G}$. Such stars evolve towards a similar magnetic field strength ($\approx 2-3 \times 10^{13} \, \text{G}$) after $10^5-10^6$ years, regardless of the initial field strength. For NSs born with weaker fields, the magnetic evolution is less affected, resulting in a slower decay.

Another intriguing outcome is the influence of the internal toroidal field components on surface temperature. The models with substantial internal toroidal fields, due to the additional energy reservoir, maintain higher effective temperatures than those with purely poloidal configurations. This suggests a substantial correlation between MF configuration and thermal distribution in relatively young NSs.

Theoretical and Practical Implications

The research indicates that observed magnetar activities and thermal emissions provide potential diagnostics for underlying magnetic and thermal structures within NSs. Practically, this work outlines a framework for predicting the long-term thermal states of NSs, which is critical for interpreting observational data from X-ray and radio telescopes.

Theoretically, these findings support models where crustal fields play a significant role in NS evolution, questioning the longevity of magnetic field retention and thermal profiles in NSs. The conclusion also hints at the potential influence of ambipolar diffusion in NS cores, particularly when considering superconducting states, which may further affect long-term cooling theories.

Future Directions

While this study enhances understanding of magneto-thermal evolution, it also raises pertinent avenues for future research. The potential influence of non-linear Hall effects, particularly at later NS stages, could modify the magnetic energy cascade and warrants computational advances beyond current capabilities. Likewise, including three-dimensional (3D) simulations could reveal more intricacies of field geometries and thermal distributions, especially in NSs with complex field configurations. Additionally, coupling the dissipation of crustal currents with ambipolar diffusion in the core, especially under superfluid conditions, should be prioritized to achieve a holistic understanding of NS magneto-thermal evolution.

This paper, through its comprehensive and numerically robust approach, lays significant groundwork for these future explorations and offers pivotal insights into the fundamental processes governing neutron star evolution.