Neutron stars generate magnetic fields a billion times stronger than any magnet on Earth, and these fields dictate whether a star will erupt as a magnetar giant flare or power a superluminous supernova. Researchers at the University of Leeds are building the first three-dimensional computer models that simultaneously track how magnetic fields and heat evolve inside a neutron star’s crust and core, coupling two physical processes—Hall evolution in the crust and ambipolar diffusion in the core—that have previously been treated separately. This matters because existing models rely on arbitrary initial conditions, leaving a gap in understanding how core and crust fields interact over thousands of years. If successful, the simulations will explain why some neutron stars become magnetars while others remain quiet, and will help decode data from future pulsar surveys such as the Square Kilometre Array. This is fundamental science: there is no immediate practical application, but understanding how the universe’s most extreme magnetic objects behave could one day inform plasma physics or high-energy astrophysics in ways not yet foreseen.
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Neutron stars have the strongest magnetic fields in the universe, reaching 1015 G. These enormous fields determine their observational properties such as magnetar giant flares or magnetar-powered supernova explosions; see for example the review by Igoshev, Popov & Hollerbach (2021). Our group previously computed the first three-dimensional simulations for magnetic field and temperature evolution in the crusts of neutron stars for a range of initial configurations, including simple dipoles, also with additional toroidal components (Igoshev, Hollerbach, Wood & Gourgouliatos 2021a), off-centred dipoles (Igoshev, Hollerbach & Wood 2023), and stochastic small-scale fields (Gourgouliatos, Hollerbach & Igoshev 2020; Igoshev, Gourgouliatos, Hollerbach & Wood 2021b). We further presented the first three-dimensional calculations of ambipolar diffusion (in the single-fluid approximation) in neutron star cores, coupled with Ohmic decay in the crust (Igoshev & Hollerbach 2023). In the past 18 months we have also developed two new collaborations to incorporate further realism in our simulations. First, J. Guilet, R. Raynaud, et al. (France) have done numerical modelling of magnetic fields in proto-neutron stars (Raynaud et al. 2020, 2022; Barrere et al. 2022, 2023). We are collaborating with them to use the end-stages of their models as the initial conditions for our models, thereby avoiding the otherwise somewhat arbitrary nature of what initial conditions to choose. Second, A. Reisenegger (Chile), M. Gusakov (Israel) and others have been interested for many years in developing more realistic equations for ambipolar diffusion that go beyond the single-fluid approximation (Hoyos, Reisenegger & Valdivia 2010; Ofengeim & Gusakov 2018; Castillo, Reisenegger & Valdivia 2020). We have been collaborating with them on numerically solving some of these equations, with very encouraging preliminary results. The objective of this proposal is to build on this work, and ultimately conduct three-dimensional modelling that couples ambipolar diffusion in the two-fluid approximation in the core together with Hall evolution in the crust, thereby allowing us to understand how the fields in the core and crust interact, and how this affects the observational properties of magnetars. This has significant implications also for our understanding of superluminous supernovae, long gamma-ray bursts, and electromagnetic precursors to gravitational wave events from double neutron star mergers. Understanding the long-term magnetic field evolution is essential if we are to understand the diversity of observed neutron stars, and to decode future pulsar surveys including from the Square-Kilometer Array. This work addresses STFC Science Challenge A5: how do stars and galaxies evolve?
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