Classical magnetars are young, isolated neutron stars whose X-ray bursts, outbursts, and persistent emission are powered by the decay of ultra-strong magnetic fields, defined observationally by spin-down-inferred surface dipole fields Bdip≳1014B_{\rm dip}\gtrsim 10^{14} G. Igoshev et al. (2025) performed the first direct simulations of neutron-star magneto-thermal evolution started from a dynamo-generated magnetic field — a Tayler–Spruit dynamo (a dynamo of a stably stratified, differentially rotating stellar interior) operating in a proto-neutron star (the hot, rapidly evolving remnant of a core-collapse supernova) spun up by supernova fallback accretion — and showed that this channel naturally reproduces the properties of low-field magnetars (Bdip≲1013B_{\rm dip}\lesssim 10^{13} G but magnetar-like activity), implying that classical and low-field magnetars may form through distinct channels linked to different dynamos. However, the formation channel of classical magnetars and the internal structure of their magnetic fields were left explicitly open: no existing modeling self-consistently produces their ultra-strong, dominantly large-scale dipolar surface fields from a specified proto-neutron-star dynamo, because the dynamo-stage fields simulated to date — including the magnetar-strength dipolar fields generated internally by the convective dynamo of Raynaud et al. (2020) — are internal proto-neutron-star fields that have not been carried through magneto-thermal evolution; and no falsifiable magneto-thermal diagnostics exist that observationally discriminate between dynamo families. The problem is to determine how classical magnetars acquire their fields — identifying the amplification mechanism and the internal poloidal/toroidal field geometry — and to establish whether observable magneto-thermal signatures can distinguish the underlying amplification mechanism from the Tayler–Spruit channel associated with low-field magnetars.

Background

Magnetars are isolated, young neutron stars whose luminous X-ray emission, short bursts, and months-long outbursts are powered by the decay of ultra-strong magnetic fields rather than by rotation. They are conventionally divided into classical magnetars, defined by spin-down-inferred surface dipolar fields Bdip≳1014B_{\rm dip}\gtrsim 10^{14} G, and low-field magnetars — roughly 5 of the ~30 known objects — whose dipolar fields are 10–100 times weaker (≲1013\lesssim 10^{13} G) yet which display the same burst and outburst activity. Any formation theory must explain both populations. The magnetic field must be built within the first seconds after core collapse, while the proto-neutron star (PNS) — the hot, rapidly evolving remnant of a core-collapse supernova, tens of kilometers in size, stably stratified in its outer parts and often differentially rotating — is still dynamically active. Candidate amplification mechanisms include: a convective dynamo driven by PNS convection, proposed by Duncan & Thompson (1992) and demonstrated in three-dimensional simulations by Raynaud et al. (2020), which generates magnetar-strength dipolar fields for sufficiently rapid birth rotation; dynamos driven by the magnetorotational instability — an instability of differentially rotating magnetized fluids that taps the free energy of differential rotation; and the Tayler–Spruit dynamo — a dynamo of a stably stratified, differentially rotating star in which the Tayler instability, a pinch-type instability of toroidal magnetic field loops, replaces convection as the turbulent driver. Barrère et al. (2022) proposed that a slowly rotating PNS spun up by fallback accretion onto the newborn star can excite a Tayler–Spruit dynamo and thereby form magnetars without requiring a rapidly rotating progenitor core. What is observed at Myr ages is shaped by magneto-thermal evolution: the crust-confined magnetic field evolves through the Hall cascade (the advection of magnetic field by the magnetized electron fluid, moving energy to small scales) and Ohmic dissipation, which both heat the crust and drive the star's cooling and spin-down. Igoshev, Barrère, Raynaud, Guilet, Wood & Hollerbach (2025) connected these stages for the first time: they extracted the magnetic field from the top (outermost) 10% of a Tayler–Spruit PNS dynamo simulation, imposed it as a crust-confined initial configuration (the field restricted to the solid crust, as appropriate when the highly conducting core does not participate in the evolution), and evolved it for 1 Myr. The result naturally reproduced the low-field-magnetar phenomenology — weak dipole (≲1013\lesssim 10^{13} G) coexisting with strong small-scale fields, magnetically induced crustal failures producing X-ray bursts, small hot spots with high pulsed fractions, and, with torques from a fallback disk in the propeller regime (the accretion state in which the star's rotating magnetosphere ejects the inner disk instead of accreting it, braking the spin), spin periods of 8–11 s. They concluded that classical and low-field magnetars likely form through two distinct channels, potentially linked to different dynamo mechanisms, while stating that 'the formation of classical magnetars as well as the internal structure of their magnetic fields remains an open question'. Notably, simulations initialized with turbulent dynamo-generated fields reproduce central compact objects (CCOs; young cooling neutron stars with weak dipole fields) and low-field magnetars but still fail to produce the ultra-strong, dominant dipolar (ℓ=1\ell=1, the lowest spherical-harmonic degree) poloidal surface component that defines classical magnetars, and the internal (core plus crust) poloidal/toroidal field geometry of classical magnetars is not directly observable and remains unconstrained.

Problem Statement

How do classical magnetars — neutron stars with spin-down-inferred surface dipolar fields Bdip≳1014B_{\rm dip}\gtrsim 10^{14} G dominating over small-scale components — acquire their ultra-strong, dominantly large-scale magnetic fields, and what is the internal structure of those fields? As left open by Igoshev et al. (2025), this comprises three linked parts: (1) identify the formation channel and magnetic-amplification mechanism — whether the same Tayler–Spruit dynamo operating in a different regime, a distinct proto-neutron-star dynamo such as the convective dynamo of a rapidly rotating remnant (Duncan & Thompson 1992; Raynaud et al. 2020) or a magnetorotational-instability-driven dynamo, a fossil field inherited from the progenitor, or another channel — that self-consistently produces a dominant ≳1014\gtrsim 10^{14} G large-scale (ℓ=1\ell=1) poloidal surface component together with an internal field structure whose geometry and strength are outputs of the solution and must be consistent with observational constraints on magnetars, in particular the strong large-scale toroidal component (of order 101510^{15} G) shown by Igoshev et al. (2021) to be required to reproduce the observed quiescent X-ray emission of magnetars and its strong rotational modulation; (2) determine the resulting internal poloidal/toroidal field geometry and show that this configuration, followed through its subsequent magneto-thermal evolution, under either a crust-confined configuration or a coupled core–crust treatment that retains the core field, remains consistent with the classical-magnetar observables (spin periods, period derivatives, quiescent and outburst luminosities, burst energetics); and (3) establish whether concrete, falsifiable magneto-thermal diagnostics — measurable surface, timing, and magnetospheric observables — can observationally discriminate between candidate magnetic-amplification channels, including, if the classical and low-field populations do arise from distinct dynamos, between the classical-magnetar channel and the Tayler–Spruit channel that produces low-field magnetars; whether such discriminants exist, and whether the two populations correspond to different dynamo families at all, are open parts of the question rather than presuppositions. Resolving part (1) requires exhibiting at least one candidate channel that self-consistently produces the required dominant ≳1014\gtrsim 10^{14} G large-scale (ℓ=1\ell=1) poloidal surface component together with an internally consistent field structure; ruling out the remaining enumerated candidates (uniqueness of the actual channel) is not required, since part (3) addresses whether the candidate channels can be discriminated at all. Resolving part (2) requires showing that the proposed configuration, followed through its subsequent magneto-thermal evolution, remains consistent with the listed classical-magnetar observables, or, where a full evolution is not performed, an explicitly bounded consistency argument that confronts the configuration with those observables.

References

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