Potter, Chitre & Tout (2012) embedded a rotationally driven α–Ω dynamo in the radiative zones of a one-dimensional stellar evolution code and left open whether the observed strong, large-scale magnetic fields of upper-main-sequence stars are produced by such a dynamo or are fossil fields, whether the model's free parameters allow its predicted mass threshold to be robust, and whether fossil fluxes large enough to survive the main sequence are physically plausible. The model's distinctive predictions are in tension with the MiMeS survey (magnetic incidence ~7–10% independent of mass, rotation, and age, with ≥20 kG fields in ~30 solar-mass O stars, far above the predicted ~15 solar-mass dynamo threshold); strong fields already exist in pre-main-sequence Herbig Ae/Be stars; and merger-generated fossil fields have been identified for at least one massive star. The open problem is therefore the physical origin of these fields — fossil channel or radiative α–Ω dynamo, which channel supplies the flux, why only ~10% of stars are magnetic, and how the fields decay — which is unresolved in the current literature.

Background

About 7–10 per cent of main-sequence stars of spectral types late B to O — stars from roughly 2 to well over 20 solar masses whose envelopes are stable against convection (radiative envelopes) rather than convective like the Sun's — host strong, stable, large-scale magnetic fields with dipolar surface strengths between a few hundred gauss and about 20 kG. In chemically peculiar A and B stars (Ap/Bp stars) these fields are associated with surface abundance anomalies. Systematic spectropolarimetric surveys — most comprehensively the MiMeS (Magnetism in Massive Stars) survey of more than 500 O and B stars — established that the incidence of such fields is approximately constant across this mass range and shows no correlation with stellar mass, effective temperature, age, or rotation, and that the field-strength distribution is bimodal: strong organized fields above roughly 300 G, ultra-weak fields below roughly 1 G, and an almost empty 'magnetic desert' in between (Aurière et al. 2007; Grunhut et al. 2017; Sikora et al. 2019; Petit et al. 2019).

Two physical origins have long been proposed. The fossil-field hypothesis holds that the field is a relic of star formation — flux inherited from the interstellar medium, or generated in a stellar merger — that relaxes into a stable mixed poloidal–toroidal configuration able to survive a stellar lifetime (Braithwaite & Spruit 2004). The competing hypothesis holds that the field is actively generated inside the radiative zone by a dynamo driven by differential rotation. The canonical mechanism is the Tayler–Spruit dynamo (Spruit 2002): differential rotation winds poloidal into toroidal field (the Ω-effect); the toroidal field becomes unstable to the pinch-type Tayler instability (a non-axisymmetric kink instability of toroidal fields in stably stratified zones); and the resulting magnetic turbulence regenerates poloidal from toroidal field (the α-effect), closing the loop — an α–Ω dynamo. Three-dimensional simulations have since shown that the radiative dynamo can be sustained in radiative zones and spin down radiative layers through internal fields that remain hidden beneath the surface.

Potter, Chitre & Tout (2012) embedded such a radiative α–Ω dynamo, coupled to angular-momentum transport and to magnetic braking through an Alfvén-radius prescription (a magnetized stellar wind carries angular momentum out to the Alfvén radius, the distance at which the wind and the field have equal dynamical influence), in a one-dimensional stellar evolution code using the shellular (latitude-averaged) approximation. The model contains free parameters — the diffusivity calibration CmC_{\rm m}, the turbulent magnetic and chemical Prandtl numbers Prm{\rm Pr}_{\rm m} and Prc{\rm Pr}_{\rm c}, the dynamo efficiency γ\gamma, and the Alfvén-radius calibration — and makes distinctive predictions: the dynamo is sustained only in stars below roughly 15 M⊙M_\odot that begin the main sequence as sufficiently rapid rotators; magnetic braking then spins these stars down, producing the observed group of slowly rotating, nitrogen-enriched stars in the Hunter diagram (a diagnostic plot of surface nitrogen abundance against rotational velocity); and the surface field decays exponentially after an initial peak. The authors stressed that the robustness of the mass threshold against the unconstrained parameters was unverified, and that the discrimination against the fossil picture was not decisive, because a fossil field with an initial strength several orders of magnitude larger could reproduce a similar late-time field — provided such large primordial fluxes are physically plausible, which they left as an open question.

Problem Statement

Determine the physical origin of the strong, large-scale magnetic fields of main-sequence A, B, and O stars — the question Potter, Chitre & Tout (2012) left open when their radiative α–Ω dynamo model could not be definitively distinguished from the fossil-field alternative. The origin is to be determined as a single dominant channel, or, where the evidence warrants, a fractional apportionment among the fossil channels (survival of primordial interstellar flux through pre-main-sequence evolution, or flux generated in stellar mergers) and a sustained rotationally driven radiative α–Ω dynamo. Resolving it requires addressing: (i) whether the dynamo interpretation's distinctive predictions — magnetism confined below a mass threshold of order 15 solar masses, with a dependence on initial rotation — can survive for any choice of the model's unconstrained free parameters consistent with the observed mass- and rotation-independent incidence; (ii) accounting quantitatively for the established observational constraints — the roughly 7–10 per cent incidence independent of mass and rotation, the bimodal field-strength distribution and magnetic desert, the presence of comparable fields in pre-main-sequence Herbig Ae/Be stars, and the evidence for field decay over the main sequence; and (iii) for the fossil side, whether the required initial fluxes are physically plausible — the specific question Potter et al. posed — including their formation and survival during star formation and collapse. Resolving the origin also requires separating the two pictures despite the confounders both tolerate: magnetic braking erasing the rotation signature a dynamo needs, and decaying or relaxing fossil fields mimicking dynamo-driven field evolution.

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