Tayler-Spruit Dynamo Research Articles

Photometric White Dwarf Rotation

We present a census of photometrically detected rotation periods for white dwarf (WD) stars. We analyzed the light curves of 9285 WD stars observed by the Transiting Exoplanet Survey Satellite up to Sector 69. Using Fourier transform analyses and the TESS_localize software, we detected variability periods for 318 WD stars. The 115 high-probability likely single WDs in our sample have a median rotational period of 3.9 hr and a median absolute deviation of 3.5 hr. Our distribution is significantly different from the distribution of the rotational period from asteroseismology, which exhibits a longer median period of 24.2 hr and a median absolute deviation of 12.1 hr. In addition, we reported nonpulsating periods for three known pulsating WDs with rotational periods previously determined by asteroseismology: NGC 1501, TIC 7675859, and G226-29. We also calculated evolutionary models including six angular momentum transfer mechanisms from the literature throughout evolution in an attempt to reproduce our findings. Our models indicate that the temperature–period relation of most observational data is best fitted by models with low metallicity, probably indicating problems with the computations of angular momentum loss during the high-mass-loss phase. Our models also generate internal magnetic fields through the Tayler–Spruit dynamo.

Tayler Instability Revisited

Tayler instability of toroidal magnetic fields B ϕ is broadly invoked as a trigger for turbulence and angular momentum transport in stars. This paper presents a systematic revision of the linear stability analysis for a rotating, magnetized, and stably stratified star. For plausible configurations of B ϕ , instability requires diffusive processes: viscosity, magnetic diffusivity, or thermal/compositional diffusion. Our results reveal a new physical picture, demonstrating how different diffusive effects independently trigger instability of two types of waves in the rotating star: magnetostrophic waves and inertial waves. It develops via overstability of the waves, whose growth rate sharply peaks at some characteristic wavenumbers. We determine instability conditions for each wave branch and find the characteristic wavenumbers. The results are qualitatively different for stars with magnetic Prandtl number Pm ≪ 1 (e.g., the Sun) and Pm ≫ 1 (e.g., protoneutron stars). The parameter dependence of unstable modes suggests a nonuniversal scaling of the possible Tayler–Spruit dynamo.

Tayler–Spruit dynamo simulations for the modeling of radiative stellar layers

Context. Maxwell stresses exerted by dynamo-generated magnetic fields have been proposed as an efficient mechanism to transport angular momentum in radiative stellar layers. Numerical simulations are still needed to understand its trigger conditions and the saturation mechanisms. Aims. The present study follows up on a recent paper where we reported on the first simulations of Tayler-Spruit dynamos. Here we extend the parameter space explored to assess in particular the influence of stratification on the dynamo solutions. We also present numerical verification of theoretical assumptions made previously that were instrumental in deriving the classical prescription for angular momentum transport implemented in stellar evolution codes. Methods. A simplified radiative layer is modeled numerically by considering the dynamics of a stably stratified, differentially rotating, magnetized fluid in a spherical shell. Results. Our simulations display a diversity of magnetic field topologies and amplitudes depending on the flow parameters, including hemispherical solutions. The Tayler-Spruit dynamos reported here are found to satisfy magnetostrophic equilibrium and achieve efficient turbulent transport of angular momentum, following Spruit’s heuristic prediction.

Angular momentum transport by magnetic fields in main-sequence stars with Gamma Doradus pulsators

Context. Asteroseismic studies show that cores of post-main-sequence stars rotate more slowly than theoretically predicted by stellar models with purely hydrodynamical transport processes. Recent studies of main-sequence stars, particularly Gamma Doradus (γ Dor) stars, have revealed the internal rotation rates for hundreds of stars, offering a counterpart on the main sequence for studies of angular momentum transport. Aims. We investigate whether such a disagreement between observed and predicted internal rotation rates is present in main-sequence stars by studying angular momentum transport in γ Dor stars. Furthermore, we test whether models of rotating stars with internal magnetic fields can reproduce their rotational properties. Methods. We computed rotating models with the Geneva stellar evolution code taking into account meridional circulation and shear instability. We also computed models with internal magnetic fields using a general formalism for transport by the Tayler-Spruit dynamo. We then compared these models to observational constraints for γ Dor stars that we compiled from the literature, thus combining the core rotation rates, projected rotational velocities from spectroscopy, and constraints on their fundamental parameters. Results. We show that combining the different observational constraints available for γ Dor stars enable us to clearly distinguish the different scenarios for internal angular momentum transport. Stellar models with purely hydrodynamical processes are in disagreement with the data, whereas models with internal magnetic fields can reproduce both core and surface constraints simultaneously. Conclusions. Similarly to results obtained for subgiant and red giant stars, angular momentum transport in radiative regions of γ Dor stars is highly efficient, in good agreement with predictions of models with internal magnetic fields.

Numerical simulations of the Tayler–Spruit dynamo in proto-magnetars

ABSTRACT The Tayler–Spruit dynamo is one of the most promising mechanisms proposed to explain angular momentum transport during stellar evolution. Its development in proto-neutron stars spun-up by supernova fallback has also been put forward as a scenario to explain the formation of very magnetized neutron stars called magnetars. Using three-dimensional direct numerical simulations, we model the proto-neutron star interior as a stably stratified spherical Couette flow with the outer sphere that rotates faster than the inner one. We report the existence of two subcritical dynamo branches driven by the Tayler instability. They differ by their equatorial symmetry (dipolar or hemispherical) and the magnetic field scaling, which is in agreement with different theoretical predictions (by Fuller and Spruit, respectively). The magnetic dipole of the dipolar branch is found to reach intensities compatible with observational constraints on magnetars.

Spin-down by dynamo action in simulated radiative stellar layers.

The evolution of a star is influenced by its internal rotation dynamics through transport and mixing mechanisms, which are poorly understood. Magnetic fields can play a role in transporting angular momentum and chemical elements, but the origin of magnetism in radiative stellar layers is unclear. Using global numerical simulations, we identify a subcritical transition from laminar flow to turbulence caused by the generation of a magnetic dynamo. Our results have many properties of the theoretically proposed Tayler-Spruit dynamo mechanism, which strongly enhances transport of angular momentum in radiative zones. The dynamo generates deep toroidal fields that are screened by the stellar outer layers. This mechanism could produce strong magnetic fields inside radiative stars without an observable field on their surface.

A new scenario for magnetar formation: Tayler-Spruit dynamo in a proto-neutron star spun up by fallback

Magnetars are isolated young neutron stars characterised by the most intense magnetic fields known in the Universe, which power a wide variety of high-energy emissions from giant flares to fast radio bursts. The origin of their magnetic field is still a challenging question. In situ magnetic field amplification by dynamo action could potentially generate ultra-strong magnetic fields in fast-rotating progenitors. However, it is unclear whether the fraction of progenitors harbouring fast core rotation is sufficient to explain the entire magnetar population. To address this point, we propose a new scenario for magnetar formation involving a slowly rotating progenitor, in which a slow-rotating proto-neutron star is spun up by the supernova fallback. We argue that this can trigger the development of the Tayler-Spruit dynamo while other dynamo processes are disfavoured. Using the findings of previous studies of this dynamo and simulation results characterising the supernova fallback, we derive equations modelling the coupled evolution of the proto-neutron star rotation and magnetic field. Their time integration for different accreted masses is successfully compared with analytical estimates of the amplification timescales and saturation value of the magnetic field. We find that the magnetic field is amplified within 20 − 40 s after the core bounce, and that the radial magnetic field saturates at intensities between ∼1013 and 1015 G, therefore spanning the full range of a magnetar’s dipolar magnetic fields. The toroidal magnetic field is predicted to be a factor of 10–100 times stronger, lying between ∼1015 and 3 × 1016 G. We also compare the saturation mechanisms proposed respectively by H.C. Spruit and J. Fuller, showing that magnetar-like magnetic fields can be generated for a neutron star spun up to rotation periods of ≲8 ms and ≲28 ms, corresponding to accreted masses of ≳ 4 × 10−2 M⊙ and ≳ 1.1 × 10−2 M⊙, respectively. Therefore, our results suggest that magnetars can be formed from slow-rotating progenitors for accreted masses compatible with recent supernova simulations and leading to plausible initial rotation periods of the proto-neutron star.

Angular-momentum Transport in Proto-neutron Stars and the Fate of Neutron Star Merger Remnants

Both the core collapse of rotating massive stars, and the coalescence of neutron star (NS) binaries result in the formation of a hot, differentially rotating NS remnant. The timescales over which differential rotation is removed by internal angular-momentum transport processes (viscosity) have key implications for the remnant’s long-term stability and the NS equation of state (EOS). Guided by a nonrotating model of a cooling proto-NS, we estimate the dominant sources of viscosity using an externally imposed angular-velocity profile Ω(r). Although the magneto-rotational instability provides the dominant source of effective viscosity at large radii, convection and/or the Tayler–Spruit dynamo dominate in the core of merger remnants where dΩ/dr ≥ 0. Furthermore, the viscous timescale in the remnant core is sufficiently short that solid-body rotation will be enforced faster than matter is accreted from rotationally supported outer layers. Guided by these results, we develop a toy model for how the merger remnant core grows in mass and angular momentum due to accretion. We find that merger remnants with sufficiently massive and slowly rotating initial cores may collapse to black holes via envelope accretion, even when the total remnant mass is less than the usually considered threshold ≈1.2 M TOV for forming a stable solid-body rotating NS remnant (where M TOV is the maximum nonrotating NS mass supported by the EOS). This qualitatively new picture of the post-merger remnant evolution and stability criterion has important implications for the expected electromagnetic counterparts from binary NS mergers and for multimessenger constraints on the NS EOS.

The magneto-rotational instability in massive stars

Context. The magneto-rotational instability (MRI) has been proposed as a mechanism to transport angular momentum (AM) and chemical elements in theoretical stellar models. Aims. Using as a prototype a massive star of 15 M⊙ with solar metallicity, we explore the effects of the MRI on the evolution of massive stars. Methods. We used the Geneva Stellar Evolution Code to simulate the evolution of various models, up to the end of oxygen burning, including the MRI through effective, one-dimensional, diffusion coefficients. We consider different trigger conditions (depending on the weighting of chemical gradients through an arbitrary but commonly used factor) and different treatments of meridional circulation as either advective or diffusive. We also compare the MRI with the Tayler-Spruit (TS) dynamo in models that included both instabilities. Results. The MRI triggers throughout stellar evolution. Its activation is highly sensitive to the treatment of meridional circulation and the existence of chemical gradients. The MRI is very efficient at transporting both matter and AM, leading to noticeable differences in rotation rates and chemical structure, which may be observable in young main sequence stars. While the TS dynamo is the dominant mechanism for transferring AM, the MRI remains relevant in models where both instabilities are included. Extrapolation of our results suggests that models that include the MRI tend to develop more compact cores, which likely produce failed explosions and black holes, than models where only the TS dynamo is included (where explosions and neutron stars may be more frequent). Conclusions. The MRI can be an important factor in massive star evolution but is very sensitive to the implementation of other processes in the model. The transport of AM and chemical elements due to the MRI alters the rotation rates and the chemical makeup of the star from the core to the surface and may change the explodability properties of massive stars.

Rotation in stellar interiors: General formulation and an asteroseismic-calibrated transport by the Tayler instability

Context. Asteroseismic measurements of the internal rotation of evolved stars indicate that at least one unknown efficient angular momentum (AM) transport mechanism is needed in stellar radiative zones in addition to hydrodynamic transport processes. Aims. We investigate the impact of AM transport by the magnetic Tayler instability as a possible candidate for such a missing physical mechanism. Methods. We derived general equations for AM transport by the Tayler instability to be able to test different versions of the Tayler-Spruit (TS) dynamo by comparing rotational properties of these models with asteroseismic constraints available for sub-giant and red giant stars. Results. These general equations highlight, in a simple way, the key role played by the adopted damping timescale of the azimuthal magnetic field on the efficiency of the resulting AM transport. Using this framework, we first show that the original TS dynamo provides an insufficient coupling in low-mass red giants that have a radiative core during the main sequence (MS), as was found previously for more massive stars that develop a convective core during the MS. We find that the core rotation rates of red giant branch (RGB) stars predicted by models computed with various prescriptions for the TS dynamo are nearly insensitive to the adopted initial rotation velocity. We then derived a new calibrated version of the original TS dynamo and find that the damping timescale adopted for the azimuthal field in the original TS dynamo has to be increased by a factor of about 200 to correctly reproduce the core rotation rates of stars on the RGB. This calibrated version predicts no correlation of the core rotation rates with the stellar mass for RGB stars in good agreement with asteroseismic observations. Moreover, it correctly reproduces the core rotation rates of clump stars similarly to a revised prescription proposed recently. Interestingly, this new calibrated version of the TS dynamo is found to be in slightly better agreement with the core rotation rates of sub-giant stars, while simultaneously better accounting for the evolution of the core rotation rates along the RGB compared to the revised dynamo version. These results were obtained with both the Geneva and the MESA stellar evolution codes.

On the Angular Momentum Transport Efficiency within the Star Constrained from Gravitational-wave Observations

Abstract The LIGO Scientific Collaboration and Virgo Collaboration (LIGO/Virgo) have recently reported in GWTC-2.1 eight additional candidate events with a probability of astrophysical origin greater than 0.5 in the LIGO/Virgo’s deeper search on O3a running. In GWTC-2.1, the majority of the effective inspiral spins (χ eff) show magnitudes consistent with zero, while two (GW190403-051519 and GW190805-211137) of the eight new events have χ eff > 0 (at 90% credibility). We note that GW190403-051519 was reported with χ eff = 0.70 − 0.27 + 0.15 and mass ratio q = 0.25 − 0.11 + 0.54 . Assuming a uniform prior probability between 0 and 1 for each black hole’s dimensionless spin magnitude, GW190403-051519 was reported with the dimensionless spin of the more massive black hole, χ 1 = 0.92 − 0.22 + 0.07 . This is the fastest black hole ever measured in all current gravitational-wave events. If the immediate progenitor of GW190403-051519 is a close binary system composed of a black hole and a helium star, which can be the natural outcome of the classical isolated binary evolution through the common envelope phase, this extremely high spin challenges, at least in that case, the existence of an efficient angular momentum transport mechanism between the stellar core and the radiative envelope of massive stars, as for instance predicted by the Tayler–Spruit dynamo or its revised version by Fuller et al.

The Implications of High Black Hole Spins for the Origin of Binary Black Hole Mergers

Abstract The LIGO–Virgo collaboration has reported 50 black hole–black hole (BH–BH) mergers and 8 candidates recovered from digging deeper into the detector noise. The majority of these mergers have low effective spins pointing toward low BH spins and efficient angular momentum (AM) transport in massive stars as proposed by several models (e.g., the Tayler–Spruit dynamo). However, out of these 58 mergers, 7 are consistent with having high effective-spin parameter (χ eff > 0.3). Additionally, two events seem to have high effective spins sourced from the spin of the primary (more massive) BH. These particular observations could be used to discriminate between the isolated binary and dynamical formation channels. It might seem that high BH spins point to a dynamical origin if AM in stars is efficient and forms low-spinning BHs. In such a case dynamical formation is required to produce second and third generations of BH–BH mergers with typically high spinning BHs. Here we show, however, that isolated binary BH–BH formation naturally reproduces such highly spinning BHs. Our models start with efficient AM in massive stars that is needed to reproduce the majority of BH–BH mergers with low effective spins. Later, some of the binaries are subject to a tidal spin-up allowing the formation of a moderate fraction (∼10%) of BH–BH mergers with high effective spins (χ eff ≳ 0.4–0.5). In addition, isolated binary evolution can produce a small fraction of BH–BH mergers with almost maximally spinning primary BHs. Therefore, the formation scenario of these atypical BH–BH mergers remains to be found.

Asteroseismology of evolved stars to constrain the internal transport of angular momentum

Context. Asteroseismic observations enable the characterisation of the internal rotation of evolved stars. These measurements reveal that an unknown efficient angular momentum (AM) transport mechanism is needed for subgiant and red giant stars in addition to hydrodynamic transport processes. A revised prescription for AM transport by the magnetic Tayler instability has been recently proposed as a possible candidate for such a missing mechanism. Aims. We compare the rotational properties predicted by this magnetic AM transport to asteroseismic constraints obtained for evolved stars with a particular focus on the subgiant phase. Methods. We computed models accounting for the recent prescription for AM transport by the Tayler instability with the Geneva stellar evolution code for subgiant and red giant stars, for which an asteroseismic determination of both core and surface rotation rates is available. Results. The revised prescription for the transport by the Tayler instability leads to low core rotation rates after the main sequence that are in better global agreement with asteroseismic measurements than those predicted by models with purely hydrodynamic processes or with the original Tayler-Spruit dynamo. A detailed comparison with asteroseismic data shows that the rotational properties of at most two of the six subgiants can be correctly reproduced by models accounting for this revised magnetic transport process. This result is obtained independently of the value adopted for the calibration parameter in this prescription. We also find that this transport by the Tayler instability faces difficulties in simultaneously reproducing asteroseismic measurements available for subgiant and red giant stars. The low values of the calibration parameter needed to correctly reproduce the rotational properties of two of the six subgiants lead to core rotation rates during the red giant phase that are too high. Inversely, the higher values of this parameter needed to reproduce the core rotation rates of red giants lead to a very low degree of radial differential rotation before the red giant phase, which is in contradiction with the internal rotation of subgiant stars. Conclusions. In its present form, the revised prescription for the transport by the Tayler instability does not provide a complete solution to the missing AM transport revealed by asteroseismology of evolved stars.

The Tayler Instability in the Anelastic Approximation

Abstract The Tayler instability (TI) is a non-axisymmetric linear instability of an axisymmetric toroidal magnetic field in magnetohydrostatic equilibrium (MHSE). In a differentially rotating radiative region of a star, the TI could drive the Tayler–Spruit dynamo, which generates magnetic fields that can significantly impact stellar structure and evolution. Heuristic prescriptions disagree on the efficacy of the dynamo, and numerical simulations have yet to definitively agree upon its existence. The criteria for the TI to develop were derived using fully compressible magnetohydrodynamics, while numerical simulations of dynamical processes in stars frequently use an anelastic approximation. This motivates us to derive new anelastic Tayler instability criteria. We find that some MHSE configurations are unstable in the fully compressible case but become stable in the anelastic case. We find and characterize the unstable modes of a simple family of cylindrical MHSE configurations using numerical calculations, and we discuss the implications for fully nonlinear anelastic simulations.

Rotation rate of the solar core as a key constraint to magnetic angular momentum transport in stellar interiors

Context. The internal rotation of the Sun constitutes a fundamental constraint when modelling angular momentum transport in stellar interiors. In addition to the more external regions of the solar radiative zone probed by pressure modes, measurements of rotational splittings of gravity modes would offer an invaluable constraint on the rotation of the solar core. Aims. We study the constraints that a measurement of the core rotation rate of the Sun could bring on magnetic angular momentum transport in stellar radiative zones. Methods. Solar models accounting for angular momentum transport by hydrodynamic and magnetic instabilities were computed for different initial velocities and disc lifetimes on the pre-main sequence to reproduce the surface rotation velocities observed for solar-type stars in open clusters. The internal rotation of these solar models was then compared to helioseismic measurements. Results. We first show that models computed with angular momentum transport by magnetic instabilities and a recent prescription for the braking of the stellar surface by magnetized winds can reproduce the observations of surface velocities of stars in open clusters. These solar models predict both a flat rotation profile in the external part of the solar radiative zone probed by pressure modes and an increase in the rotation rate in the solar core, where the stabilizing effect of chemical gradients plays a key role. A rapid rotation of the core of the Sun, as suggested by reported detections of gravity modes, is thus found to be compatible with angular momentum transport by magnetic instabilities. Moreover, we show that the efficiency of magnetic angular momentum transport in regions of strong chemical gradients can be calibrated by the solar core rotation rate independently from the unknown rotational history of the Sun. In particular, we find that a recent revised prescription for the transport of angular momentum by the Tayler instability can be easily distinguished from the original Tayler–Spruit dynamo, with a faster rotating solar core supporting the original prescription. Conclusions. By calibrating the efficiency of magnetic angular momentum transport in regions of strong chemical gradients, a determination of the solar core rotation rate through gravity modes is of prime relevance not only for the Sun, but for stars in general, since radial differential rotation precisely develops in these regions during the more advanced stages of evolution.

Slowing the spins of stellar cores

ABSTRACT The angular momentum (AM) evolution of stellar interiors, along with the resulting rotation rates of stellar remnants, remains poorly understood. Asteroseismic measurements of red giant stars reveal that their cores rotate much faster than their surfaces, but much slower than theoretically predicted, indicating an unidentified source of AM transport operates in their radiative cores. Motivated by this, we investigate the magnetic Tayler instability and argue that it saturates when turbulent dissipation of the perturbed magnetic field energy is equal to magnetic energy generation via winding. This leads to larger magnetic field amplitudes, more efficient AM transport, and smaller shears than predicted by the classic Tayler–Spruit dynamo. We provide prescriptions for the effective AM diffusivity and incorporate them into numerical stellar models, finding they largely reproduce (1) the nearly rigid rotation of the Sun and main sequence stars, (2) the core rotation rates of low-mass red giants during hydrogen shell and helium burning, and (3) the rotation rates of white dwarfs. We discuss implications for stellar rotational evolution, internal rotation profiles, rotational mixing, and the spins of compact objects.

Constraining transport of angular momentum in stars

Context. Transport of angular momentum has been a challenging topic within the stellar evolution community, even more since the recent asteroseismic surveys. All published studies on rotation using asteroseismic observations show a discrepancy between the observed and calculated rotation rates, indicating there is an undetermined process of angular momentum transport active in these stars. Aims. We aim to constrain the efficiency of this process by investigating rotation rates of 2.5 M⊙ stars. Methods. First, we investigated whether the Tayler-Spruit dynamo could be responsible for the extra transport of angular momentum for stars with an initial mass of 2.5 M⊙. Then, by computing rotating models including a constant additional artificial viscosity, we determined the efficiency of the missing process of angular momentum transport by comparing the models to the asteroseismic observations of core helium burning stars. Parameter studies were performed to investigate the effect of the stellar evolution code used, initial mass, and evolutionary stage. We evolved our models into the white dwarf phase, and provide a comparison to white dwarf rotation rates. Results. The Tayler-Spruit dynamo is unable to provide enough transport of angular momentum to reach the observed values of the core helium burning stars investigated in this paper. We find that a value for the additional artificial viscosity νadd around 107 cm2 s−1 provides enough transport of angular momentum. However, the rotational period of these models is too high in the white dwarf phase to match the white dwarf observations. From this comparison we infer that the efficiency of the missing process must decrease during the core helium burning phase. When excluding the νadd during core helium burning phase, we can match the rotational periods of both the core helium burning stars and white dwarfs.

On the Synchronizability of Tayler–Spruit and Babcock–Leighton Type Dynamos

The solar cycle appears to be remarkably synchronized with the gravitational torques exerted by the tidally dominant planets Venus, Earth and Jupiter. Recently, a possible synchronization mechanism was proposed that relies on the intrinsic helicity oscillation of the current-driven Tayler instability which can be stoked by tidal-like perturbations with a period of 11.07 years. Inserted into a simple alpha-Omega dynamo model these resonantly excited helicity oscillations led to a 22.14 years dynamo cycle. Here, we assess various alternative mechanisms of synchronization. Specifically we study a simple time-delay model of Babcock-Leighton type dynamos and ask whether periodic changes of either the minimal amplitude for rising toroidal flux tubes or the Omega effect could eventually lead to synchronization. In contrast to the easy and robust synchronizability of Tayler-Spruit dynamo models, our answer for those Babcock-Leighton type models is less propitious.

The Tayler instability at low magnetic Prandtl numbers: chiral symmetry breaking and synchronizable helicity oscillations

The current-driven, kink-type Tayler instability (TI) is a key ingredient of the Tayler-Spruit dynamo model for the generation of stellar magnetic fields, but is also discussed as a mechanism that might hamper the up-scaling of liquid metal batteries. Under some circumstances, the TI involves a helical flow pattern which goes along with some alpha effect. Here we focus on the chiral symmetry breaking and the related impact on the alpha effect that would be needed to close the dynamo loop in the Tayler-Spruit model. For low magnetic Prandtl numbers, we observe intrinsic oscillations of the alpha effect. These oscillations serve then as the basis for a synchronized Tayler-Spruit dynamo model, which could possibly link the periodic tidal forces of planets with the oscillation periods of stellar dynamos.

The Tayler instability at low magnetic Prandtl numbers: between chiral symmetry breaking and helicity oscillations

The Tayler instability is a kink-type, current driven instability that plays an important role in plasma physics but might also be relevant in liquid metal applications with high electrical currents. In the framework of the Tayler–Spruit dynamo model of stellar magnetic field generation (Spruit 2002 Astron. Astrophys. 381 923–32), the question of spontaneous helical (chiral) symmetry breaking during the saturation of the Tayler instability has received considerable interest (Zahn et al 2007 Astron. Astrophys. 474 145–54; Gellert et al 2011 Mon. Not. R. Astron. Soc. 414 2696–701; Bonanno et al 2012 Phys. Rev. E 86 016313). Focusing on fluids with low magnetic Prandtl numbers, for which the quasistatic approximation can be applied, we utilize an integro-differential equation approach (Weber et al 2013 New J. Phys.15 043034) in order to investigate the saturation mechanism of the Tayler instability. Both the exponential growth phase and the saturated phase are analysed in terms of the action of the α and β effects of mean-field magnetohydrodynamics. In the exponential growth phase we always find a spontaneous chiral symmetry breaking which, however, disappears in the saturated phase. For higher degrees of supercriticality, we observe helicity oscillations in the saturated regime. For Lundquist numbers in the order of one we also obtain chiral symmetry breaking of the saturated magnetic field.