Stability of the toroidal magnetic field in rotating stars

Bonanno, A.; Урпин, В. А.

doi:10.1051/0004-6361/201220153

Cited by 8 publications

(6 citation statements)

References 27 publications

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“…In previous works with very similar setups (Arlt & Rüdiger 2011a,b;Bonanno & Urpin 2013), such an instability has been attributed to the Tayler instability of the toroidal field. However, several arguments point to the fact that this is not a Tayler instability which is found here, but a magnetic instability of a different nature.…”

Section: Evidence For a Magnetic Instabilitymentioning

confidence: 78%

“…Indeed, Tayler (1973), Wright (1973) and Markey & Tayler (1973) were the first to show that a purely poloidal or purely toroidal magnetic field would be unstable under all general circumstances and that a stable equilibrium would thus have to be of mixed poloidal/toroidal type. This idea was then investigated more thoroughly including additional physical processes like rotation, and confirmed both by analytical studies and numerical models (Braithwaite & Nordlund 2006;Braithwaite 2007;Bonanno & Urpin 2008;Duez & Mathis 2010;Bonanno & Urpin 2013). The magneto-rotational instability (MRI) has been extensively analyzed to understand the dynamics of accretion disks, in particular the transport of angular momentum induced by such an instability (see Fromang 2013, for a complete lecture on the subject).…”

Section: Introductionmentioning

confidence: 95%

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Three-dimensional evolution of magnetic fields in a differentially rotating stellar radiative zone

Jouve

Gastine

Lignières

2015

A&A

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Context. The question of the origin and evolution of magnetic fields in stars possessing a radiative envelope, like the A-type stars, is still regarded as a challenge for stellar physics. Those zones are likely to be differentially rotating, which suggests that strong interactions between differential rotation and magnetic fields could be at play in such regions. Aims. We would like to analyse in detail the evolution of magnetic fields in a differentially rotating stellar radiative zone and the possible presence of magnetic instabilities. Methods. We numerically compute the joint evolution of the magnetic and velocity fields in a 3D spherical shell starting from an initial profile for the poloidal magnetic field and differential rotation. In order to characterise the nature of the magnetic instabilities that may be expected, we use the predictions of a local linear analysis. Results. The poloidal magnetic field is initially wound up by the differential rotation to produce a toroidal field which becomes unstable. We find that different types of instabilities may occur, depending on the balance between the shear strength and the magnetic field intensity. In the particular setup studied here where the differential rotation is dominant, the instability is not of the Tayler-type but is the magneto-rotational instability. The growth rate of the instability depends mainly on the initial rotation rate, while the background state typically oscillates over a poloidal Alfvén time. We thus find that the axisymmetric magnetic configuration is strongly modified by the instability only if the ratio between the poloidal Alfvén frequency and the rotation rate is sufficiently small. An enhanced transport of angular momentum is found in the most unstable cases: the typical time to flatten the rotation profile is then much faster than the decay time associated with the phase-mixing mechanism, which also occurs in the stable cases. When the instability saturates before reaching a significant amplitude, the magnetic configuration relaxes into a stable axisymmetric equilibrium formed by several twisted tori. Conclusions. We conclude that the magneto-rotational instability is always favoured (over the Tayler instability) in unstratified spherical shells when an initial poloidal field is sheared by a sufficiently strong cylindrical differential rotation. A possible application to the magnetic desert observed among A stars is given. We argue that the dichotomy between stars exhibiting strong axisymmetric fields (Ap stars) and those harbouring a sub-Gauss magnetism could be linked to the threshold for the instability.

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Section: Evidence For a Magnetic Instabilitymentioning

confidence: 78%

Section: Introductionmentioning

confidence: 95%

Three-dimensional evolution of magnetic fields in a differentially rotating stellar radiative zone

Jouve

Gastine

Lignières

2015

A&A

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“…If one assumes (rather arbitrarily) that the magnetic field in the solar core, where the neutrinos are produced, is of similar magnitude, this would translate to the limit µ 12 < 7.1 × 10 −13 µ B . From the requirement of the stability of toroidal magnetic fields in the radiative zone of the Sun, a much more stringent limit B 600 G can be found [79,80]. Assuming that the magnetic field in the core of the Sun is of similar magnitude, one would obtain the constraint µ 12 < 8.3 × 10 −9 µ B .…”

Section: Jhep10(2022)144 5 Discussionmentioning

confidence: 99%

Solar $$ {\overline{\nu}}_e $$ flux: revisiting bounds on neutrino magnetic moments and solar magnetic field

Akhmedov

Martínez-Miravé

2022

J. High Energ. Phys.

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The interaction of neutrino transition magnetic dipole moments with magnetic fields can give rise to the phenomenon of neutrino spin-flavour precession (SFP). For Majorana neutrinos, the combined action of SFP of solar neutrinos and flavour oscillations would manifest itself as a small, yet potentially detectable, flux of electron antineutrinos coming from the Sun. Non-observation of such a flux constrains the product of the neutrino magnetic moment μ and the strength of the solar magnetic field B. We derive a simple analytical expression for the expected $$ {\overline{\nu}}_e $$ ν ¯ e appearance probability in the three-flavour framework and we use it to revisit the existing experimental bounds on μB. A full numerical calculation has also been performed to check the validity of the analytical result. We also present our numerical results in energy-binned form, convenient for analyses of the data of the current and future experiments searching for the solar $$ {\overline{\nu}}_e $$ ν ¯ e flux. In addition, we give a comprehensive compilation of other existing limits on neutrino magnetic moments and of the expressions for the probed effective magnetic moments in terms of the fundamental neutrino magnetic moments and leptonic mixing parameters.

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“…If one assumes (rather arbitrarily) that the magnetic field in the solar core, where the neutrinos are produced, is of similar magnitude, this would translate to the limit µ 12 < 7.1 × 10 −13 µ B . From the requirement of the stability of toroidal magnetic fields in the radiative zone of the Sun, a much more stringent limit B 600 G can be found [75,76]. Assuming that the magnetic field in the core of the Sun is of similar magnitude, one would obtain the constraint µ 12 < 8.3 × 10 −9 µ B .…”

Section: Discussionmentioning

confidence: 99%

Solar $\barν_e$ flux: Revisiting bounds on neutrino magnetic moments and solar magnetic field

Akhmedov¹,

Martínez-Miravé²

2022

Preprint

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The interaction of neutrino transition magnetic dipole moments with magnetic fields can give rise to the phenomenon of neutrino spin-flavour precession (SFP). For Majorana neutrinos, the combined action of SFP of solar neutrinos and flavour oscillations would manifest itself as a small, yet potentially detectable, flux of electron antineutrinos coming from the Sun. Non-observation of such a flux constrains the product of the neutrino magnetic moment µ and the strength of the solar magnetic field B. We derive a simple analytical expression for the expected νe appearance probability in the three-flavour framework and we use it to revisit the existing experimental bounds on µB. A full numerical calculation has also been performed to check the validity of the analytical result. We also present our numerical results in energy-binned form, convenient for analyses of the data of the current and future experiments searching for the solar νe flux. In addition, we give a comprehensive compilation of other existing limits on neutrino magnetic moments and of the expressions for the probed effective magnetic moments in terms of the fundamental neutrino magnetic moments and leptonic mixing parameters.

show abstract

Stability of the toroidal magnetic field in rotating stars

Cited by 8 publications

References 27 publications

Three-dimensional evolution of magnetic fields in a differentially rotating stellar radiative zone

Three-dimensional evolution of magnetic fields in a differentially rotating stellar radiative zone

Solar $$ {\overline{\nu}}_e $$ flux: revisiting bounds on neutrino magnetic moments and solar magnetic field

Solar $\barν_e$ flux: Revisiting bounds on neutrino magnetic moments and solar magnetic field

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