Axisymmetric magnetic fields in stars: relative strengths of poloidal and toroidal components

By J. Braithwaite. 2008

246 citations recorded by the source corpus.

In this third paper in a series on stable magnetic equilibria in stars, I look at the stability of axisymmetric field configurations and, in particular, the relative strengths of the toroidal and poloidal components. Both toroidal and poloidal fields are unstable on their own, and stability is achieved by adding the two together in some ratio. I use Tayler's stability conditions for toroidal fields and other analytic tools to predict the range of stable ratios and then check these predictions by running numerical simulations. If the energy in the poloidal component as a fraction of the total magnetic energy is written as E p /E, it is found that the stability condition is a(E/U) < Ep/E ≤ 0.8 where E/U is the ratio of magnetic to gravitational energy in the star and a is some dimensionless factor whose value is of order 10 in a main-sequence star and of order 10 3 in a neutron star. In other words, whilst the poloidal component cannot be significantly stronger than the toroidal, the toroidal field can be very much stronger than the poloidal-given that in realistic stars we expect E/U < 10- 6 . The implications of this result are discussed in various contexts such as the emission of gravitational waves by neutron stars, free precession and a 'hidden' energy source for magnetars.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Oceanography

View Paper: https://www.semanticscholar.org/paper/4fa0d3f950a4f0bc82c72aaea92ddbf7bd40b1ce

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. B. Metzger
2. E. Quataert
3. T. Thompson
4. B. Margalit
5. A. Piro
6. N. Bucciantini
7. P. Lasky
8. J. Fuller

In Nuclear and High Energy Physics

1. B. Metzger
2. E. Quataert
3. T. Thompson
4. N. Bucciantini
5. B. Margalit
6. J. Fuller
7. A. Piro
8. D. Giannios

In Oceanography

1. P. Lasky
2. B. Metzger
3. N. Bucciantini
4. E. Gotthelf
5. E. Quataert
6. J. Halpern
7. B. Margalit

Citations in the corpus

• SPIN-DOWN MEASUREMENT OF PSR J1852+0040 IN KESTEVEN 79: CENTRAL COMPACT OBJECTS AS ANTI-MAGNETARS (2009, background): “Purely toroidal or poloidal fields are thought to be unstable (Tayler 1973; Flowers & Ruderman 1977), although the toroidal field may be stabilized by a poloidal field that is several orders of magnitude smaller (Braithwaite 2009), so this may be a viable configuration for a CCO.”
• Constraining the Maximum Mass of Neutron Stars from Multi-messenger Observations of GW170817 (2017, background): “However, such a strong toroidal to poloidal field configuration would be unstable (Braithwaite 2009; Akgün et al. 2013; grey shaded region in Fig.”
• Slowing the spins of stellar cores (2019, background): “However, as shown by Braithwaite (2009), Tayler instability cannot operate if Br rises above a threshold value.”
• The Proto-Magnetar Model for Gamma-Ray Bursts (2010, background): “…only consider models with Bdip ∼< 3 × 10 16 G because although fields up to ≈ 3 × 1017 G are in principle possible if ǫB ∼ 1, stable magnetic configurations generally require a total field strength which is larger than the dipole component by a factor ∼> 10 (e.g. Tayler 1973; Braithwaite 2009).”
• Gravitational Waves from Neutron Stars: A Review (2015, background): “…more applicable to main-sequence stars than to neutron stars), Braithwaite and co. showed magnetic fields evolve either to axisymmetric, twisted-tori (Braithwaite & Nordlund 2006; Braithwaite 2009), or nonaxisymmetric configurations (Braithwaite 2008), depending on the initial conditions.”