Hall equilibria with toroidal and poloidal fields: application to neutron stars

Gourgouliatos, Konstantinos N.; Cumming, Andrew; Reisenegger, Andreas; Armaza, Cristóbal; Lyutikov, Maxim; Valdivia, J. A.

doi:10.1093/mnras/stt1195

Cited by 82 publications

(118 citation statements)

References 62 publications

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“…corresponds to a Hall equilibrium, and will not evolve in the limit of zero resistivity (Cumming et al 2004;Gourgouliatos et al 2013;Fujisawa & Kisaka 2014). In the realistic case of non-zero resistivity, however, the system will start evolving and may be pushed out of Hall equilibrium (Marchant et al 2014).…”

Section: Electron-mhd Formulation In Neutron Star Crustsmentioning

confidence: 99%

Resistive tearing instability in electron MHD: application to neutron star crusts

Gourgouliatos¹,

Hollerbach²

2016

Mon. Not. R. Astron. Soc.

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We study a resistive tearing instability developing in a system evolving through the combined effect of Hall drift in the Electron-MHD limit and Ohmic dissipation. We explore first the exponential growth of the instability in the linear case and we find the fastest growing mode, the corresponding eigenvalues and dispersion relation. The instability growth rate scales as γ ∝ B 2/3 σ −1/3 where B is the magnetic field and σ the electrical conductivity. We confirm the development of the tearing resistive instability in the fully non-linear case, in a plane parallel configuration where the magnetic field polarity reverses, through simulations of systems initiating in Hall equilibrium with some superimposed perturbation. Following a transient phase, during which there is some minor rearrangement of the magnetic field, the perturbation grows exponentially. Once the instability is fully developed the magnetic field forms the characteristic islands and X-type reconnection points, where Ohmic decay is enhanced. We discuss the implications of this instability for the local magnetic field evolution in neutron stars' crusts, proposing that it can contribute to heating near the surface of the star, as suggested by models of magnetar post-burst cooling. In particular, we find that a current sheet a few meters thick, covering as little as 1% of the total surface can provide 10 42 erg in thermal energy within a few days. We briefly discuss applications of this instability in other systems where the Hall effect operates such as protoplanetary discs and space plasmas.

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Section: Electron-mhd Formulation In Neutron Star Crustsmentioning

confidence: 99%

Resistive tearing instability in electron MHD: application to neutron star crusts

Gourgouliatos¹,

Hollerbach²

2016

Mon. Not. R. Astron. Soc.

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“…Several authors (Lander & Jones 2009;Ciolfi et al 2009;Fujisawa et al 2012;Gourgouliatos et al 2013) have explored the possible axially symmetric equilibria in barotropic stars, generally finding that the fraction of the total magnetic energy corresponding to the toroidal component, E tor /E mag , is at most a few %. In addition to not being enough to account for the energy emitted by magnetars, this would be insufficient to stabilize the poloidal component (Braithwaite 2009;Akgün et al 2013), as confirmed by the simulations of Lander & Jones (2012).…”

Section: Overviewmentioning

confidence: 99%

Magnetohydrodynamic equilibria in barotropic stars

Armaza¹,

Reisenegger²,

Valdivia

et al. 2013

Proc. IAU

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Abstract. Although barotropic matter does not constitute a realistic model for magnetic stars on short timescales, it would be interesting to confirm a recent conjecture that states that magnetized stars with a barotropic equation of state would be dynamically unstable (Reisenegger 2009). In this work we construct a set of barotropic equilibria, which can eventually be tested using a stability criterion. A general description of the ideal MHD equations governing these equilibria is summarized, allowing for both poloidal and toroidal magnetic field components. A new finite-difference numerical code is developed in order to solve the so-called Grad-Shafranov equation describing the equilibrium of these configurations, and some properties of the equilibria obtained are briefly discussed.

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“…We have obtained Hall equilibrium states (see Gourgouliatos et al 2013) using Green function method with arbitrary current sheets (see Fujisawa & Eriguchi 2013). For simplicity, we divided the magnetized neutron star interior into three regions in order to include the boundary conditions systematically.…”

Section: Resultsmentioning

confidence: 99%

“…Goldreich & Reisenegger 1992). Recently, Hall MHD numerical simulations (Kojima & Kisaka 2012, Viganò et al 2013 and Hall equilibrium states (Gourgouliatos et al 2013) have been calculated. Since the boundary conditions are very important in both cases, we have calculated the Hall equilibria within the neutron star crust under various boundary conditions in order to investigate the influences of the boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Axisymmetric and stationary magnetic field structures in neutron star crusts under various boundary conditions

Fujisawa¹,

Kisaka

2013

Proc. IAU

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Abstract. We have calculated many Hall equilibrium states within the neutron star crust under various boundary conditions in order to investigate the influences of the boundary conditions clearly. We have found two important features of these solutions. First, the magnitude of the core magnetic fields affects the toroidal to total magnetic field energy ratio within the crust (Et /E). If the core magnetic fields are vanished, the crustal toroidal magnetic fields become weak and the typical energy ratio is only Et /E ∼ 0.1%. If the core magnetic fields are strong, however, the crustal toroidal magnetic fields become strong and the typical ratio reaches Et /E ∼ 15%. Second, the core toroidal magnetic fields and the twisted magnetosphere around the star make the size of the crustal toroidal magnetic field regions large. Therefore if the strong core magnetic fields have strong toroidal component, both strength and size of the crustal toroidal magnetic fields become large. These results show that the Hall MHD evolutions would be deeply affected by both inner and outer boundary conditions.

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Hall equilibria with toroidal and poloidal fields: application to neutron stars

Cited by 82 publications

References 62 publications

Resistive tearing instability in electron MHD: application to neutron star crusts

Resistive tearing instability in electron MHD: application to neutron star crusts

Magnetohydrodynamic equilibria in barotropic stars

Axisymmetric and stationary magnetic field structures in neutron star crusts under various boundary conditions

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