Non–linear magnetic field decay in neutron stars

Geppert, U.; Rheinhardt, M.

doi:10.1051/0004-6361:20020978

Cited by 58 publications

(47 citation statements)

References 26 publications

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“…Hence, the argument concerning the necessity of shear for the occurrence of an instability in the model of RS in fact supports our findings in [2,3], when the term 'shear' is no longer used to refer to macroscopic motions only, but is extended to the microscopic motions of the carriers creating the current curl B 0 /µ 0 . If the latter should be capable of replacing the shear velocity u 0 , it must not be interpretable as a rigid body motion.…”

Section: Isupporting

confidence: 87%

“…As the scheme (40) of RS is valid for nonpotential (axisymmetric) fields, too, and the quoted conclusion is drawn completely on its basis, the reader will be tempted to generalize it. He or she could then come to the end that the results on a Hall instability without shear reported in [2,3] have to be put in question. (Note, that the term 'shear' is used throughout RS to refer to the macroscopic motion of a fluid.)…”

Section: Imentioning

confidence: 99%

“…This solution is characterized by k = 0 and the mentioned curves should show that, except, there were other marginal solutions with Re = 0, but k = 0. But such solutions do not exist, because for Re = 0 and any Ha there is no (potentially) energydelivering term in the induction equation (see (3)) and the only possibility for a marginal (i.e., non-decaying) solution is the vacuum one. Thus it appears, that the vacuum solution was for unknown reasons excluded from the analysis which led to Fig.…”

Section: IIImentioning

confidence: 99%

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Comment on “Linear instability of magnetic Taylor-Couette flow with Hall effect”

Rheinhardt

Geppert

2005

Phys. Rev. E

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In the paper we comment on (Rüdiger & Shalybkov, Phys. Rev. E. 69, 016303 (2004) (RS)), the instability of the TaylorCouette flow interacting with a homogeneous background field subject to Hall effect is studied. We correct a falsely generalizing interpretation of results presented there which could be taken to disprove the existence of the Hall-drift induced magnetic instability described in Rheinhardt and Geppert, Phys. Rev. Lett. 88, 101103. It is shown that in contrast to what is suggested by RS, no additional shear flow is necessary to enable such an instability with a non-potential magnetic background field, whereas for a curl-free one it is. In the latter case, the instabilities found in RS in situations where neither a hydrodynamic nor a magneto-rotational instability exists are demonstrated to be most likely magnetic instead of magnetohydrodynamic. Further, some minor inaccuracies are clarified. I.The main purpose of this Comment on the paper [1] (further on referred to as RS) is to prevent a incorrect conclusion with respect to our work [2,3] which could be drawn from an incorrect statement in the discussion section of RS. There, at the end of the third paragraph, the authors conclude from the invariance of their results with respect to simultaneous sign inversions of shear and Hall term that no instabilities are possible without shear. Although this conclusion being looked at out of context is not comprehensible, it is nevertheless true for the special case of a homogeneous (more generally: curl-free) background field B 0 , but not in general. As the scheme (40) of RS is valid for nonpotential (axisymmetric) fields, too, and the quoted conclusion is drawn completely on its basis, the reader will be tempted to generalize it. He or she could then come to the end that the results on a Hall instability without shear reported in [2,3] have to be put in question. (Note, that the term 'shear' is used throughout RS to refer to the macroscopic motion of a fluid.) Here, we will show that conclusions on necessary conditions for the instabilities in question can reliably be drawn on the basis of energy considerations. They support the possibility of a Hall instability without shear.The linearized induction and Navier-Stokes equations describing the evolution of small perturbations B ′ and u ′ of the background field B 0 and the shear flow (here: differential rotation) u 0 , respectively, read for a curl-freewhere we used the symbols introduced in RS. Standard arguments yield the following evolution equation for the total energy E of the perturbations:with V ′ being the infinite space minus any volume with infinite conductivity and V the volume of the container. Of course, solutions with growing total energy are impossible, as long as u 0 = 0. More generally, even if we would admit a rigid body motion for u 0 , growing solutions do not exist. The situation changes qualitatively, if B 0 is no longer curl-free: The additional term −β curl(curl B 0 × B ′ ) occurring in the linearized induction equation results in ...

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Section: Isupporting

confidence: 87%

Section: Imentioning

confidence: 99%

Section: IIImentioning

confidence: 99%

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Comment on “Linear instability of magnetic Taylor-Couette flow with Hall effect”

Rheinhardt

Geppert

2005

Phys. Rev. E

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“…As another example, in mean field theory there are terms in the mean electromotive force that can build a mean field when the α coefficient is zero (Urpin, 2002). The ω×j term in this expansion is also known to generate large scale magnetic fields (Geppert and Rheinhardt, 2002). and Sokoloff, 1983;Schekochihin, Cowley, Maron, and Malyshkin, 2001;Schekochihin, Cowley, Taylor, Hammett, Maron, and McWilliams, 2004;Haugen, Brandenburg, and Dobler, 2003), and the magnetic field generated is correlated on scales much smaller than the energy containing scales of the turbulence.…”

Section: ¢ Qmentioning

confidence: 99%

Direct numerical simulations of helical dynamo action: MHD and beyond

Gomez

Mininni

2004

Nonlin. Processes Geophys.

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Abstract. Magnetohydrodynamic dynamo action is often invoked to explain the existence of magnetic fields in several astronomical objects. In this work, we present direct numerical simulations of MHD helical dynamos, to study the exponential growth and saturation of magnetic fields. Simulations are made within the framework of incompressible flows and using periodic boundary conditions. The statistical properties of the flow are studied, and it is found that its helicity displays strong spatial fluctuations. Regions with large kinetic helicity are also strongly concentrated in space, forming elongated structures. In dynamo simulations using these flows, we found that the growth rate and the saturation level of magnetic energy and magnetic helicity reach an asymptotic value as the Reynolds number is increased. Finally, extensions of the MHD theory to include kinetic effects relevant in astrophysical environments are discussed.

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“…Various explanations have been suggested. For example, it could be that there is a characteristic rate of decay of neutron star magnetic fields that is independent of external factors such as accretion, and that LMXBs simply live long enough for this decay to be significant (this would suggest that old enough isolated pulsars also experience field decay; see Geppert & Rheinhardt 2002). Alternately, accretion could speed the decay of the field (Ruderman 1995;Konar & Bhattacharya 1999) or even bury the field (for a recent study see Cumming, Zweibel, & Bildsten 2001), although magnetic instabilities may make it difficult to start the burial process.…”

Section: High-mass X-ray Binariesmentioning

confidence: 99%

Constraints on Superdensematter From X-Ray Binaries

Miller

2006

NATO Science Series II: Mathematics, Physics and Chemistry

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From the earliest measurements of the masses of binary pulsars, observations of neutron stars have placed interesting constraints on the properties of high-density matter. The last few years have seen a number of observational developments that could place strong new restrictions on the equilibrium state of cold matter at supranuclear densities. We review these astronomical constraints and their context, and speculate on future prospects.

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Non–linear magnetic field decay in neutron stars

Cited by 58 publications

References 26 publications

Comment on “Linear instability of magnetic Taylor-Couette flow with Hall effect”

Comment on “Linear instability of magnetic Taylor-Couette flow with Hall effect”

Direct numerical simulations of helical dynamo action: MHD and beyond

Constraints on Superdensematter From X-Ray Binaries

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