Generation of magnetic fields by a gravitomagnetic plasma battery

Khanna, Ramon

doi:10.1046/j.1365-8711.1998.01447.x

Cited by 13 publications

(17 citation statements)

References 11 publications

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“…Among those, the inclusion of an appropriate treatment to account for the self‐gravity of the disc is the most difficult task, despite its obvious relevance. Previous studies (Khanna & Chakrabarti 1992; Nishida et al 1996; Masuda et al 1998), based on either time‐dependent simulations with pseudo‐Newtonian potentials or stationary models in general relativity, indicate that self‐gravity seems to have a strong destabilizing effect. It has been argued (Nishida et al 1996) that in self‐gravitating accreting tori, the cusp is pushed towards the black hole by the gravitational force of the discs which, in principle, should act against the instability.…”

Section: Discussionmentioning

confidence: 96%

“…The new gravitational field allows us to compute the new position of the cusp, which controls the occurrence of the runaway instability. The self-gravity of the tori favours the instability, as shown both from studies based on a pseudo-potential for the black hole (Khanna & Chakrabarti 1992;Masuda, Nishida & Eriguchi 1998) and from fully relativistic (stationary) calculations (Nishida et al 1996). However, there are some parameters in the models which have stabilizing effects.…”

Section: Introductionmentioning

confidence: 94%

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The runaway instability of thick discs around black holes - II. Non-constant angular momentum discs

Daigne¹,

Font²

2004

Monthly Notices of the Royal Astronomical Society

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We present results from a comprehensive number of relativistic, time‐dependent, axisymmetric simulations of the runaway instability of non‐constant angular momentum thick discs around black holes. This second paper in the series extends earlier results where only constant angular momentum discs were considered. All relevant aspects of the theory of stationary thick discs around rotating black holes, necessary to build the equilibrium initial data used in our simulations, are presented in great detail. The angular momentum of the evolved discs is assumed to increase outwards with the radial distance according to a power law, l=Krα, where K > 0 corresponds to prograde discs (with respect to the black hole rotation) and K < 0 to retrograde discs. The main simplifying assumptions of our approach are not to include magnetic fields or self‐gravity in the discs (test‐fluid approximation). Furthermore, the dynamics of the space–time is accounted for by computing the transfer of mass and angular momentum from the disc to the black hole through the event horizon. In this approximation the evolution of the central black hole, which initially is non‐rotating, is assumed to follow a sequence of Kerr black holes of increasing mass and spin. All discs we build slightly overflow the potential barrier at the cusp, departing from equilibrium, so that accretion is possible. In agreement with previous results based on stationary models we find that by allowing the mass and the spin of the black hole to grow, constant angular momentum discs rapidly become unstable on a dynamical time‐scale (a few orbital periods). The comparison with the results of our first paper shows that the effect of the angular momentum transfer from the tori to the black hole is to make constant angular momentum discs less unstable, increasing the time‐scale for the runaway instability to grow. However, we find that non‐constant angular momentum discs are dramatically stabilized for very small values of the angular momentum slope α, much smaller than the Keplerian value α= 1/2. Our fully relativistic and time‐dependent simulations thus confirm the predictions of stationary studies concerning the stabilizing effect of non‐constant angular momentum distributions. For the various disc‐to‐hole mass ratios considered, we systematically find that the critical values of α below which the runaway instability can exist are slightly smaller than those reported previously in the literature based on stationary studies.

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Section: Discussionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 94%

The runaway instability of thick discs around black holes - II. Non-constant angular momentum discs

Daigne¹,

Font²

2004

Monthly Notices of the Royal Astronomical Society

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“…The above general scenario clearly presupposes that the black hole plus thick disc system is stable enough to survive for a few Wilson (1984) GR l ¼ constant yes neglected stable Khanna & Chakrabarti (1992) Pseudo-Newt. l ¼ constant yes approximate unstable Nishida et al (1996) GR l ¼ constant yes exact unstable 2 Daigne & Mochkovitch (1997) Pseudo-Newt.…”

Section: Introductionmentioning

confidence: 99%

“…From Table 1 one sees that (i) taking into account the self‐gravity of the disc seems to favour the instability (Khanna & Chakrabarti 1992; Nishida et al 1996; Masuda, Nishida & Eriguchi 1998); (ii) the rotation of the black hole has a stabilizing effect (Wilson 1984; Abramowicz, Karas & Lanza 1998); (iii) taking into account a non‐constant distribution of the angular momentum (increasing outwards) has a strong stabilizing effect (Daigne & Mochkovitch 1997; Abramowicz et al 1998); (iv) using a fully relativistic potential instead of a pseudo‐Newtonian potential for the black hole seems to act in the direction of favouring the instability (Nishida et al 1996). It also becomes evident from Table 1 that there is not still a final consensus about the very existence of the instability.…”

Section: Introductionmentioning

confidence: 99%

The runaway instability of thick discs around black holes - I. The constant angular momentum case

Font

Daigne

2002

Monthly Notices of the Royal Astronomical Society

138

199

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We present results from a numerical study of the runaway instability of thick discs around black holes. This instability is an important issue for most models of cosmic gamma‐ray bursts, where the central engine responsible for the initial energy release is such a system consisting of a thick disc surrounding a black hole. We have carried out a comprehensive number of time‐dependent simulations aimed at exploring the appearance of the instability. Our study has been performed using a fully relativistic hydrodynamics code. The general relativistic hydrodynamic equations are formulated as a hyperbolic flux‐conservative system and solved using a suitable Godunov‐type scheme. We build a series of constant angular momentum discs around a Schwarzschild black hole. Furthermore, the self‐gravity of the disc is neglected and the evolution of the central black hole is assumed to be that of a sequence of exact Schwarzschild black holes of varying mass. The black hole mass increase is thus determined by the mass accretion rate across the event horizon. In agreement with previous studies based on stationary models, we find that by allowing the mass of the black hole to grow the disc becomes unstable. Our hydrodynamical simulations show that for all disc‐to‐hole mass ratios considered (between 1 and 0.05), the runaway instability appears very fast on a dynamical time‐scale of a few orbital periods, typically a few 10 ms and never exceeding 1 s for our particular choice of the mass of the black hole (2.5 M⊙) and a large range of mass fluxes (m˙≳10‐3 M⊙ s‐1). The implications of our results in the context of gamma‐ray bursts are briefly discussed.

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“…In Khanna (1998b) I have re-formulated Biermann's theory in the Kerr metric. The base of this battery theory is Ohm's law of eq.…”

Section: The Gravitomagnetic Batterymentioning

confidence: 99%

Generation and Evolution of Magnetic Fields in the Gravitomagnetic Field of a Kerr Black Hole

Khanna¹

2003

Nonlinear Gravitodynamics

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I study the generation and evolution of magnetic fields in the plasma surrounding a rotating black hole. Attention is focused on effects of the gravitomagnetic potential. The gravitomagnetic force appears as battery term in the generalized Ohm's law. The generated magnetic field should be stronger than fields generated by the classical Biermann battery. The coupling of the gravitomagnetic potential with electric fields appears as gravitomagnetic current in Maxwell's equations. In the magnetohydrodynamic induction equation, this current re-appears as source term for the poloidal magnetic field, which can produce closed magnetic structures around an accreting black hole. In principle, even self-excited axisymmetric dynamo action is possible, which means that Cowling's anti dynamo theorem does not hold in the Kerr metric. Finally, the structure of a black hole driven current is studied.

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Generation of magnetic fields by a gravitomagnetic plasma battery

Cited by 13 publications

References 11 publications

The runaway instability of thick discs around black holes - II. Non-constant angular momentum discs

The runaway instability of thick discs around black holes - II. Non-constant angular momentum discs

The runaway instability of thick discs around black holes - I. The constant angular momentum case

Generation and Evolution of Magnetic Fields in the Gravitomagnetic Field of a Kerr Black Hole

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