Numerically solving the relativistic Grad–Shafranov equation in Kerr spacetimes: numerical techniques

Mahlmann, J. F.; Cerdá–Durán, P.; Aloy, M. Á.

doi:10.1093/mnras/sty858

Cited by 26 publications

(38 citation statements)

References 68 publications

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“…Compared to the monopole solution, in which Ω| FFE ≈ 0.5Ω H (see Paper I), the magnetic field lines of the collimated jet rotate slower. Specifically, the outmost field line rotates with angular velocity Ω| FFE ≈ 0.37Ω H , consistent with previous work (Nathanail & Contopoulos 2014;Mahlmann et al 2018). In addition, the fluid inertia drags down the rotation of all magnetic field lines further, i.e., Ω| MHD < Ω| FFE .…”

Section: Magnetic Field Linessupporting

confidence: 90%

“…The numerical techniques are similar to those in previous work (e.g. Contopoulos et al 2013;Nathanail & Contopoulos 2014;Mahlmann et al 2018;Pan et al 2017;Huang et al 2016Huang et al , 2018Huang et al , 2019. On can obtain converged {Ψ (l) , Ω (l) , L (l) } with field lines smoothly crossing the inner/outer Alfvén surface after sufficient evolution.…”

Section: Discussionmentioning

confidence: 77%

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Toward a Full MHD Jet Model of Spinning Black Holes. I. Framework and a Split Monopole Example

Huang

Pan

2019

ApJ

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In this paper, we investigate the magnetohydrodynamical structure of a jet powered by a spinning black hole, where electromagnetic fields and fluid motion are governed by the Grad-Shafranov equation and the Bernoulli equation, respectively. Assuming steady and axisymmetric jet structure, the global solution is uniquely determined with prescribed plasma loading into the jet and the poloidal shape of the outmost magnetic field line. We apply this model to the jet in the center of nearby radio galaxy M87, and we find it can naturally explain the slow flow acceleration and the flow velocity stratification within 10 5 gravitational radii from the central black hole. In particular, we find the extremal black hole spin is disfavored by the flow velocity measurements, if the plasma loading to the jet is dominated by the electron/positron pair production at the jet base.

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Section: Magnetic Field Linessupporting

confidence: 90%

Section: Discussionmentioning

confidence: 77%

Toward a Full MHD Jet Model of Spinning Black Holes. I. Framework and a Split Monopole Example

Huang

Pan

2019

ApJ

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“…We consider here the case of monopole-type asymptotics (19) of the flux function. If one computes the right-hand side of the Stream equation (12) for a generic function ψ(r, θ) with asymptotics (19) then it goes like r 2 for large r due to the terms…”

Section: Monopole-type Asymptoticsmentioning

confidence: 99%

“…Recently, it has been used to compute the expected power output relevant for the radio loud/quiet dichotomy of active galactic nuclei [11]. Moreover, it has been used as a test case for many numerical simulations [11][12][13][14][15][16][17][18][19]. This poses the question of how to reconcile the numerical studies with the results of this paper.…”

Section: Introductionmentioning

confidence: 99%

Force-free electrodynamics near rotation axis of a Kerr black hole

Grignani

Harmark²,

Orselli

2020

Class. Quantum Grav.

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Despite their potential importance for understanding astrophysical jets, physically realistic exact solutions for magnetospheres around Kerr black holes have not been found, even in the force-free approximation. Instead approximate analytical solutions such as the Blandford-Znajek (split-)monopole, as well as numerical solutions, have been constructed. In this paper we consider a new approach to the analysis and construction of such magnetospheres. We consider force-free electrodynamics close to the rotation axis of a magnetosphere surrounding a Kerr black hole assuming axisymmetry. This is the region where the force-free approximation should work the best, and where the jets are located. We perform a systematic study of the asymptotic region with (split-)monopole, paraboloidal and vertical asymptotic behaviors. Imposing asymptotics similar to a (split-)monopole, we find that demanding regularity at the rotation axis and the event horizon restricts solutions of the stream equation so much that it is not possible for a solution to be continuously connected to the static (split-)monopole around the Schwarzschild black hole in the limit where the rotation goes to zero. This provides independent evidence to the issues discovered with the asymptotics of the Blandford-Znajek (split-)monopole in Ref.[1] from which it follows that its perturbative construction is inconsistent.

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“…;Mahlmann et al (2018);Yuan et al (2019a,b). In their equilibrium solutions all closed field lines connect the BH horizon to the inner regions of an equatorial (thin) disc up to a cylindrical radius r close > r ISCO .…”

mentioning

confidence: 99%

Striped Blandford/Znajek jets from advection of small-scale magnetic field

Mahlmann

Levinson

Aloy

2020

Monthly Notices of the Royal Astronomical Society

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ABSTRACT Black hole – accretion disc systems are the central engines of relativistic jets from stellar to galactic scales. We numerically quantify the unsteady outgoing Poynting flux through the horizon of a rapidly spinning black hole endowed with a rotating accretion disc. The disc supports small-scale, concentric, flux tubes with zero net magnetic flux. Our general relativistic force-free electrodynamics simulations follow the accretion on to the black hole over several hundred dynamical time-scales in 3D. For the case of counter-rotating accretion discs, the average process efficiency reaches up to 〈ϵ〉 ≈ 0.43, compared to a stationary energy extraction by the Blandford/Znajek process. The process efficiency depends on the cross-sectional area of the loops, i.e. on the product l × h, where l is the radial loop thickness and h its vertical scale height. We identify a strong correlation between efficient electromagnetic energy extraction and the quasi-stationary setting of ideal conditions for the operation of the Blandford/Znajek process (e.g. optimal field line angular velocity and fulfillment of the so-called Znajek condition). Remarkably, the energy extraction operates intermittently (alternating episodes of high and low efficiency) without imposing any large-scale magnetic field embedding the central object. Scaling our results to supermassive black holes, we estimate that the typical variability time-scale of the system is of the order of days to months. Such time-scales may account for the longest variability scales of TeV emission observed, e.g. in M87.

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Numerically solving the relativistic Grad–Shafranov equation in Kerr spacetimes: numerical techniques

Cited by 26 publications

References 68 publications

Toward a Full MHD Jet Model of Spinning Black Holes. I. Framework and a Split Monopole Example

Toward a Full MHD Jet Model of Spinning Black Holes. I. Framework and a Split Monopole Example

Force-free electrodynamics near rotation axis of a Kerr black hole

Striped Blandford/Znajek jets from advection of small-scale magnetic field

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