fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors...

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Identification of fast magnetic reconnection events in accretion disks under the action of MHD instabilities LUÍS H.S. KADOWAKI ELISABETE M. DE GOUVEIA DAL PINO JAMES M. STONE OCTOBER 17, 2017 MAGNETIC FIELDS IN THE UNIVERSE VI: FROM LABORATORY AND STARS TO THE PRIMORDIAL STRUCTURES

Transcript of fast magnetic reconnection events in accretion disks under ...β€’4st step: Evaluate the eigenvectors...

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Identification of fast magnetic reconnection events in accretion disks under the action of MHD instabilitiesL U Í S H . S . K A D O WA K I

E L I S A B E T E M . D E G O U V E I A D A L P I N O

J A M E S M . S TO N E

O C TO B E R 1 7 , 2 0 1 7

M A G N E T I C F I E L D S I N T H E U N I V E R S E V I : F R O M L A B O R ATO R Y A N D S TA R S TO T H E P R I M O R D I A L S T R U C T U R E S

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Outline

β€’ Magnetic reconnection in accretion disk systems

β€’ Numerical simulations with a shearing-box approach

β€’ MHD instabilities in accretion disks

β€’ Identification of fast magnetic reconnection events in the surroundings of accretion disks

β€’ Conclusions

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Accretion disk systems

β€’ Accretion disks systems are believed to be very common structures in the Universe

β€’ These systems are associated to:β€’ Black Hole Binaries (BHBs)

β€’ Active Galactic Nuclei (AGNs)

β€’ Young Stellar Objects (YSOs) and so protoplanetary disks

β€’ The formation of a turbulent corona above and below accretion disks plays an important role in magnetic reconnection events

β€’ These events could explain the flare emissions in X-ray (YSOs) and in radio and gamma-ray (BHBs and AGNs)

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Turbulent magnetic reconnection in collisional flowsβ€’ Lazarian & Vishiniac (1999) model (Kowal’s talk):β€’ Reconnection triggered by tubulence

β€’ Several reconnection points (at all scales) due to the wandering magnetic field lines

β€’ β€œFast” reconnection

β€’ π‘‰π‘Ÿπ‘’π‘ ≃ 𝑉𝐴𝑀𝐴2

Numerical simulations (Kowal et al. 2009, 2012)

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MHD numerical simulations of accretion disks and coronaMAGNETIC RECONNECTION UNDER THE ACTION OF MHD INSTABILITIES

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Aims

β€’ The formation of a large scale poloidal magnetic field by the arising of loops due to the Parker-Rayleigh-Taylor instability

β€’ The role of Parker-Rayleigh-Taylor and magnetorotationalinstabilities in the formation of a turbulent magnetized corona around accretion disksβ€’ Where magnetic reconnection events could occur

β€’ The identification of fast magnetic reconnection events by the statistical analysis of the reconnection rate in the corona and disk

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Numerical method (shearing-box)

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Kadowaki (master’s thesis, 2011)

β€’ Shearing-Box (Hawley et al., 1995):β€’ A steady flow with a linear shearing velocity:

β€’ For a Keplerian disk:

Kadowaki et al. (2017, in prep.)

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Numerical method (shearing-box)β€’ MHD equations:

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Numerical method (shearing-box)β€’ Momentum equation:

Coriolis Force (Radial and Azimuthal components)

Centrifugal + Gravitational Forces (Radial component)

Gravity (Vertical component)

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Numerical method (shearing-box)β€’ Boundary Conditions:β€’ Computational domain: 𝐿π‘₯, 𝐿𝑦e 𝐿𝑧

β€’ Strictly periodic in all the boundaries at 𝑑 = 0

β€’ The shearing is produced by the slipping of the boundaries in π‘₯ direction

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Hawley et al. (1995)

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MHD instabilitiesMagnetorotational instability (MRI)

β€’ A weak magnetic field exerts an elastic force between two fluid elements

β€’ This force transfers angular momentum to the outer regionβ€’ Making possible the accretion in Keplerian

regimes

β€’ Linear regime: Amplification of the magnetic field (dynamo effect)

β€’ Non-linear regime: Saturation of the magnetic field and formation of turbulence

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MHD instabilitiesParker-Rayleigh-Taylor instability

β€’ Instability driven by strong magnetic fields:

β€’ 𝛽 =π‘ƒπ‘‘β„Žπ‘’π‘Ÿπ‘šπ‘Žπ‘™

π‘ƒπ‘šπ‘Žπ‘”π‘›π‘’π‘‘π‘–π‘= 1 (Magnetic buoyance)

β€’ Azimuthal magnetic field (βŠ₯ Ԧ𝑔)

β€’ Formation of magnetic loops β†’ Magnetic reconnection β†’ Release of energy in the coronal region

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Kadowaki et al. (2017, in prep.)Parker (1966)

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Numerical results (Resolution: 2563)β€’ Athena code (Stone et al., 2008, 2010)

β€’ Model PMRIg_21H_oxyz12

β€’ Initial conditions: β€’ Isothermal system

β€’ Magnetostatic equilibrium

β€’ Azimuthal magnetic field (𝐡𝑦)

β€’ 𝛽 = 1.0

β€’ Initial Gaussian perturbation in the Keplerian velocity field

β€’ Boundaries conditions: β€’ π‘₯: Shearing-periodic

β€’ 𝑦: Periodic

β€’ 𝑧: Outflow

β€’ 12𝐻 Γ— 12𝐻 Γ— 12𝐻 (𝐻 = πΆπ‘†Ξ©βˆ’1)

β€’ 256𝐻 Γ— 256𝐻 Γ— 256𝐻 cells

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Numerical results (Resolution: 2563)

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Numerical results (Resolution: 2563)

β€’ Transition between PRTI and MRI

β€’ Polarity inversions due to the action of the dynamo triggered by MRI

β€’ Zero net flux field ( 𝐡𝑧 β‰… 0)

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Numerical results (Resolution: 2563)

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Numerical results (Comparison)

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Identification of fast magnetic reconnection events in accretion disksSTATISTICAL ANALYSIS OF THE MAGNETIC RECONNECTION RATE

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Algorithm

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β€’ We have adapted the algorithm of Zhdankin et al. (2013) and extended to a 3D analysis

β€’ 1st step: Sample of cells with 𝑗0 > πœ€ 𝛻 Γ— 𝐡

1 1 2 5 1

1 4 6 4 2

1 3 4 3 1

| 𝑗 | = 2.6

𝒙

π’š

In this work, we have used:πœ€ = 5

For Ξ΅ = 1

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Algorithm

20Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017

β€’ We have adapted the algorithm of Zhdankin et al. (2013) and extended to a 3D analysis

β€’ 2nd step: Sample of cells with local maxima π‘—π‘šπ‘Žπ‘₯ = 𝑀𝐴𝑋 𝑗 𝑛π‘₯×𝑛𝑦×𝑛𝑧

1 1 2 5 1

1 4 6 4 2

1 3 4 3 1

π‘—π‘šπ‘Žπ‘₯ = 6 =𝑀𝐴𝑋 𝑗 3Γ—3

𝒙

π’š

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Algorithm

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β€’ We have adapted the algorithm of Zhdankin et al. (2013) and extended to a 3D analysis

β€’ 3st step: Check if the local maxima is between opposite magnetic field polarity

π‘—π‘šπ‘Žπ‘₯Confirmed!

𝒙

π’š

𝑩𝒙

𝑩𝒙

π‘©π’šπ‘©π’š

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Algorithm

22Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017

β€’ We have adapted the algorithm of Zhdankin et al. (2013) and extended to a 3D analysis

β€’ 3st step: Check if the local maxima is between opposite magnetic field polarity

π‘—π‘šπ‘Žπ‘₯ Confirmed!

𝒙

π’š

𝑩𝒙

𝑩𝒙

π‘©π’šπ‘©π’š

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Algorithm

23Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017

β€’ We have adapted the algorithm of Zhdankin et al. (2013) and extended to a 3D analysis

β€’ 3st step: Check if the local maxima is between opposite magnetic field polarity

π‘—π‘šπ‘Žπ‘₯ Rejected!

𝒙

π’š

𝑩𝒙

𝑩𝒙

π‘©π’šπ‘©π’š

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Algorithm

24Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017

β€’ We have adapted the algorithm of Zhdankin et al. (2013) and extended to a 3D analysis

β€’ 4st step: Evaluate the eigenvectors of the Hessian matrix

𝐻 =

πœ•π‘₯π‘₯𝑗 πœ•π‘₯𝑦𝑗 πœ•π‘₯𝑧𝑗

πœ•π‘¦π‘₯𝑗 πœ•π‘¦π‘¦π‘— πœ•π‘¦π‘§π‘—

πœ•π‘§π‘₯𝑗 πœ•π‘§π‘¦π‘— πœ•π‘§π‘§π‘—

𝒙

π’š

π’†πŸ π’†πŸβ€’ π’†πŸ: Indicates the fastest decaying of 𝑗 (Thickness)

β€’ Projection of the magnetic and velocity fields along π’†πŸ, π’†πŸ and π’†πŸ‘ directions

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Algorithm

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β€’ We have adapted the algorithm of Zhdankin et al. (2013) and extended to a 3D analysis

β€’ 5st step: Evaluate the magnetic reconnection rate

π’†πŸ

π’†πŸ

𝑉𝑖𝑛𝑉𝐴

=1

2ቀ

𝑉𝑒1𝑉𝐴 π‘™π‘œπ‘€π‘’π‘Ÿ

βˆ’ ቀ𝑉𝑒1𝑉𝐴 π‘’π‘π‘π‘’π‘Ÿ

𝑉𝐴 =𝐡𝑒1

2 + 𝐡𝑒22 + 𝐡𝑒3

2

πœŒπ‘™π‘œπ‘€π‘’π‘Ÿ

π‘’π‘π‘π‘’π‘Ÿ

𝑗 <1

2π‘—π‘šπ‘Žπ‘₯

𝑗 <1

2π‘—π‘šπ‘Žπ‘₯

𝑗 >1

2π‘—π‘šπ‘Žπ‘₯

Similar to Kowal et al. (2009)

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Magnetic reconnection rate (Resolution: 2563)

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Upper Corona

Confirmed!Rejected!

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Magnetic reconnection rate (Resolution: 2563)

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Upper Corona

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Magnetic reconnection rate (Resolution: 2563)

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Magnetic reconnection rate (Resolution: 2563)

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Magnetic reconnection rate (Resolution: 2563)

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Power spectrum (Resolution: 2563)

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t = 1 (Orbits) t = 2 (Orbits)

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Power spectrum (Resolution: 2563)

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t = 4 (Orbits) t = 5 (Orbits)

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Conclusions

β€’ Our simulations have revealed the arising of magnetic loops due to the PRTI followed by the development of turbulence due to PRTI and MRI

β€’ Even with an initial high magnetized regime, the disk evolves to a gas-pressure dominant regime with a magnetized coronaβ€’ Transport of magnetic field from the disk to the corona by buoyance process

β€’ We have evaluated the magnetic reconnection rates and detected the presence of fast magnetic reconnection events, as predicted by the theory of turbulence-induced fast reconnection (Lazarian & Vishiniac, 1999)

β€’ The algorithm applied to this work has demonstrated to be an efficient tool for the identification of magnetic reconnection sites in numerical simulations

Kadowaki, de Gouveia Dal Pino & Stone (2017, in prep.)

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Thank you!


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