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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
Outline
• Magnetic reconnection in accretion disk systems
• Numerical simulations with a shearing-box approach
• MHD instabilities in accretion disks
• Identification of fast magnetic reconnection events in the surroundings of accretion disks
• Conclusions
Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 2
Accretion disk systems
• Accretion disks systems are believed to be very common structures in the Universe
• These systems are associated to:• Black Hole Binaries (BHBs)
• Active Galactic Nuclei (AGNs)
• Young Stellar Objects (YSOs) and so protoplanetary disks
• The formation of a turbulent corona above and below accretion disks plays an important role in magnetic reconnection events
• These events could explain the flare emissions in X-ray (YSOs) and in radio and gamma-ray (BHBs and AGNs)
Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 3
Turbulent magnetic reconnection in collisional flows• Lazarian & Vishiniac (1999) model (Kowal’s talk):• Reconnection triggered by tubulence
• Several reconnection points (at all scales) due to the wandering magnetic field lines
• “Fast” reconnection
• 𝑉𝑟𝑒𝑐 ≃ 𝑉𝐴𝑀𝐴2
Numerical simulations (Kowal et al. 2009, 2012)
Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 4
MHD numerical simulations of accretion disks and coronaMAGNETIC RECONNECTION UNDER THE ACTION OF MHD INSTABILITIES
Aims
• The formation of a large scale poloidal magnetic field by the arising of loops due to the Parker-Rayleigh-Taylor instability
• The role of Parker-Rayleigh-Taylor and magnetorotationalinstabilities in the formation of a turbulent magnetized corona around accretion disks• Where magnetic reconnection events could occur
• The identification of fast magnetic reconnection events by the statistical analysis of the reconnection rate in the corona and disk
Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 6
Numerical method (shearing-box)
Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 7
Kadowaki (master’s thesis, 2011)
• Shearing-Box (Hawley et al., 1995):• A steady flow with a linear shearing velocity:
• For a Keplerian disk:
Kadowaki et al. (2017, in prep.)
Numerical method (shearing-box)• MHD equations:
Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 8
Numerical method (shearing-box)• Momentum equation:
Coriolis Force (Radial and Azimuthal components)
Centrifugal + Gravitational Forces (Radial component)
Gravity (Vertical component)
Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 9
Numerical method (shearing-box)• Boundary Conditions:• Computational domain: 𝐿𝑥, 𝐿𝑦e 𝐿𝑧
• Strictly periodic in all the boundaries at 𝑡 = 0
• The shearing is produced by the slipping of the boundaries in 𝑥 direction
Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 10
Hawley et al. (1995)
MHD instabilitiesMagnetorotational instability (MRI)
• A weak magnetic field exerts an elastic force between two fluid elements
• This force transfers angular momentum to the outer region• Making possible the accretion in Keplerian
regimes
• Linear regime: Amplification of the magnetic field (dynamo effect)
• Non-linear regime: Saturation of the magnetic field and formation of turbulence
Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 11
MHD instabilitiesParker-Rayleigh-Taylor instability
• Instability driven by strong magnetic fields:
• 𝛽 =𝑃𝑡ℎ𝑒𝑟𝑚𝑎𝑙
𝑃𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐= 1 (Magnetic buoyance)
• Azimuthal magnetic field (⊥ Ԧ𝑔)
• Formation of magnetic loops → Magnetic reconnection → Release of energy in the coronal region
Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 12
Kadowaki et al. (2017, in prep.)Parker (1966)
Numerical results (Resolution: 2563)• Athena code (Stone et al., 2008, 2010)
• Model PMRIg_21H_oxyz12
• Initial conditions: • Isothermal system
• Magnetostatic equilibrium
• Azimuthal magnetic field (𝐵𝑦)
• 𝛽 = 1.0
• Initial Gaussian perturbation in the Keplerian velocity field
• Boundaries conditions: • 𝑥: Shearing-periodic
• 𝑦: Periodic
• 𝑧: Outflow
• 12𝐻 × 12𝐻 × 12𝐻 (𝐻 = 𝐶𝑆Ω−1)
• 256𝐻 × 256𝐻 × 256𝐻 cells
Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 13
Numerical results (Resolution: 2563)
Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 14
Numerical results (Resolution: 2563)
• Transition between PRTI and MRI
• Polarity inversions due to the action of the dynamo triggered by MRI
• Zero net flux field ( 𝐵𝑧 ≅ 0)
Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 15
Numerical results (Resolution: 2563)
Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 16
Numerical results (Comparison)
Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 17
Identification of fast magnetic reconnection events in accretion disksSTATISTICAL ANALYSIS OF THE MAGNETIC RECONNECTION RATE
Algorithm
19Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017
• We have adapted the algorithm of Zhdankin et al. (2013) and extended to a 3D analysis
• 1st step: Sample of cells with 𝑗0 > 𝜀 𝛻 × 𝐵
1 1 2 5 1
1 4 6 4 2
1 3 4 3 1
| 𝑗 | = 2.6
𝒙
𝒚
In this work, we have used:𝜀 = 5
For ε = 1
Algorithm
20Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017
• We have adapted the algorithm of Zhdankin et al. (2013) and extended to a 3D analysis
• 2nd step: Sample of cells with local maxima 𝑗𝑚𝑎𝑥 = 𝑀𝐴𝑋 𝑗 𝑛𝑥×𝑛𝑦×𝑛𝑧
1 1 2 5 1
1 4 6 4 2
1 3 4 3 1
𝑗𝑚𝑎𝑥 = 6 =𝑀𝐴𝑋 𝑗 3×3
𝒙
𝒚
Algorithm
21Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017
• We have adapted the algorithm of Zhdankin et al. (2013) and extended to a 3D analysis
• 3st step: Check if the local maxima is between opposite magnetic field polarity
𝑗𝑚𝑎𝑥Confirmed!
𝒙
𝒚
𝑩𝒙
𝑩𝒙
𝑩𝒚𝑩𝒚
Algorithm
22Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017
• We have adapted the algorithm of Zhdankin et al. (2013) and extended to a 3D analysis
• 3st step: Check if the local maxima is between opposite magnetic field polarity
𝑗𝑚𝑎𝑥 Confirmed!
𝒙
𝒚
𝑩𝒙
𝑩𝒙
𝑩𝒚𝑩𝒚
Algorithm
23Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017
• We have adapted the algorithm of Zhdankin et al. (2013) and extended to a 3D analysis
• 3st step: Check if the local maxima is between opposite magnetic field polarity
𝑗𝑚𝑎𝑥 Rejected!
𝒙
𝒚
𝑩𝒙
𝑩𝒙
𝑩𝒚𝑩𝒚
Algorithm
24Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017
• We have adapted the algorithm of Zhdankin et al. (2013) and extended to a 3D analysis
• 4st step: Evaluate the eigenvectors of the Hessian matrix
𝐻 =
𝜕𝑥𝑥𝑗 𝜕𝑥𝑦𝑗 𝜕𝑥𝑧𝑗
𝜕𝑦𝑥𝑗 𝜕𝑦𝑦𝑗 𝜕𝑦𝑧𝑗
𝜕𝑧𝑥𝑗 𝜕𝑧𝑦𝑗 𝜕𝑧𝑧𝑗
𝒙
𝒚
𝒆𝟏 𝒆𝟐• 𝒆𝟏: Indicates the fastest decaying of 𝑗 (Thickness)
• Projection of the magnetic and velocity fields along 𝒆𝟏, 𝒆𝟐 and 𝒆𝟑 directions
Algorithm
25Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017
• We have adapted the algorithm of Zhdankin et al. (2013) and extended to a 3D analysis
• 5st step: Evaluate the magnetic reconnection rate
𝒆𝟏
𝒆𝟐
𝑉𝑖𝑛𝑉𝐴
=1
2ቤ
𝑉𝑒1𝑉𝐴 𝑙𝑜𝑤𝑒𝑟
− ቤ𝑉𝑒1𝑉𝐴 𝑢𝑝𝑝𝑒𝑟
𝑉𝐴 =𝐵𝑒1
2 + 𝐵𝑒22 + 𝐵𝑒3
2
𝜌𝑙𝑜𝑤𝑒𝑟
𝑢𝑝𝑝𝑒𝑟
𝑗 <1
2𝑗𝑚𝑎𝑥
𝑗 <1
2𝑗𝑚𝑎𝑥
𝑗 >1
2𝑗𝑚𝑎𝑥
Similar to Kowal et al. (2009)
Magnetic reconnection rate (Resolution: 2563)
26Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017
Upper Corona
Confirmed!Rejected!
Magnetic reconnection rate (Resolution: 2563)
27Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017
Upper Corona
Magnetic reconnection rate (Resolution: 2563)
28Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017
Magnetic reconnection rate (Resolution: 2563)
Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 29
Magnetic reconnection rate (Resolution: 2563)
Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 31
Power spectrum (Resolution: 2563)
Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 32
t = 1 (Orbits) t = 2 (Orbits)
Power spectrum (Resolution: 2563)
Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 33
t = 4 (Orbits) t = 5 (Orbits)
Conclusions
• Our simulations have revealed the arising of magnetic loops due to the PRTI followed by the development of turbulence due to PRTI and MRI
• Even with an initial high magnetized regime, the disk evolves to a gas-pressure dominant regime with a magnetized corona• Transport of magnetic field from the disk to the corona by buoyance process
• 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)
• 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.)
Kadowaki, de Gouveia Dal Pino and Stone MFU VI - 2017 34
Thank you!