Tendex and Vortex Lines around Spinning Supermassive Black Holes

Talk presented at the 30th Midwest Relativity Meeting (Virtual), University of Notre Dame, IN, USA, October 2020

Transcript

1. Tendex and Vortex Lines
   around Spinning
   Supermassive Black Holes
   Ashkbiz Danehkar, Postdoc
   Department of Astronomy, University of Michigan
   danehkar@umich.edu
   The 30th Midwest Relativity Meeting, University of Notre Dame, Indiana, USA, October 23, 2020
   Image Credit: J. Bergeron, Sky & Telescope Magazine
   Image Credit: J. Bergeron, Sky & Telescope Magazine
   

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   Motivation for Tendex and Vortex
   Observational Background
   X-ray Observations of AGN (1999-present)
   Chandra X-ray Observatory (1999-present)
   XMM-Newton, X-ray Multi-Mirror Mission (2000-present)
   NuSTAR, Nuclear Spectroscopic Telescope Array (2012-present)
   Gierlinski + 1999
   Lonanov 2007
   Credit: Roen Kelly @ Astronomy
   

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   Observational Background
   AGN Classification: Radio-loud & Radio-quiet AGN
   Dermer & Giebles 2016
   

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   Observational Background
   Evidence for Unified AGN Outflow Model
   Correlation between outflow kinematics and physical conditions
   Tombesi + 2013
   (Ultra-fast outflows)
   (Warm Absorbers)
   

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   Observational Background
   Evidence for Unified AGN Outflow Model
   Implication of SMBH Angular Momentum for Unified AGN Outflow Model
   Danehkar +
   

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   Problems
   Radio-quiet and radio-loud AGN
   Garofalo + 2010
   ●
   Radio-quiet AGN
   – Compact outflows
   – Weak (or no) radio emission
   ●
   Radio-loud AGN
   – Strong radio source
   – Extended jets
   – Typically in elliptical massive
   galaxies that may evolve
   from recent mergers (binary SMBH?)
   ●
   Observation Tests:
   – If correlation between BH Spin and Outflow kinematics?
   – If binary SMBH present in radio-load galaxies with extended jets?
   – If BH spinning prograde to accetion disk (a<0) in radio-load galaxies?
   

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   Weyl Curvature
   Vacuum Riemann tensor
   Einstein’s 70th birthday, Institute for Advanced Study, 1949
   Weyl, Mathematische Zeitschrift, 2, 384, 1918
   

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   Weyl Curvature
   ●
   Gravitoelectric & Gravitomagnetic fields
   – Names coined by Kip Thorne (IAU, 97, 255, 1982)
   – Thorne et al. Black holes: The membrane paradigm (Yale
   University, 1986)
   ●
   Gravitoelectric Tensor
   – Newtonian Tidal Force
   ●
   Gravitomagnetic Tensor
   – Frame-dragging vortex & Gravitational Waves
   ●
   Bianchi Identities
   – Constraints for gravitoelectric & gravitomagnetic
   (see e.g. Relativistic Cosmology, Ellis, Maartens, &
   MacCallum, Cambridge, 2012)
   Kip Thorne’s 60th birthday, Caltech, 2000
   

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   Weyl Curvature
   Tendex and Vortex Lines
   ●
   Visualization of Gravitoelectric & Gravitomagnetic tensors
   – Nichols et al. PRD 84, 124012, 2011; PRD 86, 104028, 2012
   ●
   Tidal Tendex Line
   – Tendex coined by David Nichols (tendere: ‘to stretch’)
   – integral curves of eigenvectors of gravitoeletric tensor
   – Owen el al. PRL 106, 151101, 2011
   – Zhang et al. PRD 86, 084049, 2012
   ●
   Frame-dragging Vortex Line
   – integral curves of eigenvectors of gravitomagnetic tensor
   eigenvector eigenvalue
   eigenvector eigenvalue Owen el al. PRL 106, 151101, 2011
   

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    Weyl Curvature
    Tendex and Vortex Lines of Slowly Spinning SMBH
    Danehkar, IJMPD, 2020, arXiv:2006.13287 [gr-qc]
    ●
    Visualization of Eab & Hab around a slow Kerr BH
    – slow Kerr metric (Zhang et al. PRD 86, 084049, 2012)
    – gravitoelectric tensor
    – gravitomagnetic tensor (Zhang et al. PRD 86, 084049, 2012)
    

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    Weyl Curvature
    Tendex and Vortex Lines of Fast Spinning BH
    ●
    Visualization of Eab & Hab around a fast Kerr BH
    Tidal Tendex Line Frame-dragging Vortex Line
    Zhang et al. PRD 86, 084049, 2012
    

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    Weyl Curvature
    Tendex and Vortex Lines of Binary BH
    ●
    Visualization of Eab & Hab around binary BHs
    Tidal Tendex Line Frame-dragging Vortex Line
    ●
    Spectral Einstein Code (SpEC)
    – https://www.black-holes.org/code/SpEC.html
    – SpEC is not publicity available
    ●
    New version: SpECTRE
    – https://github.com/sxs-collaboration/spectre
    – SpECTRE is still under development by the SXS (Simulating eXtreme Spacetimes) Collaboration, and not yet ready
    – Updates on SpECTRE code: https://icerm.brown.edu/programs/sp-f20/w3/ (next week talk, Oct 28)
    Owen el al. PRL 106, 151101, 2011
    

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    Weyl Curvature
    Tendex and Vortex Lines of Binary BH
    ●
    Visualization of Eab & Hab around binary BHs
    – Gravitational Wave Simulations by SpEC
    Owen el al. PRL 106, 151101, 2011
    LIGO detection of gravitational waves, 2016
    

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    Weyl Curvature
    Tendex and Vortex Lines of Exact Solutions
    ●
    The Einstein Toolkit (https://einsteintoolkit.org/)
    – Cactus Framework and Computational Toolkit (http://cactuscode.org/)
    – Cactus Thorns (http://svn.einsteintoolkit.org/cactus/)
    – Recent Tutorial: https://icerm.brown.edu/programs/sp-f20/w1/
    ●
    Einstein Toolkit Thorn: EinsteinAnalysis/WeylScal4
    – calculates Weyl scalars in the Einstein Toolkit
    – developed using Mathematica notations
    – converted to Thorn using Kranc (http://kranccode.org/)
    ●
    Thorn for gravitoelectric and gravitomagnetic tensors in the Einstein Toolkit
    – can be made by Mathemtica scripts and converted to Thorn using Kranc
    ●
    Kranc: Mathematica program turns tensorial equations into a thorn for the Cactus Computational Toolkit
    – can be written in LaTex notations and converted to NRPy+
    ●
    NRPy+: Python-based code generation for numerical relativity that can turn tensorial formulas into a
    thorn for the Cactus Einstein Toolkit
    transverse wave component for GW simulations of mergers
    ●
    VisIt
    ●
    ParaView
    ●
    Python packages (yt, etc)
    

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    Summary
    Tendex and Vortex Lines around SMBHs
    ●
    Observational Motivations:
    – Observational Evidence for a Unified AGN Outflow Model
    – Possible correlation between SMBH angular momentum and AGN outflows
    – Physical mechanism behind radio-quiet and radio-loud AGN: binary SMBH in radio-loud?
    ●
    Gravitoelectric and Gravitiomagnetic tensors
    are visualized using their eigenvectors and eigenvalues:
    called Tidal Tendex and Frame-dragging Vortex Lines.
    – Visualization of Eab and Hab for a slowly spinning BH can be easily done in weak-
    field limit using analytically obtained linear solutions
    – Visualization of Eab and Hab for a fast spinning BH can be done in strong fields
    using approximation solutions, but requires higher resolutions and computations
    – Visualization of Eab and Hab for exact solutions and binary BHs are very complex,
    but can be implemented using a new Thorn made by either Kranc or NRPy+ for
    the Einstein Toolkit. These simulations require supercomputers. As its simulation
    outputs (HDF5) are very big, they also require very large storage devices.
    

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    Image Credit: J. Bergeron, Sky & Telescope Magazine
    Image Credit: J. Bergeron, Sky & Telescope Magazine
    Thank you for your attention
    Thank you for your attention
    

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