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
2. 10/23/2020 Midwest Relativity Meeting 2 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
3. 10/23/2020 Midwest Relativity Meeting 3 Observational Background AGN Classification: Radio-loud & Radio-quiet AGN Dermer & Giebles 2016
4. 10/23/2020 Midwest Relativity Meeting 4 Observational Background Evidence for Unified AGN Outflow Model Correlation between outflow kinematics and physical conditions Tombesi + 2013 (Ultra-fast outflows) (Warm Absorbers)
5. 10/23/2020 Midwest Relativity Meeting 5 Observational Background Evidence for Unified AGN Outflow Model Implication of SMBH Angular Momentum for Unified AGN Outflow Model Danehkar +
6. 10/04/2019 Midwest Relativity Meeting 6 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?
7. 10/23/2020 Midwest Relativity Meeting 7 Weyl Curvature Vacuum Riemann tensor Einstein’s 70th birthday, Institute for Advanced Study, 1949 Weyl, Mathematische Zeitschrift, 2, 384, 1918
8. 10/23/2020 Midwest Relativity Meeting 8 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
9. 10/23/2020 Midwest Relativity Meeting 9 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
10. 10/23/2020 Midwest Relativity Meeting 10 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)
11. 10/23/2020 Midwest Relativity Meeting 11 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
12. 10/23/2020 Midwest Relativity Meeting 12 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
13. 10/23/2020 Midwest Relativity Meeting 13 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
14. 10/23/2020 Midwest Relativity Meeting 14 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)
15. 10/23/2020 Midwest Relativity Meeting 15 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.
16. 10/23/2020 Midwest Relativity Meeting 16 Image Credit: J. Bergeron, Sky & Telescope Magazine Image Credit: J. Bergeron, Sky & Telescope Magazine Thank you for your attention Thank you for your attention