Ashkbiz Danehkar, Postdoc Department of Astronomy, University of Michigan [email protected] Challenges and Innovations in Computational Astrophysics - II, November 20, 2020 Image Credit: J. Bergeron, Sky & Telescope Magazine Image Credit: J. Bergeron, Sky & Telescope Magazine
Black Hole Spin Measurement (see Brenneman 2013) • Thermal Continuum Fitting (UV observation) – stellar-mass black hole – AGN (may problematic due to UV absorption lines!) • Inner Disk Reflection Modeling – AGN (X-ray) • High Frequency Quasi-Periodic Oscillations – AGN + stellar-mass black hole (fully not developed) • X-ray Polarimetry – Need sensitive X-ray polarimter (not available now!) • Imaging the Event Horizon Shadow – Need Very Long Baseline Interferometry (in development) – Suitable only for Sgr A* and M87 a = J c / G M2 (a: BH spin, J: angular momentum, M: BH mass, G: gravitational constant, c: speed of light)
Relativistically broadened Kα iron line (6.4 keV) Compton hump (> 10keV) Black Hole Spin Measurement from X-ray a = - 1 a = 0 a = 1 Image credit: NASA/JPL-Caltech
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
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
Lines of Merging 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/ (see talk, Oct 28) Owen el al. PRL 106, 151101, 2011
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
Toolkit • The Einstein Toolkit (https://einsteintoolkit.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 – converted to Thorn using Kranc (http://kranccode.org/) • New Module 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 transverse wave component for GW simulations of mergers
via BH Spin Survey & Numerical Relativity • Observational Background – Observational Evidence for a Unified AGN Outflow Model – Possible correlation between SMBH angular momentum and AGN outflows – Physical mechanism behind radio-loud AGN: binary SMBH in radio-loud? • Black Hole Spin Surveys Relativistically broadened Fluorescence Iron Line + Compton continuum Relativistic Reflection Model (relxill + xillver) • Numerical Relativity – Gravitoelectric and Gravitiomagnetic tensors visualized using their Tidal Tendex and Frame-dragging Vortex Lines. – Visualization of Tendex and Vortex lines for exact solutions and binary BHs are very complex, but can be done using a new module made by either Kranc or NRPy+ for the Einstein Toolkit. These simulations are computationally expensive (need HPC)