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Oscillations in Accretion Discs around Black Holes

Oscillations in Accretion Discs around Black Holes. B árbara Trovão Ferreira & Gordon Ogilvie DAMTP, University of Cambridge. no standing waves. Problems. 1. Turbulent viscosity  damping No reflection boundaries

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Oscillations in Accretion Discs around Black Holes

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  1. Oscillations in Accretion Discs around Black Holes Bárbara Trovão Ferreira & Gordon Ogilvie DAMTP, University of Cambridge

  2. no standing waves Problems 1. Turbulent viscositydamping No reflection boundaries 2. Linear oscillations (small amplitude) need an excitation mechanism to be detected

  3. Equilibrium state: • Linear perturbations: • Further separation of variables (approx):  System of 1st order ODEs in for Disc Oscillations e.g. Kato 2001 Lubow & Pringle 1993

  4.  f / 2D modes •  p modes r modes Let (simpler 3D mode) Dispersion Relation • Far from resonances: DR

  5. p r Keplerian Disc freq2 [in units of (c3/10GM)2] radius [in units of GM/c2]

  6. p r Relativistic Disc Using particle orbit, relativistic expressions for characteristic frequencies (Kato 1990) freq2 [in units of (c3/10GM)2] Kato & Fukue 1980 Okazaki, Kato, Fukue 1987 radius [in units of GM/c2]

  7. eigenvalue matrix ≠ identity depending on b. c. eigenvector Numerical Calculation of Trapped r mode

  8. Deformed Disc Kato 2004, 2007

  9. Wave Coupling

  10. CR r mode interm.mode • warp/eccentricity energy ≈ zero - interm. & r mode exchanges: damping of negative energy wave  draws positive energy from disc rotation  available to excite r mode (who replenishes intermediate mode negative energy) dissipation term () to be included in equations for interm. mode Energy Exchanges • Co-rotation resonance:

  11. complicated matrix includes coupling terms & interm.mode dissipation eigenvalue matrix ≠ identity depending on b. c. eigenvector - r and interm. modes quantities evaluated at discrete points Numerical Calculations of Growth Rate

  12. Growth of Oscillations - Results Ferreira & Ogilvie 2008

  13. Conclusions • In a relativistic disc, inertial modes can, in principle, avoid turbulent effects by being trapped in a small region; • These modes can be excited via the coupling mechanism described here, provided that: • Negative energy (intermediate) mode dissipates in order to remove rotational energy from the disc; • Global deformations reach the inner disc region with non-negligible amplitude; • Measure black hole spin.

  14. The End

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