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Oscillations in Accretion Discs around Black Holes

Explore linear oscillations and growth rates in relativistic discs, studying energy exchanges and wave coupling mechanisms. Investigate numerical calculations for trapped modes and assess the impact of global deformations on disc behavior.

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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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