Problems

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Problems
1. Turbulent viscosity ? damping No
reflection boundaries 2. Linear oscillations
(small amplitude) need an excitation mechanism to
be detected
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Disc Oscillations
e.g. Kato 2001 Lubow Pringle 1993
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Dispersion Relation

• Far from resonances
  DR

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Keplerian Disc
freq2 in units of (c3/10GM)2
radius in units of GM/c2
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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
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Numerical Calculation of Trapped r mode
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Deformed Disc
Kato 2004, 2007
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Wave Coupling
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Energy Exchanges

• Co-rotation resonance

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Numerical Calculations of Growth Rate
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Growth of Oscillations - Results
Ferreira Ogilvie 2008
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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.

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The End