Exciting Waves/Modes in Black-Hole Accretion Disks

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1 Exciting Waves/Modes in Black-Hole Accretion Disks Dong Lai Cornell University L Observatoire de Paris Meudon, Dec.1, 2008

2 Edwin E. Salpeter Autobiography: Annual Review Astro & Astrophys. 2002, 40: 1-25

3 Exciting Waves/Modes in Black-Hole Accretion Disks Dong Lai Cornell University L Observatoire de Paris Meudon, Dec.1, 2008

4 Global modes and instabilities in accretion disks Super-reflection Role of corotation resonance Trapped modes: stability vs overstability GR effects Various diskoseismic modes in BH accretion disks QPOs in black-hole X-ray binaries with David Tsang (Cornell graduate student)

5 Instabilities in rotating fluid/disks Local Instabilities: Rayleigh centrifugal instability Gravitational instability MRI Global Instabilities: corotation amplifier (e.g. Mark 1976) SWING amplifier (Goldreich & Lynden-Bell 1965; Julian & Toomre 1966) Papaloizou-Pringle instability (in accretion tori) (1980s) Rossby wave instability (Lovelace et al. 1999) Accretion-ejection instability (Tagger & Pellat 1999)

6 Free waves in 2D disks (Spiral density waves): Dispersion relation: Lindblad Resonance: Wave can propagates in the region:

7 Effective potential

8 Super-reflection

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10 Analogy with Rotating (NS) Stars: Chandrasekhar-Friedman-Schutze (CFS) Instability Inertial frame Corotating frame ===> Unstable due to gravitational radiation

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12 This is not the whole story: So far we have neglected the corotation resonance, where

13 Fluid equations for reduce to (for barotropic flow): (vortensity)

14 Local dispersion relation: Corotation resonance/singularity:

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16 Wave dissipation at corotation

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18 WKB calculations of reflectivity/transmission: Solve wave equation in different regions Match the solutions using asymptotic expansions Around corotation: Whittaker function; Stokes phenomenon

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20 Summary:

21 Summary: Overstable mode Damped mode

22 GR Effect ISCO

23 Wave propagation zone:

24 Growing mode Damping mode

25 Disk model: a=0 m=2

26 Disk model: a=0 m=2

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28 Disk model: a=0 m=3

29 Boundary Conditions at the Inner Disk Edge For thin disks, radial velocity goes through sonic point near r ISCO. (viscous slim disk solution) Fluid perturbation must also be regular at the sonic point ===> Boundary conditions. We found: Radial inflow tends to damp the mode The disk inner edge is partially reflective due to steep radial gradient in density and radial velocity ===> Even with radial inflow, global unstable mode is still possible under some (realistic) conditions (when the density/velocity gradient is large).

30 Real accretion disk is more complicated Global MHD simulations of inner disks (still in the early of development. e.g. Noble, Krolik & Hawley 2008) Magnetic fields may accumulate in the inner disk and inside (e.g. Rothstein & Lovelace 2008) ==> The inner disk edge may be more reflective than transonic flow (cf. Tagger & Varniere 2006: Accretion-ejection instability)

31 High-Frequency QPOs in Black-Hole X-ray Binaries Remillard & McClintock 2006

32 X-ray QPO (P ~ 1 hr) from active galaxy RE J Gierlinski et al 2008, Nature

33 Some Ideas/Models of High-Freq QPOs Orbiting blobs (hot spots) in disks (Stella et al 1999; Schnittman & Bertschinger 2004) Acoustic modes in torus (Rezzolla el al 2003; Blaes et al. 2007) Nonlinear resonances of some kind (Abramowicz & Kluzniak, Rebusco) Diskoseismology in relativistic disks (Kato, Wagoner etc) Diskoseismic modes driven by Accretion-Ejection/Rossby wave Instabilities in magnetized disks (Tagger & Pellat 1999; Tagger & Varniere 2006 etc)

34 Diskoseismic Modes in Black-Hole Accretion Disks Inertial-Acoustic Modes (P-Modes) = What I have been discussing so far Inertial-Gravity Modes (G-Modes) Corrugation modes (C-Modes)

35 P-Modes (Inertial-acoustic modes) Dispersion relation (away from corotation):

36 High-Freq. QPOs from Overstable P-Modes Low-order p-modes trapped between inner boundary and ILR provides a possible explanation for HFQPOs Overstable due to corotation resonance (vortensity gradient and GR plays important role) Robust in the presence of disk turbulence (Arras et al. 2004; Reynolds & Miller 2008; Fu & Lai 2008) Enhanced instability (accretion-ejection) with strong B field (Tagger & Pallet 1999; Tagger & Varniere 2006)

37 G-Modes (Inertial-Gravity Modes) (studied extensively by Kato, Wagoner, etc) Dispersion relation: Can propagate only between ILR and OLR

38 G-Modes (Inertial-Gravity Modes) This is too high (for the measured BH Mass) Damping at Corotation (Kato 2003; Li, Goodman & Narayan 2003) In addition, G-modes can be easily destroyed by (subthermal) B field (Fu & Lai 2008)

39 C-Modes Dispersion relation: Trapped between inner inner edge and IVR (inner-vertical resonance) Damped due to wave tunneling and absoption at corotation.

40 Global instabilities/modes in accretion disks Super-reflection Role of corotation resonance Trapped p-modes: overstable due to wave absorption at corotation GR effects QPOs in black-hole X-ray binaries Overstable p-modes are promising Other modes (g- and c-modes) have problems Many unsolved issues Role of MHD turbulence Summary How disk oscillation manifests observationally Why HFQPOs only observed in very high states, etc.

41 Merci Beaucoup!