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Theoretical Calculations of the Inner Disk’s Luminosity

Theoretical Calculations of the Inner Disk’s Luminosity. Scott C. Noble, Julian H. Krolik (JHU) (John F. Hawley, Charles F. Gammie) 37 th COSPAR 2008, E17 July 16 th , 2008. GR model of radiatively efficient disks F(r,a)  T(r,a) and R in Observations  M BH , a BH. W r f. F.

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Theoretical Calculations of the Inner Disk’s Luminosity

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  1. Theoretical Calculations of the Inner Disk’s Luminosity Scott C. Noble, Julian H. Krolik (JHU) (John F. Hawley, Charles F. Gammie) 37th COSPAR 2008, E17 July 16th, 2008

  2. GR model of radiatively efficient disks F(r,a)  T(r,a) and Rin Observations  MBH, aBH Wrf F Steady-State Model:Novikov & Thorne (1973)

  3. Assumptions: Stationary gravity Equatorial Keplerian Flow Thin, cold disks Tilted disks? Time-independent Prompt, local dissipation of stress to heat Conservation of M, E, L Zero Stress at ISCO Magnetic fields? Need dynamic simulations! Wrf F Steady-State Model:Novikov & Thorne (1973) For steady-state model context: Shafee, Narayan, McClintock (2008)

  4. De Villiers, Hawley, Hirose, Krolik (2003-2006) MRI develops from weak initial field. Significant field within ISCO up to the horizon Beckwith, Hawley, Krolik (2008) Rad. Flux ~ Stress Uncontrolled loss of dissipated energy Previous Work Krolik, Hawley, Hirose (2005)

  5. HARM: Gammie, McKinney, Toth (2003) Axisymmetric (2D) Total energy conserving Modern Shock Capturing techniques (greater accuracy) Improvements: 3D More accurate (higher effective resolution) Stable low density flows Our Method: Simulations

  6. Improvements: 3D More accurate (higher effective resolution) Stable low density flows Cooling function: Control energy loss rate Parameterized by H/R tcool ~ torb Only cool when T > Ttarget Passive radiation Radiative flux is stored for self-consistent post-simulation radiative transfer calculation Our Method: Simulations H/R ~ 0.1 aBH = 0.9

  7. Full GR radiative transfer GR geodesic integration Doppler shifts Gravitational redshift Relativistic beaming Uses simulation’s fluid vel. Inclination angle survey Time domain survey Our Method: Radiative Transfer

  8. Disk Thermodynamics

  9. Disk Thickness dVH HARM3D

  10. Departure from Keplerian Motion HARM3D dVH

  11. Magnetic Stress dVH HARM3D NT

  12. Fluid Frame Flux

  13. Observer Frame Luminosity: Angle/Time Average HARM3D NT

  14. Observer Frame Luminosity: Angle/Time Average HARM3D NT

  15. Observer Frame Luminosity: Angle/Time Average HARM3D Assume NT profile for r > 12M . NT DL = 4% L

  16. Observer Frame Luminosity: Angle/Time Average HARM3D Assume NT profile for r > 12M . Assume no difference at large radius. NT DL = 9% L

  17. Summary & Conclusions • We now have the tools to self-consistently measure dL/dr from GRMHD disks • 3D Conservative GRMHD simulations • GR Radiative Transfer • Luminosity from within ISCO diminished by • Photon capture by the black hole • Gravitational redshift • tcool < tinflow • Possibly greater difference for aBH < 0.9 when ISCO is further out of the potential well.

  18. Future Work • Explore parameter space: • More spins • More H/R ‘s • More H(R) ‘s • Time variability analysis • Impossible with steady-state models

  19. EXTRA SLIDES

  20. Accretion Rate Steady State Period = 7000 – 15000M 1000 Steady State Region = Horizon – 12M

  21. Observer Frame Luminosity: Time Average NT HARM

  22. De Villiers, Hawley, Hirose, Krolik (2003-2006) MRI develops from weak initial field. Significant field within ISCO up to the horizon. Previous Work Hirose, Krolik, De Villiers, Hawley (2004)

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