What Can We Learn From Simulations of Tilted Black Hole Accretion Disks?

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1 What Can We Learn From Simulations of Tilted Black Hole? Dr. P. Chris Fragile College of Charleston, SC Collaborators: Omer Blaes (UCSB), Ken Henisey (UCSB), Bárbara Ferreira (Cambridge), Chris Done (Durham), Adam Ingram (Durham), Jason Dexter (U. of Washington), Peter Anninos (LLNL), Jay Salmonson (LLNL) Students: Christopher Lindner (UT-Austin), Will DuPre (CofC), Tim Monahan (CofC), Sam Cook (CofC)

2 Model 1i M0.2 Mod Tilted Black Hole Astrophysical motivation Active Galactic Nuclei (AGN) Post merger Black hole X-ray Binaries (BHXRB s) Asymmetric supernova kick Model 1i M0.2 Model 1i M0.9 (Fragos et al. 2010)

3 Simulations of tilted disks Initialization similar to model KDP from DeVilliers, Hawley, & Krolik (2003) Initial tilt (15 ) added Γ =5/3 r Pmax = 25r G r in = 15r G a =0.9 β 0 = 15

4 Epicyclic motion induced by tilt 915h 90h Fragile & Blaes (2008)

5 Epicyclic motion induced by tilt 915h 90h pericenter apocenter apocenter pericenter Fragile & Blaes (2008)

6 Take-away points 1. Global radial epicyclic motion 180 out of phase across the midplane

7 Standing shocks standing shock plunging stream evacuated lobe plunging stream evacuated lobe standing shock (Fragile & Blaes 2008)

8 Eccentricity of tilted orbits In terms of twisting coordinates e = ξ 6M RΨ= ξ 6M R (β cos γ) R (R, ψ, ξ) orbits are more eccentric at smaller radii (Fragile & Blaes 2008)

9 Crowding of orbits near apocenter low eccentricity at large radius high eccentricity at small radius crowding of orbits

10 Schematic diagram of results

11 Take-away points 1. Global radial epicyclic motion 180 out of phase across the midplane 2. Standing shocks near apocenters of orbits One above and one below midplane Aligned with line-of-nodes

12 Inner radius of tilted disks Surface density H ISCO r/m

13 Inner radius of tilted disks Surface density Tilted disk truncates significantly further out 90H 915H ISCO r/m

14 Determining spin of a black hole If rin can be measured continuum fitting Fe α line If rin = rms 8 } can get a directly r/m Schwarzschild r ms Maximal Kerr a/m

15 Inner radius of tilted disks Simulation a/m Tilt Angle Grid 0H a 0... Spherical-polar 315H b 50H a 515H-S a 515H-C a 715H b 90H c 915H c Simulation Parameters a Fragile, Lindner, Anninos & Salmonson, 2009, ApJ, 691, 428 b Fragile, 2009, ApJ, 706, L246 c Fragile, Blaes, Anninos & Salmonson, 2007, ApJ, 668, 417 Spherical-polar Cubed-sphere Spherical-polar Cubed-sphere Spherical-polar Spherical-polar Spherical-polar

16 Inner radius of tilted disks Σ(r in )=Σ max /3e 8 r/m r ms rin nearly independent of spin for tilted disks untilted tilted β 0 = a/m (Fragile 2009)

17 8 Inner radius of tilted disks r/m 5 4 r/m Surface density 3 2 Inflow time a/m a/m r/m 5 4 r/m Turbulent velocity 2 Magnetic stress a/m a/m (Fragile 2009)

18 Take-away points 1. Global radial epicyclic motion 180 out of phase across the midplane 2. Standing shocks near apocenters of orbits One above and one below midplane Aligned with line-of-nodes 3. rin nearly independent of spin for tilted disks at least for simulated disks with H/r ~ 0.2 and β0 = 15

19 Disk precession Torque of BH causes disk to precess After initial twisting phase, disk precesses as solid body

20 Low Frequency QPOs XTE J QPOs

21 LFQPOs from tilted disks ν prec = (5 2ζ) π(1 + 2ζ) r 5/2 ζ o a 1 (ri /r o ) 1/2+ζ r 1/2+ζ i 1 (ri /r o ) 5/2 ζ c R g (Ingram, Done, & Fragile 2009)

22 LFQPOs from tilted disks ν prec = (5 2ζ) π(1 + 2ζ) r 5/2 ζ o a 1 (ri /r o ) 1/2+ζ r 1/2+ζ i 1 (ri /r o ) 5/2 ζ c R g (Ingram, Done, & Fragile 2009)

23 LFQPOs from tilted disks (Ingram, Done, & Fragile 2009) How is the hot, thick inner disk coupled to the cold, thin outer disk? Can the inner disk precess freely as assumed in our naive picture?

24 Take-away points 1. Global radial epicyclic motion 180 out of phase across the midplane 2. Standing shocks near apocenters of orbits One above and one below midplane Aligned with line-of-nodes 3. rin nearly independent of spin for tilted disks at least for simulated disks with H/r ~ 0.2 and β0 = precessing tilted disks provide a possible model for low-frequency QPOs give right frequency range for large range of black hole parameters

25 Standing shocks precess with disk (Fragile & Blaes 2008) Tilted Black Hole

26 Jet orientation What determines the orientation of a jet? angular momentum (spin) of BH (Blandford & Znajek, 1977; Koide et al., 2002) to BH symmetry plane

27 Jet orientation What determines the orientation of a jet? angular momentum (spin) of BH (Blandford & Znajek, 1977; Koide et al., 2002) to BH symmetry plane angular momentum or net magnetic flux of disk (Blandford & Payne, 1982; Lynden-Bell, 2006) to disk midplane precess with disk

28 Jet orientation What determines the orientation of a jet? angular momentum (spin) of BH (Blandford & Znajek, 1977; Koide et al., 2002) to BH symmetry plane angular momentum or net magnetic flux of disk (Blandford & Payne, 1982; Lynden-Bell, 2006) to disk midplane precess with disk properties of ambient medium????

29 Jet orientation McKinney & Gammie (2004) 0.5 P jet Ω 2 H a/m 0.36 H 0.4 ISCO!(c 3 /GM) jet power dominated by disk jet power dominated by BH a/m

30 Spherical-polar grid mathematical singularity at pole large variation in zone sizes small zones near pole prohibit reasonable timesteps

31 Cubed-sphere grid no singularities except at origin nearly uniform zone sizes

32 Acknowledgments Thank you to LOC and SOC NSF SCSGC & SC EPSCoR Dr. P. Chris Fragile