1. From the Event Horizon to Infinity: Connecting Simulations with Observations of Accreting Black Holes Jason Dexter 8/27/2009

2. General Exam 8/27/20092/30 Accretion Material falling onto a central object Gravitational binding energy  radiation Any angular momentum  disk, spin+fields  jets It’s everywhere: –Stars Planetary, debris disks –Compact Objects (Super)novae X-ray bursts AGN, microquasars

3. Black Holes a, M Innermost stable circular orbit Photon orbit General Exam 8/27/20093/30

4. General Exam 8/27/20094/30 Astrophysical Black Holes Types: –Stellar mass (10 0 -10 1 M sun ) –Supermassive (10 6 -10 9 M sun ) –IMBH? (10 3 -10 6 M sun ) No hard surface –Energy lost to black hole –Inner accretion flow probes strong field GR Astronomy↔Physics Non-accreting BH

5. Accretion Power General Exam 8/27/20095/30 M87 Jet (HST) Black, but brightest persistent objects in universe Ultrarelativistic jets Black hole, galaxy evolution AGN feedback

6. General Exam 8/27/20096/30 Accretion Disk Theory Thin Disk Accretion (‘standard’, ‘alpha’) –Shakura & Sunyaev (1973), Novikov & Thorne (1973) –Cold & Bright (10 7 K, 10 5 L sun ) –AGN, “soft state” x-ray binaries Advection Dominated Accretion (‘ADAF’,’RIAF’) –Ichimaru (1977), Narayan & Yi (1995), Yuan et al (2003) –Hot & Thick (10 10 K) –Sgr A*, Low luminosity AGN, quiescent x- ray binaries Narayan & Quataert (2005)

7. General Exam 8/27/20097/30 The MRI How does matter lose angular momentum? Magnetized fluid with Keplarian rotation is unstable: “magnetorotational instability” –Velikhov (1959), Chandrasekhar (1961), Balbus & Hawley (1991) Not viscosity, but transports angular momentum out  accretion! Toy model -- assume ideal MHD: –Field tied to fluid elements –Tension force along field lines, “spring”

8. General Exam 8/27/20098/30 Toy Model of the MRI 1.Radially separated fluid elements differentially rotate. 2.“Spring” stretches, slows down inner element and accelerates outer. 3.Inner element loses angular momentum and falls inward. Outer element moves outward. 4.Differential rotation is enhanced and process repeats.  Strong magnetic field growth, turbulence

9. General Exam 8/27/20099/30 GRMHD Simulations More physics –3D, global, fully relativistic –Produce MRI, turbulence, accretion Difficult computationally –Short run times –No radiation Need to compare to observations! De Villiers et al (2003)

10. General Exam 8/27/200910/30 Ray Tracing  Method for performing relativistic radiative transfer –Turn fluid variables in accretion flow into observed emission at infinity. –Radiative transfer equation  Path integral –Two parts : 1.Calculate light trajectories. 2.Solve radiative transfer equation along ray

11. General Exam 8/27/200911/30 Ray Tracing Assume light rays are geodesics. (ω >> ω p, ω c ) Observer “camera”  constants of motion Trace backwards to ensure that all rays used make it to observer simultaneously. Integrate along portions of rays intersecting flow. Intensities  Image, many frequencies  spectrum, many times  light curve Schnittman et al (2006)

12. General Exam 8/27/200912/30 New Geodesics Code Dexter & Agol (2009) : –New fast, accurate, analytic code to compute photon trajectories around spinning black holes. –Includes time, azimuth dependence. Ideal for GRMHD! Luke Barnes Master’s Thesis

13. General Exam 8/27/200913/30 Toy Ray Tracing Problems: Thin Disk Mapping of camera to equatorial plane Image of Novikov & Thorne BH Schnittman & Bertschinger (2004); Dexter & Agol (2009)

14. Toy Ray Tracing Problems: Black Hole Shadow General Exam 8/27/200914/30 Bardeen (1973); Dexter & Agol (2009)Falcke, Melia & Agol (2000)

15. Sagittarius A* General Exam 8/27/200915/30 Discovered as radio source by Balick & Brown (1974) Mass, distance from stellar orbits (4x10 6 M sun at 8 kpc) Extremely faint (10 2-3 L sun )

16. General Exam 8/27/200916/30 Sgr A* Best candidate for high-res VLBI imaging, but still tiny! (10 -10 rad) –High resolution: ~λ/D –Sub-mm: scattering~λ 2 Doeleman et al, Nature, 2008: –Detections of Sgr A* at 1.3mm using an Arizona-Hawaii baseline. –Gaussian: size ~ 4 R s

17. VLBI fits from a RIAF model General Exam 8/27/200917/30 Broderick et al (2008)

18. Emission from GRMHD Units –Black hole mass sets length, time scales –Mass scale independent: free parameter scaled to produce observed flux and set accretion rate Thermal synchrotron emission, absorption –Electron temperature? General Exam 8/27/200918/30 Yuan et al (2003)

19. VLBI fits from GRMHD General Exam 8/27/200919/30 Dexter, Agol & Fragile (2009); Doeleman et al (2008) Images and visibilities of a=0.9 simulation from Fragile et al (2007) i=10 degreesi=70 degrees  10,000 km   100 μas 

20. Accretion Rate Constraint General Exam 8/27/200920/30 From VLBI measurements alone Independent of, consistent with constraints from polarimetry, spectral fitting Strong spin, T e dependence?

21. Light Curves General Exam 8/27/200921/30

22. Millimeter Flares General Exam 8/27/200922/30 Eckart et al (2008)Marrone et al (2008)

23. Sgr A* Summary First time-dependent synchrotron images, light curves from 3D GRMHD Excellent fits at all inclinations –If Sgr A* is face-on, may soon detect black hole shadow New (model-dependent) method to constrain accretion rate Magnetic turbulence can produce observed mm flares without magnetic reconnection General Exam 8/27/200923/30

24. Limitations and Future Work Non-conservative simulation Equal ion/electron temperatures –T e (r) agrees with RIAF Single spin, wavelength –Spin dependence of accretion rate constraint –Black hole mass constraint? Polarization General Exam 8/27/200924/30

25. Event Horizon Telescope General Exam 8/27/200925/18 UV coverage (Phase I: black) From Shep Doeleman’s Decadal Survey Report on the EHT Doeleman et al (2009)

26. General Exam 8/27/200926/30 Tilted Disks “Tilted” GRMHD: Black hole spin axis not aligned with torus axis. Solid body precession Standing shocks, plunging streams. Fragile et al (2007), Fragile & Blaes (2008)

27. Tilted Disk Sgr A* Images Low spin  Higher accretion rate to match observed flux  Optically thick flows Tilted disks look funny –Need observational signatures! General Exam 8/27/200927/30 a=0.3, i=50 degreesa=0.7, i=0 degreesa=0.9, i=70 degrees

28. Inner Edge of Tilted Disks Attempts to extract spin use thin disk spectra to locate r in, r in  a Toy model: emissivity=density 2, cut out fluid inside some radius General Exam 8/27/200928/30

29. Summary Ray tracing important for connecting state of the art simulations to observations! New analytic geodesics code (Dexter & Agol 2009) –Fast, accurate, public First synchrotron light curves, VLBI fits from GRMHD (Dexter, Agol & Fragile 2009) –May be on verge of directly observing “shadow” –Simulated flares agree with observations Inner edge of tilted disks –May bias towards low spins General Exam 8/27/200929/30

30. General Exam 8/27/200930/30 The Beautiful Future Sgr A* –Expand VLBI analysis –Incorporate spectral constraints Tilted Disks –Inner edge as a function of spin –QPOs? Other systems –M87! –X-ray binaries, AGN McKinney & Blandford (2009)