1. Connecting Simulations with Observations of the Galactic Center Black Hole Jason Dexter University of Washington With Eric Agol, Chris Fragile and Jon McKinney

2. Accretion CofC Colloquium2 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 Gamma ray bursts Active Galactic Nuclei

3. Black Holes CofC Colloquium3 a, M Innermost stable circular orbit Photon orbit

4. Astrophysical Black Holes CofC Colloquium4 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. The MRI CofC Colloquium5 How does matter lose angular momentum? Magnetized fluid with Keplerian rotation is unstable: “magnetorotational instability” –Velikhov (1959), Chandrasekhar (1961), Balbus & Hawley (1991) Transports angular momentum out  accretion! Toy model based on ideal MHD –Field tied to fluid elements –Tension force along field lines, “spring”

6. Toy Model of the MRI CofC Colloquium6 1.Radially separated fluid elements differentially rotate. 2.“Spring” 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, saturated growth, turbulence

7. GRMHD Advantages: – Fully relativistic – Generate MRI, turbulence, accretion from first principles Limitations: – Numerical & Difficult – Thermodynamics – Radiation – Spatial extent & Shape Compare to observations! CofC Colloquium7 Gammie et al (2004)

8. Galactic Center CofC Colloquium8

9. Sagittarius A* CofC Colloquium9 Figure: Moscibrodzka et al. (2009) Jet or nonthermal electrons far from BH Thermal electrons at BH Simultaneous IR/x-ray flares close to BH? no data available Charles Gammie

10. Sgr A* VLBI CofC Colloquium10 Largest angular size of any BH –Microarcseconds; baby penguin on moon. Very long baseline interferometry –High resolution: ~λ/D –Scattering: ~λ 2 –Interferometry  Fourier transforms

11. Millimeter Sgr A* Precision black hole astrophysics 11CofC Colloquium Doeleman et al (2008) Gaussian FWHM ~4 R s !

12. Black Hole Shadow Signature of event horizon Sensitive to details of accretion flow Bardeen (1973); Dexter & Agol (2009)Falcke, Melia & Agol (2000) 12CofC Colloquium

13. GRMHD Models of Sgr A* mm Sgr A* is an excellent application of GRMHD! – Geometrically thick – Insignificant cooling(?) (L/L edd ~ 10 -9 ) – Thermal electrons near BH Not perfect… – Collisionless (mfp = 10 4 R s ) – Electrons CofC Colloquium13 Moscibrodzka et al (2009)

14. Ray Tracing CofC Colloquium14 Method for performing relativistic radiative transfer Fluid variables  radiation at infinity Calculate light rays assuming geodesics. (no refraction) Observer “camera”  constants of motion Trace backwards and integrate along portions of rays intersecting flow. Intensities  Image, many frequencies  spectrum, many times  light curve  Schnittman et al (2006)

15. Modeling Dexter, Agol & Fragile (2009): Geodesics from public, analytic code geokerr (Dexter & Agol 2009) Time-dependent, relativistic radiative transfer 3D simulation from Fragile et al (2007) Fit images to 1.3mm (230 GHz) VLBI data over grid in M tor, i, ξ, t obs Single temperature UIUC CTA Seminar15

16. GRMHD Fits to VLBI Data CofC Colloquium16 Dexter, Agol & Fragile (2009); Doeleman et al (2008) i=10 degreesi=70 degrees  10,000 km   100 μas 

17. Improved Modeling Dexter et al (2010): Fit to millimeter flux at.4-1.3mm (Marrone 2006) Add simulations from McKinney & Blandford (2009); Fragile et al (2009) Two-temperature models (parameter T i /T e ; Goldston et al 2005, Moscibrodzka et al 2009) Joint fits to spectral, VLBI data over grid in M tor, i, a, T i /T e CofC Colloquium17

18. Parameter Estimates i = 50 degrees T e /10 10 K = 5.4±3.0 ξ = -23 degrees dM/dt = 5 x 10 -9 M sun yr -1 All to 90% confidence CofC Colloquium18 +35 -15 +97 -22 Inclination Electron Temperature Sky Orientation Accretion Rate +15 -2

19. Comparison to RIAF Values CofC Colloquium19 Broderick et al (2009) Inclination Sky Orientation

20. Millimeter Flares Models reproduce observed flare duration, amplitude, frequency Stronger variability at higher frequency CofC Colloquium20 Solid – 230 GHz Dotted – 690 GHz

21. Comparison to Observed Flares CofC Colloquium21 Eckart et al (2008)Marrone et al (2008)

22. Shadow of Sgr A* CofC Colloquium22 Shadow may be detected on chile- lmt, smto-chile baselines; otherwise need south pole.

23. Crescents CofC Colloquium23

24. Constraining Models CofC Colloquium24 Similar standard deviation to Fish et al (2009) Chile/Mexico are best bets for further constraining models Simultaneous measurement of total flux at 345 GHz would provide a significant constraint Fish et al (2009)Dexter et al (2010) 230 GHz345 GHz

25. Tilted Disks CofC Colloquium25 No reason to expect Sgr A* isn’t tilted Best fit images are still crescents Shadow still visible

26. Conclusions Fit 3D GRMHD images of Sgr A* to mm observations Estimates of inclination, sky orientation agree with RIAF fits (Broderick et al 2009) Electron temperature well constrained Consistent, but independent accretion rate constraint Reproduce observed mm flares LMT-Chile next best chance for observing shadow Future: Tilted disks, M87, polarization. CofC Colloquium26

27. Event Horizon Telescope CofC Colloquium27 UV coverage (Phase I: black) From Shep Doeleman’s Decadal Survey Report on the EHT Doeleman et al (2009)

28. M87 CofC Colloquium28 New mass estimate  BH angular size ~4/5 of Sgr A*! (Gebhardt & Thomas 2009)

29. Interferometry CofC Colloquium29 Morales & Wythe (2009)

30. Log-Normal Ring Models CofC Colloquium30

31. Exciting Observations of Accreting Black Holes X-ray binaries – State transitions – QPOs – Iron lines AGN – QPO(?) – Microlensing – Multiwavelength surveys CofC Colloquium31 L / L Edd SWIFT J1247 LMC X-3: 1983 – 2009 Steiner et al. 2010 Morgan et al (2010) Fairall-9 Schmoll et al (2009)

32. Sagittarius A* CofC Colloquium32 Dodds-Eden et al (2009) Yuan et al (2003)

33. Exciting Observations of Accreting Black Holes X-ray binaries – State transitions – QPOs – Iron lines AGN – QPO(?) – Microlensing – Multiwavelength surveys CofC Colloquium33 L / L Edd MCG-6-30-15 Miniutti et al 2007 Fender et al (2004) Middleton et al (2010)

34. Finite Speed of Light CofC Colloquium34 Toy emissivity, i=50 degrees690 GHz, i=50 degrees

35. Finite Speed of Light CofC Colloquium35 Emission dominated by narrow range in observer time Time delays are 10-15% effect on light curves

36. Modeling Dexter, Agol & Fragile (2009): Geodesics from public, analytic code geokerr (Dexter & Agol 2009) Time-dependent, relativistic radiative transfer 3D simulation from Fragile et al (2007) Need 3D for accurate MRI, variability a=0.9, doesn’t conserve energy! Fit images to 1.3mm (230 GHz) VLBI data over grid in M tor, i, ξ, t obs Unpolarized; single temperature CofC Colloquium36

37. Light Curves CofC Colloquium37

38. Face-on Fits CofC Colloquium38 Excellent fits to 1.3mm VLBI at all inclinations with 90h, T i =T e (Dexter, Agol and Fragile 2009) Low inclinations now ruled out by: – Spectral index constraint (Moscibrodzka et al 2009) – Scarcity of VLBI fits in other models

39. Sgr A* Models Quiescent: – ADAF/RIAF or jet: steady state, no MRI, non-rel Toy flare models: -Hotspots -Expanding blobs -Density perturbations But we have a more physical theory! CofC Colloquium39

40. Modeling CofC Colloquium40 Sample limited by existing 3D simulations Misleading p(a) – For low spin, need hotter accretion flow

41. Millimeter Flares CofC Colloquium41 Strong correlation with accretion rate variability Approximate emissivity: – J ν ~ nB α, α ≈ 1-2. – Isothermal emission region, ν/ν c ≈ 10. – Not heating from magnetic reconnection

42. Caveats Limited sample Constant T i /T e Unpolarized millimeter emission Aligned disk/hole CofC Colloquium42