1. Radiative Models of Sagittarius A* and M87 from Relativistic MHD Simulations Jason Dexter 7/8/2011

2. Black Holes Final Exam2 a, M, (Q) Innermost stable circular orbit Circular photon orbit 7/16/2015

3. Accretion Final Exam3 Material falling onto a central object Gravitational binding energy  radiation Any angular momentum  disk, rotation+fields  jets It’s everywhere: –Stars Protostellar, debris disks –Compact Objects (Super)novae X-ray & γ-ray bursts Active Galactic Nuclei (AGN) X-ray Binaries 7/16/2015

4. Accreting Black Holes Power brightest objects in Universe (GRB, AGN) Center of every galaxy? Final Exam47/16/2015

5. Accreting Black Holes Final Exam5 Types: –Stellar mass (10 0-1 M sun ) –Supermassive (10 6-9 M sun ) –IMBH? (10 3-6 M sun ) No hard surface –Cold, bright, thin (‘thin disk’) or hot, thick, often faint (‘ADAF’ or ‘RIAF’) –Thin disk: AGN, ‘thermal’ state –ADAF: Sgr A*, M87, LLAGN, ‘quiescent’ –Inner accretion flow probes strong field GR 7/16/2015 Narayan & Quataert (2005)

6. Accretion Theory Time-steady, axisymmetric, vertically-averaged No accretion mechanism Predictive, qualitatively correct Final Exam6 Kriss et al. (1999))Steiner et al. (2010)Reynolds et al. (1996) 7/16/2015

7. Accretion Theory Final Exam7 Thin disk problems: – Thermal & inflow instabilities – UV Emission, Simultaneous variability, Microlensing Sizes ADAF  RIAF to explain linear polarization of Sgr A* (Agol 2000, Quataert & Gruzinov 2000) Dexter & Agol (2011) 7/16/2015

8. The MRI Final Exam8 How does matter lose angular momentum? Magnetized fluid with Keplerian rotation is unstable: “magnetorotational instability” –Velikhov (1959), Chandrasekhar (1961), Balbus & Hawley (1991) Nonlinear, saturates, drives magnetic turbulence Transports angular momentum out  accretion! Pro: physical accretion, con: numerical computation 7/16/2015

9. GRMHD Advantages: – Fully relativistic – Generate MRI, turbulence, accretion from first principles Limitations: – Numerical & Difficult – Thermodynamics – Radiation – Spatial extent & shape (thick!) Compare to observations! Final Exam9 Gammie et al. (2004) 7/16/2015

10. Tilted GRMHD Final Exam10 Black hole spin axis not aligned with torus axis. Thin: Alignment Thick: – Precession – Standing shocks, plunging streams. – Compare to observations! Fragile et al. (2007), Fragile & Blaes (2008) 7/16/2015 Bardeen & Petterson (1975), Fragile et al. (2000)

11. Radiative Transfer Connecting theory & observation requires photons Examples across astrophysics: – Numerical simulations of galaxy formation, supernovae, irradiated exoplanets Final Exam11  Governato et al. (2009) Kasen et al. (2009) 7/16/2015

12. Ray Tracing Final Exam12 Method for performing relativistic radiative transfer Fluid variables  radiation at infinity Calculate light rays assuming geodesics (no refraction) Trace backwards and integrate radiative transfer equation along portions of rays intersecting flow. Intensities  Image, many frequencies  spectrum, many times  light curve  Schnittman et al. (2006) 7/16/2015

13. Black Hole Shadow Signature of event horizon Sensitive to details of accretion flow Bardeen (1973); Dexter & Agol (2009)Falcke, Melia & Agol (2000) 13Final Exam7/16/2015

14. grtrans Relativistic radiative transfer via ray tracing To compute observables: – Photon trajectories ( geokerr, Dexter & Agol 2009) – Dynamical model (GRMHD) – Particle model (electrons) Convert code to physical units with M BH, dM/dt – Emission/absorption (unpol synchrotron) Flexible, applicable to non-BH problems Final Exam147/16/2015

15. Radiation Edge of Tilted Disks Inner edge usually associated with ISCO Independent of spin for 15 degree tilt! Final Exam15 Dexter & Fragile (2011) 7/16/2015

16. Inner Edge of Tilted Disks Non-axisymmetric standing shocks transport angular momentum, truncate disk Final Exam16 UntiltedTilted Angular momentum deficit increases with spin Top: Angular momentumBottom: Entropy 7/16/2015

17. Galactic Center Final Exam177/16/2015

18. Sagittarius A* Final Exam18 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 7/16/2015

19. Millimeter VLBI of Sgr A* Precision black hole astrophysics 19Final Exam Doeleman et al (2008) Gaussian FWHM ~4 R s ! 7/16/2015 Arizona— Hawaii baseline

20. GRMHD Models of Sgr A* mm Sgr A* is an excellent application of GRMHD! Particle: Maxwell with constant T i /T e, emission: synchrotron radiation 5 (4) simulations: Fragile et al. (2007, 2009); McKinney & Blandford (2009) mm images over grid in: dM/dt, i, a, T i /T e Joint fits to spectral (Marrone 2006), VLBI data (Doeleman et al. 2008, Fish et al. 2011) Final Exam20 Moscibrodzka et al. (2009) 7/16/2015

21. GRMHD Fits to VLBI Data Final Exam21 Dexter, Agol & Fragile (2009); Doeleman et al. (2008) i=10 degreesi=70 degrees  10,000 km   100 μas  7/16/2015

22. Parameter Estimates i = 60 degrees ξ = -70 degrees T e /10 10 K = 6 ± 2 dM/dt = 3 x 10 -9 M sun yr -1 All to 90% confidence Final Exam22 +15 -15 +86 -15 +7 Dexter et al. (2010) Sky Orientation Inclination Electron Temperature Accretion Rate All VLBI 2007 7/16/2015

23. Comparison to RIAF Values Final Exam23 Broderick et al. (2011) Inclination Sky Orientation All VLBI 2007 7/16/2015

24. Millimeter Flares Correlation with accretion rate Driven by magnetic turbulence Models reproduce observed mm flares IR/X-ray? Final Exam24 Solid – 230 GHz (1.3mm) Dotted – 690 GHz (0.4mm) 7/16/2015

25. Comparison to Observed Flares Final Exam25 Eckart et al. (2008)Marrone et al. (2008) 7/16/2015

26. Black Hole Shadow in Sgr A* Final Exam26 Shadow may be detected on Chile-Mexico baseline (in closure phase too) Shadow 230 GHz 345 GHz 7/16/2015

27. Crescents Final Exam27 Images: gravitational lensing & doppler beaming Ring, crescent, Gaussian Wide range of physical models 7/16/2015

28. Tilted Sgr A* Final Exam28 Nice picture, but no reason to expect Sgr A* isn’t tilted Unconstrained parameters Best fit images are still crescents Shadow still visible Shadow 7/16/2015

29. M87 1600 M Sgr A* at 2000 D Sgr A* Jet launching physics? Known viewing geometry? Final Exam29 7mm Junor et al. (1999) 2cm Kovalev et al. (2007) Hubble 7/16/2015

30. Modeling M87 mm-VLBI: Large mass, long timescales, northern sky, no scattering, direct image! Particle: disk/jet, emission: synchrotron – Magnetic jet, let u jet =ηB 2 – n(γ)=Aγ -p, γ > γ min – Inner radii only Final Exam30 McKinney & Blandford (2009) 7/16/2015

31. Fiducial Models Representative models: Disk/jet or jet Unlike previous models – Can’t have disk peak in radio – Can’t match radio at all! (similar to Sgr A*) Final Exam31 Broderick & Loeb ( 2009) 7/16/2015

32. Images & Visibilities Images are still crescents! Jets are smaller than disks Final Exam32 Disk Jet Total 230 GHz345 GHz 230 GHz 345 GHz 7/16/2015

33. mm-VLBI Predictions Predict Gaussian size 36-41 μas Shadow on Hawaii-Mexico or Mexico-Chile Final Exam33 Shadow 7/16/2015

34. Summary Connect GRMHD simulations with observations grtrans, geokerr (Dexter & Agol 2009) Radiation edge of thick disks independent of spin for 15 degree tilt (Dexter & Fragile 2011) Sgr A* (Dexter et al. 2009, 2010) – Excellent fits with GRMHD & images are crescents! – Estimates for viewing geometry and physical conditions – Reproduce observed mm flares – Mexico—Chile next best chance for observing shadow M87 – Disk/jet or jet models – Predict 36-41 μas size, shadow on Hawaii—Chile or Mexico—Chile – Robust results if geometry is correct Final Exam347/16/2015

35. Future Work Exciting times in BH astrophysics Detailed models – Add polarization, complete sim sample – Make grtrans public More speculative – Inhomogeneous disks & implications Branch out: explosive astrophysics Final Exam357/16/2015

36. Thanks! Eric Agol & committee – Especially reading committee! Chris Fragile, Omer Blaes & collaborators My family & Kalista Classmates Astronomy department Final Exam367/16/2015

37. Event Horizon Telescope Final Exam37 UV coverage (Phase I: black) From Shep Doeleman’s Decadal Survey Report on the EHT Doeleman et al (2009) 7/16/2015

38. Modeling M87 Five(!) free parameters for fixed viewing geometry Final Exam387/16/2015

39. Interferometry Final Exam39 Morales & Wythe (2009) 7/16/2015

40. Sgr A* VLBI Final Exam40 Largest angular size of any BH (w/ M87) –Microarcseconds; baby penguin on moon. Very long baseline interferometry –High resolution: ~λ/D –Scattering: ~λ 2 –Interferometry  Fourier transforms 7/16/2015

41. Log-Normal Ring Models Final Exam417/16/2015

42. Toy Model of the MRI Final Exam42 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 7/16/2015

43. Sagittarius A* Final Exam43 Dodds-Eden et al (2009) Yuan et al (2003) 7/16/2015

44. Constraining Models Final Exam44 Similar standard deviation to RIAF Chile/Mexico are best bets for further constraining models Significant constraint from simultaneous total flux at 345 GHz Nice picture! Fish et al (2009)Dexter et al (2010) 230 GHz345 GHz 7/16/2015

45. Exciting Observations of Accreting Black Holes X-ray binaries – State transitions – QPOs – Iron lines AGN – QPO(?) – Microlensing – Multiwavelength surveys Final Exam45 L / L Edd MCG-6-30-15 Miniutti et al 2007 Fender et al (2004) Middleton et al (2010) 7/16/2015

46. Exciting Observations of Accreting Black Holes X-ray binaries – State transitions – QPOs – Iron lines AGN – QPO(?) – Microlensing – Multiwavelength surveys Final Exam46 L / L Edd SWIFT J1247 LMC X-3: 1983 – 2009 Steiner et al. 2010 Morgan et al (2010) Fairall-9 Schmoll et al (2009) 7/16/2015

47. Finite Speed of Light Final Exam47 Toy emissivity, i=50 degrees690 GHz, i=50 degrees 7/16/2015

48. Finite Speed of Light Final Exam48 Emission dominated by narrow range in observer time Time delays are 10-15% effect on light curves 7/16/2015

49. Light Curves Final Exam497/16/2015

50. Face-on Fits Final Exam50 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 7/16/2015

51. 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! Final Exam517/16/2015

52. Modeling Final Exam52 Sample limited by existing 3D simulations Misleading p(a) – For low spin, need hotter accretion flow 7/16/2015

53. Millimeter Flares Final Exam53 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 7/16/2015

54. Caveats Limited sample Constant T i /T e Unpolarized millimeter emission Aligned disk/hole Final Exam547/16/2015

55. grtrans convergence Final Exam557/16/2015

56. grtrans convergence Final Exam56 Total flux to < 1% at 150x150 pixels Pixel convergence to < 5% for 200-400 points 300x300 150x150 7/16/2015