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Connecting Simulations to Observations of Accreting Black Holes: From Event Horizon to Infinity

This paper explores the intricate relationship between simulations and observations of accreting black holes, emphasizing the role of accretion processes in various astrophysical phenomena. It delves into the fundamentals of accretion disk theory, including thin disk accretion and magnetorotational instability (MRI), while also discussing the implications of these processes for understanding black hole evolution. By leveraging advanced simulations and ray tracing methods, the study aims to enhance our capability in predicting radiation signatures and interpreting observational data, particularly from notable sources such as Sagittarius A*.

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Connecting Simulations to Observations of Accreting Black Holes: From Event Horizon to Infinity

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

  2. 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 General Exam 8/27/2009

  3. Black Holes • a, M • Innermost stable circular orbit • Photon orbit General Exam 8/27/2009

  4. Astrophysical Black Holes • Types: • Stellar mass (100-101 Msun) • Supermassive (106-109 Msun) • IMBH? (103-106 Msun) • No hard surface • Energy lost to black hole • Inner accretion flow probes strong field GR • Astronomy↔Physics Non-accreting BH General Exam 8/27/2009

  5. Accretion Power • Black, but brightest persistent objects in universe • Ultrarelativistic jets • Black hole, galaxy evolution • AGN feedback M87 Jet (HST) General Exam 8/27/2009

  6. Accretion Disk Theory • Thin Disk Accretion (‘standard’, ‘alpha’) • Shakura & Sunyaev (1973), Novikov & Thorne (1973) • Cold & Bright (107 K, 105 Lsun) • AGN, “soft state” x-ray binaries • Advection Dominated Accretion (‘ADAF’,’RIAF’) • Ichimaru (1977), Narayan & Yi (1995), Yuan et al (2003) • Hot & Thick (1010 K) • Sgr A*, Low luminosity AGN, quiescent x-ray binaries Narayan & Quataert (2005) General Exam 8/27/2009

  7. 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” General Exam 8/27/2009

  8. Toy Model of the MRI • Radially separated fluid elements differentially rotate. • “Spring” stretches, slows down inner element and accelerates outer. • Inner element loses angular momentum and falls inward. Outer element moves outward. • Differential rotation is enhanced and process repeats. Strong magnetic field growth, turbulence General Exam 8/27/2009

  9. 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) General Exam 8/27/2009

  10. 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: • Calculate light trajectories. • Solve radiative transfer equation along ray  General Exam 8/27/2009

  11. Ray Tracing • Assume light rays are geodesics. (ω >> ωp, ωc) • 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) General Exam 8/27/2009

  12. 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 General Exam 8/27/2009

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

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

  15. Sagittarius A* • Discovered as radio source by Balick & Brown (1974) • Mass, distance from stellar orbits (4x106 Msun at 8 kpc) • Extremely faint (102-3 Lsun) General Exam 8/27/2009

  16. Sgr A* • Best candidate for high-res VLBI imaging, but still tiny! (10-10 rad) • High resolution: ~λ/D • Sub-mm: scattering~λ2 • Doeleman et al, Nature, 2008: • Detections of Sgr A* at 1.3mm using an Arizona-Hawaii baseline. • Gaussian: size ~ 4 Rs General Exam 8/27/2009

  17. VLBI fits from a RIAF model Broderick et al (2008) General Exam 8/27/2009

  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? Yuan et al (2003) General Exam 8/27/2009

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

  20. Accretion Rate Constraint • From VLBI measurements alone • Independent of, consistent with constraints from polarimetry, spectral fitting • Strong spin, Te dependence? General Exam 8/27/2009

  21. Light Curves General Exam 8/27/2009

  22. Millimeter Flares Marrone et al (2008) Eckart et al (2008) General Exam 8/27/2009

  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 8/27/2009

  24. Limitations and Future Work • Non-conservative simulation • Equal ion/electron temperatures • Te(r) agrees with RIAF • Single spin, wavelength • Spin dependence of accretion rate constraint • Black hole mass constraint? • Polarization General Exam 8/27/2009

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

  26. 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) General Exam 8/27/2009

  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! a=0.3, i=50 degrees a=0.7, i=0 degrees a=0.9, i=70 degrees General Exam 8/27/2009

  28. Inner Edge of Tilted Disks • Attempts to extract spin use thin disk spectra to locate rin, rina • Toy model: emissivity=density2, cut out fluid inside some radius General Exam 8/27/2009

  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 8/27/2009

  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) General Exam 8/27/2009

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