From the Event Horizon to Infinity:

Connecting Simulations with Observations of Accreting Black Holes

Jason Dexter

8/27/2009

General Exam 8/27/2009 2/30

Accretion

• Material falling onto a central object• Gravitational binding energyradiation• Any angular momentumdisk, spin+fieldsjets• It’s everywhere:

– Stars• Planetary, debris disks

– Compact Objects• (Super)novae• X-ray bursts• AGN, microquasars

Black Holes

• a, M

• Innermost stable circular orbit

• Photon orbit

General Exam 8/27/2009 3/30

General Exam 8/27/2009 4/30

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

Accretion Power

General Exam 8/27/2009 5/30

M87 Jet (HST)

• Black, but brightest persistent objects in universe

• Ultrarelativistic jets

• Black hole, galaxy evolution

• AGN feedback

General Exam 8/27/2009 6/30

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)

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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 outaccretion!

• Toy model -- assume ideal MHD:– Field tied to fluid elements– Tension force along field lines, “spring”

General Exam 8/27/2009 8/30

Toy Model of the MRI1. 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

General Exam 8/27/2009 9/30

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)

General Exam 8/27/2009 10/30

Ray Tracing

• Method for performing relativistic radiative transfer– Turn fluid variables in accretion flow into observed emission at infinity.

– Radiative transfer equationPath integral– Two parts:

1. Calculate light trajectories.

2. Solve radiative transfer equation along ray

General Exam 8/27/2009 11/30

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.

• IntensitiesImage, many frequenciesspectrum, many timeslight curve

Schnittman et al (2006)

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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 13/30

Toy Ray Tracing Problems: Thin Disk

• Mapping of camera to equatorial plane

• Image of Novikov & Thorne BH

Schnittman & Bertschinger (2004); Dexter & Agol (2009)

Toy Ray Tracing Problems:Black Hole Shadow

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Bardeen (1973); Dexter & Agol (2009) Falcke, Melia & Agol (2000)

Sagittarius A*

General Exam 8/27/2009 15/30

• 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 16/30

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

VLBI fits from a RIAF model

General Exam 8/27/2009 17/30

Broderick et al (2008)

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 8/27/2009 18/30

Yuan et al (2003)

VLBI fits from GRMHD

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Dexter, Agol & Fragile (2009); Doeleman et al (2008)

Images and visibilities of a=0.9 simulation from Fragile et al (2007)

i=10 degrees i=70 degrees

10,000 km

100 μas

Accretion Rate Constraint

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• From VLBI measurements alone

•Independent of, consistent with constraints from polarimetry, spectral fitting

• Strong spin, Te dependence?

Light Curves

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Millimeter Flares

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Eckart et al (2008)Marrone et al (2008)

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 23/30

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

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Event Horizon Telescope

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UV coverage (Phase I: black)

From Shep Doeleman’s Decadal Survey Report on the EHT

Doeleman et al (2009)

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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)

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 8/27/2009 27/30

a=0.3, i=50 degrees a=0.7, i=0 degrees a=0.9, i=70 degrees

Inner Edge of Tilted Disks• Attempts to extract spin use thin disk spectra to

locate rin, rina

• Toy model: emissivity=density2, cut out fluid inside some radius

General Exam 8/27/2009 28/30

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 29/30

General Exam 8/27/2009 30/30

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)