Connecting Simulations with Observations of the

Galactic Center Black Hole

Jason DexterUniversity of Washington

With Eric Agol, Chris Fragile and Jon McKinney

Accretion

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• 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• Gamma ray bursts• Active Galactic Nuclei

Black Holes

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• a, M

• Innermost stable circular orbit

• Photon orbit

Astrophysical Black Holes

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• 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

The MRI

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• 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 outaccretion!

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

Toy Model of the MRI

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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

GRMHD• Advantages:

– Fully relativistic– Generate MRI, turbulence,

accretion from first principles

• Limitations:– Numerical & Difficult– Thermodynamics– Radiation– Spatial extent & Shape

• Compare to observations!CofC Colloquium 7

Gammie et al (2004)

Galactic Center

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Sagittarius A*

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Jet or nonthermal electrons far from BH

Thermal electrons at BH

Simultaneous IR/x-ray flares close to BH?

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Sgr A* VLBI

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• Largest angular size of any BH– Microarcseconds; baby penguin on moon.

• Very long baseline interferometry– High resolution: ~λ/D– Scattering: ~λ2

– Interferometry Fourier transforms

Millimeter Sgr A*

• Precision black hole astrophysics

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Doeleman et al (2008)

Gaussian FWHM ~4 Rs!

Black Hole Shadow

• Signature of event horizon• Sensitive to details of accretion flow

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

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GRMHD Models of Sgr A*

• mm Sgr A* is an excellent application of GRMHD!– Geometrically thick– Insignificant cooling(?) (L/Ledd ~ 10-

9)– Thermal electrons near BH

• Not perfect…– Collisionless (mfp = 104 Rs)

– ElectronsCofC Colloquium 13

Moscibrodzka et al (2009)

Ray Tracing

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• 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.

• IntensitiesImage, many frequenciesspectrum, many timeslight curve

Schnittman et al (2006)

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 Mtor, i, ξ, tobs

• Single temperature

UIUC CTA Seminar 15

GRMHD Fits to VLBI Data

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Dexter, Agol & Fragile (2009); Doeleman et al (2008)i=10 degrees i=70 degrees

10,000 km

100 μas

Improved ModelingDexter 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 Ti/Te; Goldston

et al 2005, Moscibrodzka et al 2009)• Joint fits to spectral, VLBI data over grid in Mtor, i, a,

Ti/Te

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Parameter Estimates• i = 50 degrees

• Te /1010 K = 5.4±3.0

• ξ = -23 degrees

• dM/dt = 5 x 10-9 Msun yr-1

• All to 90% confidence

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+35-15

+97-22

Inclination

Electron Temperature

Sky Orientation

Accretion Rate+15-2

Comparison to RIAF Values

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Broderick et al (2009)

Inclination Sky Orientation

Millimeter Flares• Models

reproduce observed flare duration, amplitude, frequency

• Stronger variability at higher frequency

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Solid – 230 GHz Dotted – 690 GHz

Comparison to Observed Flares

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

Shadow of Sgr A*

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Shadow may be detected on chile-lmt, smto-chile baselines; otherwise need south pole.

Crescents

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Constraining Models

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• 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 GHz 345 GHz

Tilted Disks

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• No reason to expect Sgr A* isn’t tilted• Best fit images are still crescents• Shadow still visible

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.

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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)

M87

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New mass estimate BH angular size ~4/5 of Sgr A*! (Gebhardt & Thomas 2009)

Interferometry

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Log-Normal Ring Models

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Exciting Observations of Accreting Black Holes

• X-ray binaries– State transitions– QPOs– Iron lines

• AGN– QPO(?)– Microlensing– Multiwavelength

surveysCofC Colloquium 31L / LEdd

SWIFT J1247

LMC X-3: 1983 – 2009

Steiner et al. 2010

Morgan et al (2010)

Fairall-9

Schmoll et al (2009)

Sagittarius A*

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Dodds-Eden et al (2009)

Yuan et al (2003)

Exciting Observations of Accreting Black Holes

• X-ray binaries– State transitions– QPOs– Iron lines

• AGN– QPO(?)– Microlensing– Multiwavelength

surveysCofC Colloquium 33L / LEdd

MCG-6-30-15 Miniutti et al 2007

Fender et al (2004)Middleton et al (2010)

Finite Speed of Light

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Toy emissivity, i=50 degrees 690 GHz, i=50 degrees

Finite Speed of Light

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• Emission dominated by narrow range in observer time

• Time delays are 10-15% effect on light curves

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 Mtor, i, ξ, tobs

• Unpolarized; single temperature

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Light Curves

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Face-on Fits

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• Excellent fits to 1.3mm VLBI at all inclinations with 90h, Ti=Te (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

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!

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Modeling

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• Sample limited by existing 3D simulations

• Misleading p(a)– For low spin, need

hotter accretion flow

Millimeter Flares

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• Strong correlation with accretion rate variability

• Approximate emissivity:– Jν ~ nBα, α ≈ 1-2.

– Isothermal emission region, ν/νc ≈ 10.

– Not heating from magnetic reconnection

Caveats

• Limited sample

• Constant Ti/Te

• Unpolarized millimeter emission

• Aligned disk/holeCofC Colloquium 42