Connecting Simulations with Observations of the

Galactic Center Black Hole

Jason DexterUniversity of Washington

With Eric Agol, Chris Fragile and Jon McKinney

Exciting Observations of Accreting Black Holes

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

• AGN– QPO(?)– Microlensing– Multiwavelength

surveysUIUC CTA Seminar 2L / LEdd

MCG-6-30-15 Miniutti et al 2007

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

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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ata

avai

labl

e

no d

ata

avai

labl

eCharles Gammie

Sub-mm Sgr A*

• Precision black hole astrophysics• Need accurate emission models

5UIUC CTA Seminar

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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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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Global GRMHD

• Advantages:– Fully relativistic, 2D & 3D– Generate MRI, turbulence,

accretion

• Limitations:– Thermodynamics– Radiation– Spatial extent– Morphology

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Gammie et al (2004)

GRMHD Models of Sgr A*

• Sub-mm Sgr A* is an excellent application of GRMHD!– Thick accretion flow (ADAF/RIAF)– Insignificant cooling(?) (L/Ledd ~

10-9)– Thermal electrons near BH

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

– ElectronsUIUC CTA Seminar 9

Moscibrodzka et al (2009)

Ray Tracing

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• Method for performing relativistic radiative transfer

• Fluid variables emission at infinity

• Calculate light rays assuming geodesics. (ω >> ωp, ωc)

• 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)• 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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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

Light Curves

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Comparison to Observed Flares

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

Improved ModelingDexter et al (2010; submitted):• Sub-mm spectral index (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

• Angle-dependent emissivity (Leung et al 2010)

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Improved Modeling

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• Sample limited by existing 3D simulations

• Misleading p(a)– For low spin, need

hotter accretion flow

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

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

Millimeter Flares• Models

reproduce observed flare duration, amplitude, frequency

• Stronger variability at higher frequency

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Solid – 230 GHz Dotted – 690 GHz

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

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

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 variance 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

Caveats

• Limited sample

• Constant Ti/Te

• Unpolarized millimeter emission

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Conclusions

• Fit 3D GRMHD images/light curves 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: polarized emission, tilted disks, M87.

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M87

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

Tilted Disks

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Interferometry

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Morales & Wythe (2009)

Log-Normal Ring Models

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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)

Exciting Observations of Accreting Black Holes

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

• AGN– QPO(?)– Microlensing– Multiwavelength

surveysUIUC CTA Seminar 34L / 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)