connecting simulations with observations of the galactic center black hole
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Connecting Simulations with Observations of the Galactic Center Black Hole. Jason Dexter University of Washington. With Eric Agol, Chris Fragile and Jon McKinney. Accretion. Material falling onto a central object Gravitational binding energy radiation - PowerPoint PPT PresentationTRANSCRIPT
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Connecting Simulations with Observations of the
Galactic Center Black Hole
Jason DexterUniversity of Washington
With Eric Agol, Chris Fragile and Jon McKinney
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Accretion
CofC Colloquium 2
• 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
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Black Holes
CofC Colloquium 3
• a, M
• Innermost stable circular orbit
• Photon orbit
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Astrophysical Black Holes
CofC Colloquium 4
• 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
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The MRI
CofC Colloquium 5
• 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”
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Toy Model of the MRI
CofC Colloquium 6
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
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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)
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Galactic Center
CofC Colloquium 8
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Sagittarius A*
CofC Colloquium 9
Jet or nonthermal electrons far from BH
Thermal electrons at BH
Simultaneous IR/x-ray flares close to BH?
no d
ata
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ata
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eCharles Gammie
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Sgr A* VLBI
CofC Colloquium 10
• Largest angular size of any BH– Microarcseconds; baby penguin on moon.
• Very long baseline interferometry– High resolution: ~λ/D– Scattering: ~λ2
– Interferometry Fourier transforms
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Millimeter Sgr A*
• Precision black hole astrophysics
11CofC Colloquium
Doeleman et al (2008)
Gaussian FWHM ~4 Rs!
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Black Hole Shadow
• Signature of event horizon• Sensitive to details of accretion flow
Bardeen (1973); Dexter & Agol (2009) Falcke, Melia & Agol (2000)
12CofC Colloquium
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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)
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Ray Tracing
CofC Colloquium 14
• 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)
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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
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GRMHD Fits to VLBI Data
CofC Colloquium 16
Dexter, Agol & Fragile (2009); Doeleman et al (2008)i=10 degrees i=70 degrees
10,000 km
100 μas
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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
CofC Colloquium 17
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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
CofC Colloquium 18
+35-15
+97-22
Inclination
Electron Temperature
Sky Orientation
Accretion Rate+15-2
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Comparison to RIAF Values
CofC Colloquium 19
Broderick et al (2009)
Inclination Sky Orientation
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Millimeter Flares• Models
reproduce observed flare duration, amplitude, frequency
• Stronger variability at higher frequency
CofC Colloquium 20
Solid – 230 GHz Dotted – 690 GHz
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Comparison to Observed Flares
CofC Colloquium 21
Eckart et al (2008)Marrone et al (2008)
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Shadow of Sgr A*
CofC Colloquium 22
Shadow may be detected on chile-lmt, smto-chile baselines; otherwise need south pole.
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Crescents
CofC Colloquium 23
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Constraining Models
CofC Colloquium 24
• 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
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Tilted Disks
CofC Colloquium 25
• No reason to expect Sgr A* isn’t tilted• Best fit images are still crescents• Shadow still visible
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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.
CofC Colloquium 26
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Event Horizon Telescope
CofC Colloquium 27
UV coverage (Phase I: black)
From Shep Doeleman’s Decadal Survey Report on the EHT
Doeleman et al (2009)
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M87
CofC Colloquium 28
New mass estimate BH angular size ~4/5 of Sgr A*! (Gebhardt & Thomas 2009)
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Interferometry
CofC Colloquium 29Morales & Wythe (2009)
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Log-Normal Ring Models
CofC Colloquium 30
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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)
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Sagittarius A*
CofC Colloquium 32
Dodds-Eden et al (2009)
Yuan et al (2003)
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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)
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Finite Speed of Light
CofC Colloquium 34
Toy emissivity, i=50 degrees 690 GHz, i=50 degrees
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Finite Speed of Light
CofC Colloquium 35
• Emission dominated by narrow range in observer time
• Time delays are 10-15% effect on light curves
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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
CofC Colloquium 36
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Light Curves
CofC Colloquium 37
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Face-on Fits
CofC Colloquium 38
• 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
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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!
CofC Colloquium 39
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Modeling
CofC Colloquium 40
• Sample limited by existing 3D simulations
• Misleading p(a)– For low spin, need
hotter accretion flow
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Millimeter Flares
CofC Colloquium 41
• Strong correlation with accretion rate variability
• Approximate emissivity:– Jν ~ nBα, α ≈ 1-2.
– Isothermal emission region, ν/νc ≈ 10.
– Not heating from magnetic reconnection
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Caveats
• Limited sample
• Constant Ti/Te
• Unpolarized millimeter emission
• Aligned disk/holeCofC Colloquium 42