From the Event Horizon to Infinity: Connecting Simulations with Observations of Accreting Black...
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Transcript of From the Event Horizon to Infinity: Connecting Simulations with Observations of Accreting Black...
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)
General Exam 8/27/2009 7/30
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)
General Exam 8/27/2009 12/30
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
General Exam 8/27/2009 14/30
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
General Exam 8/27/2009 19/30
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
General Exam 8/27/2009 20/30
• From VLBI measurements alone
•Independent of, consistent with constraints from polarimetry, spectral fitting
• Strong spin, Te dependence?
Light Curves
General Exam 8/27/2009 21/30
Millimeter Flares
General Exam 8/27/2009 22/30
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
General Exam 8/27/2009 24/30
Event Horizon Telescope
General Exam 8/27/2009 25/18
UV coverage (Phase I: black)
From Shep Doeleman’s Decadal Survey Report on the EHT
Doeleman et al (2009)
General Exam 8/27/2009 26/30
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)