How do Black Hole Accretion How do Black Hole Accretion Disks Radiate?Disks Radiate?

Shane DavisShane DavisUCSBUCSB

Standard Accretion PictureStandard Accretion Picture

Issues Addressed in This TalkIssues Addressed in This Talk

• How does the release of gravitational How does the release of gravitational binding energy lead to ~ thermal radiation?binding energy lead to ~ thermal radiation?

• Are thin disk (Are thin disk (-disk) models sufficient to -disk) models sufficient to explain observations? (yes and no)explain observations? (yes and no)

• How do lifting the simple assumptions of How do lifting the simple assumptions of the the -disk model alter the spectra?-disk model alter the spectra?

I: Summary of Models and I: Summary of Models and ObservationsObservations

The thin disk modelThe thin disk model

• H/R << 1H/R << 1

• Constant accretion rate; time-steadyConstant accretion rate; time-steady

• Gravitational binding energy released Gravitational binding energy released locallylocally

as radiation:as radiation:

The The -disk model-disk model• determines surface density determines surface density • Vertical dissipationVertical dissipation

distribution:distribution:

The Multicolor Disk Model The Multicolor Disk Model (MCD)(MCD)

• Consider simple Consider simple temperature distribution:temperature distribution:

• Spectrum assumed to be Spectrum assumed to be color-corrected color-corrected blackbody:blackbody:

F

F

Spectral States of BHBsSpectral States of BHBs

• Spectral states Spectral states specified by relative specified by relative contributions of contributions of thermal (disk) and thermal (disk) and non-thermal emission non-thermal emission (corona)(corona)

• High/Soft state is High/Soft state is dominated by thermal dominated by thermal disk-like componentdisk-like component

Done & Gierlinski 2004

Disk Dominated SpectraDisk Dominated Spectra

• L prop. to TL prop. to T44 suggests f suggests fcolcol and emitting area are and emitting area are constantconstant

LMC X-3

Gierlinski & Done 2004

Comparison with Previous Comparison with Previous Spectral ModelsSpectral Models

• Previous Previous -disk models -disk models provide mixed resultsprovide mixed results

• Shimura & Takahara (1995); Shimura & Takahara (1995); full atmosphere calculation, full atmosphere calculation, free-free emission and free-free emission and Compton scattering: starsCompton scattering: stars

• Merloni, Fabian & Ross Merloni, Fabian & Ross (2000); relativistic effects, (2000); relativistic effects, constant density, f-f emission constant density, f-f emission and Compton scattering: blue and Compton scattering: blue curvecurve

• Small scatter in L-T relation Small scatter in L-T relation as L varies by over an order as L varies by over an order of magnitudeof magnitude

Gierlinski & Done 2004

How do we Improve on these Models

• Include metals; non-LTE populationsInclude metals; non-LTE populations

• Improved radiative transfer and better Improved radiative transfer and better treatment of Compton Scatteringtreatment of Compton Scattering

• Examine the effects of:Examine the effects of:

dissipation, magnetic stresses, and dissipation, magnetic stresses, and inhomogeneitiesinhomogeneities

Our Models, BrieflyOur Models, Briefly

• Use conservation laws with Kerr metric to Use conservation laws with Kerr metric to calculate one-zone modelcalculate one-zone model

• Full disk model is determined by ~4 parameters: Full disk model is determined by ~4 parameters: M, a, L/LM, a, L/LEddEdd, ,

• Calculate self-consistent vertical structure and Calculate self-consistent vertical structure and radiative transfer in a series of concentric annuliradiative transfer in a series of concentric annuli

• Each annulus is determined by 3 parametersEach annulus is determined by 3 parameters

(+ assumptions): T(+ assumptions): Teffeff, Q, (g=Q z), , Q, (g=Q z), • Calculate photon geodesics in a relativistic Calculate photon geodesics in a relativistic

spacetime for an observer at inclination i (ray spacetime for an observer at inclination i (ray tracing)tracing)

L/LEdd

MassSpin

Inclination

Model ParametersModel Parameters

‘‘Broadband’ Fits to LMC X-3Broadband’ Fits to LMC X-3MCDOur

Model

• MCD model is too narrow -- need relativistic MCD model is too narrow -- need relativistic broadening broadening 22 ~ 100 ~ 100

• Best fit find spinning black hole with aBest fit find spinning black hole with a**=0.45, =0.45, consistent with consistent with RXTERXTE fits fits

Spectral FormationSpectral Formation• Depth of formation Depth of formation **: optical : optical

depth where (depth where (eses absabs))1/21/2~1~1

> > **: absorbed: absorbed

< < **: escape: escape

• Therefore Thomson scattering Therefore Thomson scattering produces modified blackbody:produces modified blackbody:

• Compton scattering gives softer Compton scattering gives softer Wien spectrumWien spectrum

• From these considerations From these considerations Shimura & Takahara (1995) Shimura & Takahara (1995) find ffind fcolcol=1.7+/-0.2=1.7+/-0.2

Luminosity vs. TemperatureLuminosity vs. Temperature

• We generate artificial We generate artificial spectra and fit MCD spectra and fit MCD modelmodel

• Then, we follow the Then, we follow the procedure of Gierlinski & procedure of Gierlinski & Done (2004) to calculate Done (2004) to calculate LLdiskdisk/L/Leddedd and T and Tmax max

• Model: a=0, i=70Model: a=0, i=70oo, M=10 , M=10 solar masses, and solar masses, and =0.01=0.01

Previous Models

Our Model

Luminosity vs. TemperatureLuminosity vs. Temperature

• Slight hardening is Slight hardening is consistent with some consistent with some observationsobservations

• Allows one to constrain Allows one to constrain surface density and surface density and accretion stressaccretion stress

• Models become Models become effectively optically thin effectively optically thin at high accretion ratesat high accretion rates

=0.01

=0.001

=0.1

Summary of Fit ResultsSummary of Fit Results

• Lack of hardening suggests hottest annuli remain Lack of hardening suggests hottest annuli remain effectively thick (especially LMC X-3)effectively thick (especially LMC X-3)

• Models consistent with moderate spins, small torques for Models consistent with moderate spins, small torques for disk inclination = binary inclination (adisk inclination = binary inclination (a**~0.7, 0.1, 0.4)~0.7, 0.1, 0.4)

II. Adding ‘Real’ Physics: II. Adding ‘Real’ Physics: Dissipation, Magnetic Stresses & Dissipation, Magnetic Stresses &

InhomogeneitiesInhomogeneities

Local MRI SimulationsLocal MRI Simulations(with radiaton)(with radiaton)

• Shakura & Sunyaev (1973):Shakura & Sunyaev (1973):

• Turner (2004): Mass more Turner (2004): Mass more centrally concentrated centrally concentrated towards midplane in towards midplane in simulations.simulations.

• Magnetic fields produced Magnetic fields produced near midplane are buoyantnear midplane are buoyantand dissipate near surfaceand dissipate near surface

Turner (2004)

Dissipation ProfileDissipation Profile

• Modified dissipation Modified dissipation profile changes profile changes structure significantlystructure significantly

• Where -dF/dm is small Where -dF/dm is small (large), density is (large), density is larger (smaller)larger (smaller)

• Note that T and Note that T and near near ** are similar are similar

Turner ProfileSS73 Profile

Dissipation ProfileDissipation Profile

• … … but modified but modified dissipation profile has dissipation profile has limited affect on the limited affect on the spectrum.spectrum.

• This particular annulus This particular annulus is very effectively is very effectively optically thick and optically thick and * * is is close to surfaceclose to surface

Turner Profile

SS73 Profile

Dissipation ProfileDissipation Profile

• Consider same Consider same dissipation profile, but dissipation profile, but in an annulus that is in an annulus that is not effectively not effectively optically thick.optically thick.

• Spectrum with Spectrum with modified dissipation modified dissipation profile is effectively profile is effectively optically thick, but has optically thick, but has a much greater surface a much greater surface temperaturetemperature

Turner ProfileSS73 Profile

Dissipation ProfileDissipation Profile

• For this annulus, the For this annulus, the spectra from the spectra from the modified dissipation modified dissipation profile is considerably profile is considerably harderharder

• This will exacerbate This will exacerbate the discrepancy the discrepancy between observations between observations and models unless and models unless disks stay optically disks stay optically thickthick

Turner Profile

SS73 Profile

Magnetic StressesMagnetic Stresses

• BB22/8/8& dF/dm taken & dF/dm taken from simulations of from simulations of Hirose, Krolik, & StoneHirose, Krolik, & Stone

• Gas pressure dominated -- Gas pressure dominated -- dF/dm has little effect on dF/dm has little effect on the structurethe structure

• Extra magnetic pressure Extra magnetic pressure support lengthens scale support lengthens scale height hheight h

• **~~**/(/(es es hh))

No B fieldB field

Simulation

Magnetic StressesMagnetic Stresses

• Lower Lower * * and higher Tand higher T**

combine to give somewhat combine to give somewhat harder spectrumharder spectrum

• In this case lower In this case lower * * alters alters

statistical equilibrium -- statistical equilibrium -- lower recombination rate lower recombination rate relative to photoionization relative to photoionization rate give more highly rate give more highly ionized matter with lower ionized matter with lower bound-free opacitybound-free opacity

No B field

B field

InhomogeneitiesInhomogeneities

• Radiation pressure dominated Radiation pressure dominated accretion disks expected to be accretion disks expected to be homogeneous due to photon bubble homogeneous due to photon bubble instability and/or compressible MRIinstability and/or compressible MRI

• May make disk thinner and May make disk thinner and (therefore) denser (Begelman 2001, (therefore) denser (Begelman 2001, Turner et al. 2005)Turner et al. 2005)

• May also affect the radiative May also affect the radiative transfer…transfer…

Neal Turner

InhomogeneitiesInhomogeneities

• 2-D Monte Carlo 2-D Monte Carlo calculations: photon calculations: photon bubbles help thermalize bubbles help thermalize the spectrum, making it the spectrum, making it softersofter

• Photon emission and Photon emission and absorption dominated absorption dominated by denser regions.by denser regions.

What Have We Learned?What Have We Learned?

• Our detailed accretion disk models can reproduce the Our detailed accretion disk models can reproduce the spectra of disk dominated BHBs (better than the spectra of disk dominated BHBs (better than the MCD in LMC X-3)MCD in LMC X-3)

• Models reproduce the observed evolution with Models reproduce the observed evolution with luminosity; spectral modeling may constrain the luminosity; spectral modeling may constrain the nature of angular momentum transport and black nature of angular momentum transport and black hole spin (torques?)hole spin (torques?)

• Dissipation, magnetic stresses, and inhomogeneities Dissipation, magnetic stresses, and inhomogeneities may affect the spectra -- more simulations or may affect the spectra -- more simulations or analytical progress needed.analytical progress needed.

Non-aligned JetNon-aligned Jet• XTE J1550-564 is a microquasarXTE J1550-564 is a microquasar• Hannikainen et al. (2001) observe superluminal Hannikainen et al. (2001) observe superluminal

ejections with v > 2 cejections with v > 2 c• Ballistic model:Ballistic model:• Orosz et al. (2002) found i=72Orosz et al. (2002) found i=72oo

• Non-aligned jets not uncommon -- usually Non-aligned jets not uncommon -- usually assumed that BH spin differs from binary orbit assumed that BH spin differs from binary orbit and inner disk aligns with BH -- Bardeen-and inner disk aligns with BH -- Bardeen-Petterson effectPetterson effect

• Best fit inclination, spin: i=43Best fit inclination, spin: i=43oo, a=0.44, a=0.44

Spectral Dependence on Surface Spectral Dependence on Surface DensityDensity

• Spectra largely Spectra largely

independent of independent of SS for for

large surface density large surface density

(( >~ 10>~ 103 3 g/cmg/cm22))

• As disk becomes As disk becomes marginally effectively marginally effectively thin, spectra become thin, spectra become

sensitive to sensitive to and harden and harden

rapidly with decreasing rapidly with decreasing

Binaries Provide Independent Binaries Provide Independent Constraints on ModelsConstraints on Models

• Orosz and Orosz and collaborators derive collaborators derive reasonably precise reasonably precise estimates from estimates from modeling the light modeling the light curve of secondarycurve of secondary

• e.g. XTE J1550-564:e.g. XTE J1550-564:

Luminosity vs. TemperatureLuminosity vs. Temperature

• Measured binary Measured binary properties limit properties limit parameter space of fitsparameter space of fits

• Simultaneous fits to Simultaneous fits to multiple observations multiple observations of same source of same source constrain spin/torqueconstrain spin/torque

• Spectra are too soft to Spectra are too soft to allow for extreme allow for extreme spin/large torquesspin/large torques

Stellar Atmospheres: Disk Annuli Stellar Atmospheres: Disk Annuli vs. Stellar Envelopesvs. Stellar Envelopes

• The spectra of stars are determined by TThe spectra of stars are determined by Teffeff, ,

g, and the compositiong, and the composition

• Annuli are determined by, TAnnuli are determined by, Teffeff, Q (where , Q (where

g=Q z), g=Q z), SS, the composition, and the vertical , the composition, and the vertical dissipation profile: F(m)dissipation profile: F(m)

• TTeffeff, Q, and , Q, and SS can be derived from radial can be derived from radial

disk structure equationsdisk structure equations

• Standard assumption is:Standard assumption is:

Luminosity vs. TemperatureLuminosity vs. Temperature

Gierlinski & Done 2004

Effect of bound-free opacityEffect of bound-free opacity

• Bound-free opacity Bound-free opacity decreases depth of decreases depth of formation: formation: **

• • Absorption opacity Absorption opacity

approximately greyapproximately grey• Spectrum still Spectrum still

approximated by approximated by diluted blackbody:diluted blackbody:

The Multicolor Disk Model The Multicolor Disk Model (MCD)(MCD)

• Consider simplest temperature distribution:Consider simplest temperature distribution:

• Assume blackbody and integrate over R Assume blackbody and integrate over R replacing R with T (Treplacing R with T (Tmaxmax~f~fcolcolTTeffeff):):

Effective Temperature: TEffective Temperature: Teffeff

Gravity Parameter: QGravity Parameter: Q

Comparison Between Comparison Between Interpolation and Exact ModelsInterpolation and Exact Models

• Interpolation best at Interpolation best at high L/Lhigh L/Leddedd

• Exact: Blue curve Exact: Blue curve

Interpolation: Red Interpolation: Red Curve Curve