Shane DavisShane DavisIASIAS

Probing Accretion and Spacetime Probing Accretion and Spacetime with Black Hole Binarieswith Black Hole Binaries

Omer BlaesOmer BlaesIvan HubenyIvan HubenyNeal TurnerNeal TurnerJulian KrolikJulian KrolikJim StoneJim StoneShigenobu HiroseShigenobu Hirose

Chris DoneChris DoneMatthew MiddletonMatthew MiddletonMarek GierlinskiMarek GierlinskiRebecca ShafeeRebecca ShafeeRamesh NarayanRamesh NarayanJeff McClintockJeff McClintockRon RemillardRon RemillardLi-Xin LiLi-Xin Li

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 black hole X-ray binary (BHB) explain black hole X-ray binary (BHB) observations?observations?

• 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?

• Black hole spin estimatesBlack hole spin estimates

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)

• Assumes simple Assumes simple temperature distribution:temperature distribution:

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

F

F

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 spectrum which Shimura Wien spectrum which Shimura & Takahara claim is consistent & Takahara claim is consistent with fwith fcolcol~1.7 for BHBs~1.7 for BHBs

= 0= 0

absabs= 1= 1

eses= 1= 1

((es es absabs))1/21/2= 1= 1

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 can we improve on these models?

• Include metals with bound-free opacity; Include metals with bound-free opacity; solve non-LTE populationssolve non-LTE populations

• More accurate radiative transfer and better More accurate radiative transfer and better treatment of Compton Scatteringtreatment of Compton Scattering

• Can consider the effects of more Can consider the effects of more complicated physics: e.g. dissipation, complicated physics: e.g. dissipation, magnetic stresses, and inhomogeneitiesmagnetic stresses, and inhomogeneities

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, aM, a**, L/L, 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 (ray tracing) -- determined by aspacetime (ray tracing) -- determined by a** and i and i

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**=0.27=0.27

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

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

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 more energy and dissipate more energy near the surface …near the surface …

Turner (2004)

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

• For effectively optically For effectively optically thin annulus, the spectra thin annulus, the spectra from the modified from the modified dissipation profile is dissipation profile is considerably harderconsiderably harder

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

Turner Profile

SS73 Profile

Magnetically Dominated Magnetically Dominated AtmospheresAtmospheres

• Magnetic pressure support Magnetic pressure support leads to lower leads to lower * * and and higher Thigher T** to give to give somewhat harder somewhat harder spectrumspectrum

• 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

Spin EstimatesSpin Estimates

• With independent estimates With independent estimates for the i, M, and D, thermal for the i, M, and D, thermal component only has two free component only has two free parameters: L/Lparameters: L/LEddEdd and a and a** -- --same number as diskbb same number as diskbb

(T(Tmaxmax, normalization), normalization)• Fits with our models suggest Fits with our models suggest

moderate (amoderate (a** < 0.9) values for < 0.9) values for most sources (with possible most sources (with possible exception of GRS 1915-105)exception of GRS 1915-105)

Shafee et al. 2005

Summary of Spin EstimatesSummary of Spin Estimates

SourceSource __i_i_ a/Ma/M

GRO J1655-40GRO J1655-40 7070oo ~ 0.7~ 0.7

LMC X-3LMC X-3 6767oo < 0.3< 0.3

XTE J1550-564XTE J1550-564 7272oo < 0.6< 0.6

XTE 4U 1543XTE 4U 1543 20.720.7oo ~ 0.8~ 0.8

GRS 1915-105GRS 1915-105 6666oo > 0.98 or ~ 0.8> 0.98 or ~ 0.8

Dependence on InclinationDependence on Inclination

Davis, Done & Blaes 2005

LMC X-3

Misaligned Jets?Misaligned Jets?• e.g. microquasar XTE J1550-564e.g. microquasar XTE J1550-564• 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 assumed Non-aligned jets not uncommon -- usually assumed that BH spin differs from binary orbit and inner that BH spin differs from binary orbit and inner disk aligns with BH -- Bardeen-Petterson effectdisk aligns with BH -- Bardeen-Petterson effect

• Best fit inclination, spin: i=43Best fit inclination, spin: i=43oo, a, a**=0.44=0.44• More examples: Maccarone (2002)More examples: Maccarone (2002)

What Have We Learned?What Have We Learned?

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

• Models qualitatively reproduce the observed evolution with Models qualitatively reproduce the observed evolution with luminosity; spectral modeling may constrain the nature of angular luminosity; spectral modeling may constrain the nature of angular momentum transport and black hole spinmomentum transport and black hole spin

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

• BB22/8/8& dF/dm taken from simulations of Hirose et al.& dF/dm taken from simulations of Hirose et al.• Gas pressure dominated -- dF/dm has little effect on the structureGas pressure dominated -- dF/dm has little effect on the structure• Extra magnetic pressure support lengthens scale height hExtra magnetic pressure support lengthens scale height h

• **~~**/(/(es es hh))