1. Shane Davis IAS Probing Accretion and Spacetime with Black Hole Binaries Omer Blaes Ivan Hubeny Neal Turner Julian Krolik Jim Stone Shigenobu Hirose Chris Done Matthew Middleton Marek Gierlinski Rebecca Shafee Ramesh Narayan Jeff McClintock Ron Remillard Li-Xin Li

2. Issues Addressed in This Talk How does the release of gravitational binding energy lead to thermal radiation?How does the release of gravitational binding energy lead to thermal radiation? Are thin disk (  -disk) models sufficient to explain black hole X-ray binary (BHB) observations?Are thin disk (  -disk) models sufficient to explain black hole X-ray binary (BHB) observations? How do lifting the simple assumptions of the  -disk model alter the spectra?How do lifting the simple assumptions of the  -disk model alter the spectra? Black hole spin estimatesBlack hole spin estimates

3. The thin disk model H/R << 1H/R << 1 Constant accretion rate; time-steadyConstant accretion rate; time-steady Gravitational binding energy released locallyGravitational binding energy released locally as radiation: The  -disk model determines surface density  determines surface density  Vertical dissipationVertical dissipationdistribution:

4. The Multicolor Disk Model (MCD) Assumes simple temperature distribution:Assumes simple temperature distribution: Spectrum assumed to be color-corrected blackbody:Spectrum assumed to be color-corrected blackbody: F F

5. Spectral Formation Depth of formation  * : optical depth where (  es  abs ) 1/2 ~1Depth of formation  * : optical depth where (  es  abs ) 1/2 ~1  >  * : absorbed  >  * : absorbed  <  * : escape  <  * : escape Therefore Thomson scattering produces modified blackbody:Therefore Thomson scattering produces modified blackbody: Compton scattering gives softer Wien spectrum which Shimura & Takahara claim is consistent with f col ~1.7 for BHBsCompton scattering gives softer Wien spectrum which Shimura & Takahara claim is consistent with f col ~1.7 for BHBs  = 0  abs = 1  es = 1 (  es  abs ) 1/2 = 1

6. Disk Dominated Spectra L prop. to T 4 suggests f col and emitting area are constantL prop. to T 4 suggests f col and emitting area are constant LMC X-3 Gierlinski & Done 2004

7. Comparison with Previous Spectral Models Previous  -disk models provide mixed resultsPrevious  -disk models provide mixed results Shimura & Takahara (1995); full atmosphere calculation, free-free emission and Compton scattering: starsShimura & Takahara (1995); full atmosphere calculation, free-free emission and Compton scattering: stars Merloni, Fabian & Ross (2000); relativistic effects, constant density, f-f emission and Compton scattering: blue curveMerloni, Fabian & Ross (2000); relativistic effects, constant density, f-f emission and Compton scattering: blue curve Small scatter in L-T relation as L varies by over an order of magnitudeSmall scatter in L-T relation as L varies by over an order of magnitude Gierlinski & Done 2004

8. How can we improve on these models? Include metals with bound-free opacity; solve non-LTE populationsInclude metals with bound-free opacity; solve non-LTE populations More accurate radiative transfer and better treatment of Compton ScatteringMore accurate radiative transfer and better treatment of Compton Scattering Can consider the effects of more complicated physics: e.g. dissipation, magnetic stresses, and inhomogeneitiesCan consider the effects of more complicated physics: e.g. dissipation, magnetic stresses, and inhomogeneities

9. Our Models, Briefly Use conservation laws with Kerr metric to calculate one-zone modelUse conservation laws with Kerr metric to calculate one-zone model Full disk model is determined by ~4 parameters: M, a *, L/L Edd, Full disk model is determined by ~4 parameters: M, a *, L/L Edd,  Calculate self-consistent vertical structure and radiative transfer in a series of concentric annuliCalculate self-consistent vertical structure and radiative transfer in a series of concentric annuli Each annulus is determined by 3 parametersEach annulus is determined by 3 parameters (+ assumptions): T eff, Q, (g=Q z),  Calculate photon geodesics in a relativistic spacetime (ray tracing) -- determined by a * and iCalculate photon geodesics in a relativistic spacetime (ray tracing) -- determined by a * and i

10. L/L Edd Mass Spin Inclination Model Parameters

11. ‘Broadband’ Fits to LMC X-3 MCD Our Model MCD model is too narrow -- need relativistic broadening  2 ~ 100MCD model is too narrow -- need relativistic broadening  2 ~ 100 Best fit find spinning black hole with a * =0.27Best fit find spinning black hole with a * =0.27

12. Luminosity vs. Temperature We generate artificial spectra and fit MCD modelWe generate artificial spectra and fit MCD model Then, we follow the procedure of Gierlinski & Done (2004) to calculate L disk /L edd and T maxThen, we follow the procedure of Gierlinski & Done (2004) to calculate L disk /L edd and T max Model: a=0, i=70 o, M=10 solar masses, and  =0.01Model: a=0, i=70 o, M=10 solar masses, and  =0.01

13. Luminosity vs. Temperature Slight hardening is consistent with some observationsSlight hardening is consistent with some observations Allows one to constrain surface density and accretion stressAllows one to constrain surface density and accretion stress Models become effectively optically thin at high accretion ratesModels become effectively optically thin at high accretion rates  =0.01  =0.001  =0. 1

14. Summary of Fit Results

15. Local MRI Simulations (with radiaton) Shakura & Sunyaev (1973):Shakura & Sunyaev (1973): Turner (2004): Mass more centrally concentrated towards midplane in simulations.Turner (2004): Mass more centrally concentrated towards midplane in simulations. Magnetic fields produced near midplane are buoyantMagnetic fields produced near midplane are buoyant and dissipate more energy near the surface … Turner (2004)

16. Dissipation Profile … but modified dissipation profile has limited affect on the spectrum.… but modified dissipation profile has limited affect on the spectrum. This particular annulus is very effectively optically thick and  * is close to surfaceThis particular annulus is very effectively optically thick and  * is close to surface Turner Profile SS73 Profile

17. Dissipation Profile For effectively optically thin annulus, the spectra from the modified dissipation profile is considerably harderFor effectively optically thin annulus, the spectra from the modified dissipation profile is considerably harder This will exacerbate the discrepancy between observations and models unless disks stay optically thickThis will exacerbate the discrepancy between observations and models unless disks stay optically thick Turner Profile SS73 Profile

18. Magnetically Dominated Atmospheres Magnetic pressure support leads to lower  * and higher T * to give somewhat harder spectrumMagnetic pressure support leads to lower  * and higher T * to give somewhat harder spectrum In this case lower  * alters statistical equilibrium -- lower recombination rate relative to photoionization rate give more highly ionized matter with lower bound-free opacityIn this case lower  * alters statistical equilibrium -- lower recombination rate relative to photoionization rate give more highly ionized matter with lower bound-free opacity No B field B field

19. Spin Estimates With independent estimates for the i, M, and D, thermal component only has two free parameters: L/L Edd and a * -- same number as diskbbWith independent estimates for the i, M, and D, thermal component only has two free parameters: L/L Edd and a * -- same number as diskbb (T max, normalization) Fits with our models suggest moderate (a * < 0.9) values for most sources (with possible exception of GRS 1915-105)Fits with our models suggest moderate (a * < 0.9) values for most sources (with possible exception of GRS 1915-105) Shafee et al. 2005

20. Summary of Spin Estimates Source_i_ a/M GRO J1655-4070 o ~ 0.7 LMC X-367 o < 0.3 XTE J1550-56472 o < 0.6 XTE 4U 154320.7 o ~ 0.8 GRS 1915-10566 o > 0.98 or ~ 0.8

21. Dependence on Inclination Davis, Done & Blaes 2005 LMC X-3

22. Misaligned Jets? e.g. microquasar XTE J1550-564e.g. microquasar XTE J1550-564 Hannikainen et al. (2001) observe superluminal ejections with v > 2 cHannikainen et al. (2001) observe superluminal ejections with v > 2 c Ballistic model:Ballistic model: Orosz et al. (2002) found i=72 oOrosz et al. (2002) found i=72 o Non-aligned jets not uncommon -- usually assumed that BH spin differs from binary orbit and inner disk aligns with BH -- Bardeen- Petterson effectNon-aligned jets not uncommon -- usually assumed that BH spin differs from binary orbit and inner disk aligns with BH -- Bardeen- Petterson effect Best fit inclination, spin: i=43 o, a * =0.44Best fit inclination, spin: i=43 o, a * =0.44 More examples: Maccarone (2002)More examples: Maccarone (2002)

23. What Have We Learned? Our detailed accretion disk models can reproduce the spectra of disk dominated BHBs (better than the MCD for “broadband” spectra of LMC X-3)Our detailed accretion disk models can reproduce the spectra of disk dominated BHBs (better than the MCD for “broadband” spectra of LMC X-3) Models qualitatively reproduce the observed evolution with luminosity; spectral modeling may constrain the nature of angular momentum transport and black hole spinModels qualitatively reproduce the observed evolution with luminosity; spectral modeling may constrain the nature of angular momentum transport and black hole spin Dissipation, magnetic stresses, and inhomogeneities can affect the spectra -- more simulations or analytical progress needed.Magnetic StressesDissipation, magnetic stresses, and inhomogeneities can affect the spectra -- more simulations or analytical progress needed.Magnetic Stresses B 2 /8  & dF/dm taken from simulations of Hirose et al.B 2 /8  & 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 h Extra magnetic pressure support lengthens scale height h   * ~  * /(  es h  )  * ~  * /(  es h  )