Shane Davis IAS

1. Probing Accretion and Spacetime with Black Hole Binaries Shane DavisIAS Omer BlaesIvan HubenyNeal TurnerJulian KrolikJim StoneShigenobu Hirose Chris DoneMatthew MiddletonMarek GierlinskiRebecca ShafeeRamesh NarayanJeff McClintockRon RemillardLi-Xin Li

2. Issues Addressed in This Talk • 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? • How do lifting the simple assumptions of the -disk model alter the spectra? • Black hole spin estimates

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

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

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

6. Disk Dominated Spectra LMC X-3 • L prop. to T4 suggests fcol and emitting area are constant Gierlinski & Done 2004

7. Comparison with Previous Spectral Models • Previous -disk models provide mixed results • Shimura & 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 curve • Small 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 populations • More accurate radiative transfer and better treatment of Compton Scattering • Can 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 model • Full disk model is determined by ~4 parameters: M, a*, L/LEdd,  • Calculate self-consistent vertical structure and radiative transfer in a series of concentric annuli • Each annulus is determined by 3 parameters (+ assumptions): Teff, Q, (g=Q z),  • Calculate photon geodesics in a relativistic spacetime (ray tracing) -- determined by a* and i

10. Model Parameters L/LEdd Inclination Spin Mass

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

12. Luminosity vs. Temperature • We generate artificial spectra and fit MCD model • Then, we follow the procedure of Gierlinski & Done (2004) to calculate Ldisk/Ledd and Tmax • Model: a=0, i=70o, M=10 solar masses, and =0.01

13. Luminosity vs. Temperature • Slight hardening is consistent with some observations • Allows one to constrain surface density and accretion stress • Models become effectively optically thin at high accretion rates =0.1 =0.01 =0.001

14. Summary of Fit Results

15. Local MRI Simulations(with radiaton) • Shakura & Sunyaev (1973): • Turner (2004): Mass more centrally concentrated towards midplane in simulations. • Magnetic 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. • This 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 harder • This 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 spectrum • In 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/LEdd and a* --same number as diskbb (Tmax, normalization) • 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 J1655-40 70o ~ 0.7 LMC X-3 67o < 0.3 XTE J1550-564 72o < 0.6 XTE 4U 1543 20.7o ~ 0.8 GRS 1915-105 66o > 0.98 or ~ 0.8

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

22. Misaligned Jets? • e.g. microquasar XTE J1550-564 • Hannikainen et al. (2001) observe superluminal ejections with v > 2 c • Ballistic model: • Orosz et al. (2002) found i=72o • Non-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=43o, a*=0.44 • 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) • Models 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 Stresses • B2/8 & dF/dm taken from simulations of Hirose et al. • Gas pressure dominated -- dF/dm has little effect on the structure • Extra magnetic pressure support lengthens scale height hr • *~*/(es hr)