1. Measuring the Spins of Stellar-Mass Black Holes by Fitting the X-ray Continuum Spectrum Jeff McClintock Credit: A. Broderick & E. Mer Probing Strong Gravity Near Black Holes Prague: 2010 February 15-18

2. Our Team Jeff McClintock Ramesh Narayan Charles Bailyn Andy Cantrell Shane Davis Vivek Dhawan Ken Ebisawa Lijun Gou Li-Xin Li Jifeng Liu Jon McKinney Jerry Orosz Bob Penna Mark Reid Ron Remillard Rebecca Shafee Danny Steeghs Jack Steiner Manuel Torres

3. Black Holes are Extremely Simple Mass: M Spin: a * = J/(M 2 G/c) (-1  a *  1) (Electric Charge: Q)

4. Innermost Stable Circular Orbit (ISCO) a * = 0 R ISCO = 6MG/c 2 = 90 km a * = 1 R ISCO = 1MG/c 2 = 15 km Extreme Kerr for M = 10 M 

5. Innermost Stable Circular Orbit (ISCO) Dependence on Spin Parameter a * a * = 0 R ISCO = 6MG/c 2 = 90 km a * = 1 R ISCO = 1MG/c 2 = 15 km for M = 10 M 

6. Radius of ISCO vs. Spin 0 0.2 0.4 0.6 0.8 1 Spin a * 6 4 2 0 R ISCO /M(G/c 2 ) 90 km 15 km (for 10 M  ) R ISCO /M a *

7. Measuring R ISCO is Analogous to Measuring the Radius of a Star Bottom Line: R ISCO & M  a * R R ISCO R

8. Measuring R ISCO is Analogous to Measuring the Radius of a Star Bottom Line: R ISCO / M  a * R R ISCO Require accurate values of M, i, D F(R)? R R ISCO

9. Novikov & Thorne Thin-Disk Model: F(R) R/M(G/c 2 ) 0.10 0.05 0 dF/d(lnR) a * = 0 Novikov & Thorne 1973 Li et al. 2005 (kerrbb2)

10. Novikov & Thorne Thin-Disk Model: F(R) Four Identical Black Holes Differing Only in Spin R/M(G/c 2 ) 0.10 0 0.05 a * = 0.98 a * = 0.9 a * = 0.7 a * = 0 dF/d(lnR) Testing NT model via GRMHD simulations Narayan, Shafee, Penna, McKinney…

11. 3D GRMHD Simulation Results for Thin Disks Angular momentum profiles agree closely with NT (within (within 2-3% ) Shafee, McKinney, Narayan+ 2008 Penna et al. 2010 NT Model R/(MG/c 2 )

12. 3D GRMHD Simulation Results for Thin Disks Angular momentum profiles agree closely with NT (within (within 2-3% ) Very little torque at the ISCO (few% ) Shafee, McKinney, Narayan+ 2008 Penna et al. 2010 NT Model R/(MG/c 2 )

13. 3D GRMHD Simulation Results for Thin Disks Angular momentum profiles agree closely with NT (within (within 2-3% ) Very little torque at the ISCO (few% ) Luminosity inside ISCO modest (4-11% ) Shafee, McKinney, Narayan+ 2008 Penna et al. 2010 NT Model R/(MG/c 2 )

14. Requirements for the Continuum Fitting Method Zhang, Cui & Chen 1997 Theoretical profile of disk flux F(R) Disk atmosphere model of spectral hardening Davis et al. 2005, 2006, 2009; Davis & Hubeny 2006; Blaes et al. 2006 Spectrum dominated by strong thermal component Thin disk: H/R < 0.1 equivalent to L/L edd < 0.3 McClintock et al. 2006 Accurate estimates of M, D, i

15. New Results for LMC X-3 The Constant Inner-Disk Radius of LMC X-3: A Basis for Measuring Black Hole Spin James F. Steiner, Jeffrey E. McClintock, Ronald A. Remillard, Lijun Gou, Ramesh Narayan Submitted to ApJL on 25 January 2010 Adopt M = 10 M , i = 67 , D = 48 kpc XSPEC model = phabs(simpl  kerrbb2) 

16. LMC X-3: 1983 - 2009 Steiner et al. 2010 L D / L Edd

17. LMC X-3: 1983 - 2009 Steiner et al. 2010 L D / L Edd

18. LMC X-3: 1983 - 2009 Steiner et al. 2010 L D / L Edd R in (GM/c 2 )

19. LMC X-3: 1983 - 2009 Steiner et al. 2010 R in (GM/c 2 ) L / L Edd

20. LMC X-3: 1983 - 2009 Steiner et al. 2010 R in (GM/c 2 ) L / L Edd R in = 3.85  0.12 GM/c 2 (  3%)

21. Spin Results to Date Source a*a* Reference GRS 1915+105 0.99  0.01 McClintock et al. 2006 LMC X-1 0.92  0.06 Gou et al. 2009 4U 1543-47 0.80  0.05 Shafee et al. 2006 M33 X-7 0.77  0.05 Liu et al. 2008 GRO J1655-40 0.70  0.05 Shafee et al. 2006 A0620-00 0.12  0.18 Gou et al. 2009

22. Spin Results to Date: 2 Featured Sources Source a*a* Reference GRS 1915+105 0.99  0.01 McClintock et al. 2006 LMC X-1 0.92  0.06 Gou et al. 2009 4U 1543-47 0.80  0.05 Shafee et al. 2006 M33 X-7 0.77  0.05 Liu et al. 2008 GRO J1655-40 0.70  0.05 Shafee et al. 2006 A0620-00 0.10  0.18 Gou et al. 2010

23. Microquasar GRS 1915+105: a * = 0.98 - 1 VLA 3.5 cm V jet = (0.92  0.08)c 1 month 1 arcsec Mirabel & Rodriguez 1994 McClintock et al. 2006

24. Soft X-ray Transient A0620-00: a * = 0.12  0.18 a * -0.56 0 10 20 30 Time (days) Intensity (Crab) 50 25 0 2 - 18 keV August 1975 50 Crab! (3  ) Gou et al. 2010

25. Soft X-ray Transient A0620-00: a * = 0.12  0.18 a * -0.56 0 10 20 30 Time (days) Intensity (Crab) 50 25 0 2 - 18 keV Flux density (mJy) _ _ 200 100 0 940 MHz Strong evidence for a relativistic jet  Multiple jet ejections  Arcsec scale  Initially optically thick Kuulkers, Fender, Spencer, Davis & Morrison 1999 (3  ) Gou et al. 2010

26. Three Spin Measurements in the Works for 2010 XTE J1550-564 Dynamical model (Orosz et al.) Spin (Steiner et al.) Cygnus X-1 VLBA parallax (Reid et al.) Dynamical model (Orosz et al.) Spin (Gou et al.) LMC X-3 Dynamical model (Orosz et al). Spin (Steiner et al.)

27. Conclusions LMC X-3 is a confidence builder: R in is constant to 3% over 26 years and for 7 missions 3D GRMHD tests to date indicate NT model is sound Six spins measured -- three more in 2010 A0620-00 with a * ~ 0.1 indicates high spin not required to drive microquasar jets -- jets are likely disk driven