Estimating the Spin of Stellar-Mass Black Holes

1. Estimating the Spin of Stellar-Mass Black Holes Jeffrey McClintock Harvard-Smithsonian CfA STScI Black Hole Symposium April 25, 2007

2. Chronological List of Team Members This effort to measure spin requires a 50-50 mix of theory & observation.

3. Introduction

4. The Essentials • Objects: Stellar-mass BHs in X-ray binaries • Method: Spin via fitting the X-ray continuum • Absolute Requirements: Accurate values of BH mass, i & D “Thermal-Dominant” X-ray data State-of-the-art relativistic models Li, Zimmerman, Narayan & McClintock 2005 Shaffee, McClintock, Narayan, Davis, Li & Remillard 2006 McClintock, Shafee, Narayan, Remillard, Davis & Li 2006

5. Ii Number of BH binaries known = 21 M ~ 10 Msun Courtesy J. Orosz

6. Ii Number of BH binaries known = 21 M ~ 10 Msun Courtesy J. Orosz

7. Black Holes are Extremely Simple • Mass:M • Spin:J = a*GM2/c (0 < a* < 1) • (Electric Charge: Q) 21 BH massesM have been measured Obvious next frontier: Measure BH spina* (much harder)

8. f RISCO: Extreme-Kerr vs. Schwarzschild T ~ 2 keV 42% a* = 1 RISCO = 15 km a* = 0 T ~ 1 keV 6% RISCO = 90 km

9. Two Foundations1.ISCO2. Thermal Dominant State

10. First Foundation Innermost Stable Circular Orbit (ISCO) • A disk terminates at RISCO and gas falls freely onto the BH inside this radius. • Thus, disk emission has a “hole” of radius RISCO at center. • If we measure the size of the hole, we will obtain a*  90 km RISCO  a* 15 km 

11. Second Foundation • Typical X-ray nova 2-20 keV light curve • 170 RXTE/PCA observations over 9 months • Fit spectra with MCD model (diskbb) + power law • Non-relat. MCD model has 2 params:Tin&Rin Mitsuda et al. 1984 Makishima et al. 1986 Tanaka & Lewin 1995 Remillard & McClintock 2006

12. Second Foundation (cont.) • Consider disk component of emission only • Focus on 4-month monotonic decay of accretion disk

13. Second Foundation (cont.) Thermal Dominant State • Ldisk / Ltotal > 75% (2-20 keV) • No QPOs • Weak power continuum (r < 0.075) • Power-law/Comptonization minimal • Remillard & McClintock 2006, ARAA, 44,49

14. Second Foundation (cont.) • Smooth, monotonic decline of temperature as disk decays on a thermal time scale

15. Second Foundation (cont.) Second Foundation (cont.) • Inner disk radius Rin quite constant • Compare Tanaka & Lewin 1995 in XRBs

16. Second Foundation (cont.) Second Foundation (cont.) • Now, plot Ldisk/Llotal versus Tin

17. Second Foundation (cont.) H1743-322 Tin4 Kubota et al. 2001 Kubota & Makishima 2004 Kubota & Done 2004 Gierlinski & Done 2004

18. Tin4 Second Foundation fcol = Tin/Teff Davis et al. 2005, 2006 Teff4 Conclusion: There exists a constant radius

19. Outline of Method for Estimating Spin Fitting the X-ray continuum 

20. Measuring the Radius of a Star • Measure the flux Freceived from the star • Measure the temperature T (from spectrum) • Then, assuming blackbody radiation: • F and T give solid angle of star • If we know distanceD,we directly obtainR R

21. Measuring the Radius of the Disk Inner Edge • We want to measure the radius of the ‘hole’ in the disk emission • Same principle as before • From Fand T get solid angle of hole • Knowing D and i get RISCO • From RISCO and M get a* Zhang et al. (1997) Gierlinski et al. 2001; Li et al. (2005); Shafee et al. (2006); McClintock et al. (2006); Davis et al. (2006);… RISCO

22. Estimates of Spin Obtained with this Method

23. Diving into the Method

24. How to Get Reliable Results? • Need good estimates of M, D, i • Should include all relativistic effects: Doppler beaming, grav. redshift, ray deflections  KERRBB (Li et al. 2006) • The system should be in the Thermal Dominant state • H/R < 0.1 L/Ledd < 0.3 • Deviations from blackbody (parameter f) should be estimated via a disk atmosphere model Shimura & Takahara (1995); Davis et al. (2005, 2006)

25. How to Get Reliable Results?(cont.) • Need accurate theoretical profiles of disk flux F(R) and temperature T(R)

26. RISCO S Flux vs. Radius Shafee, Narayan & McClintock (Poster #31) a* = 0 RISCO a* = 0.95 aa Zero-torque at ISCO H/R < 0.1 L/Ledd < 0.3

27. Bottom Line Errors due to hydro effects are modest. Shafee et al. (Poster #31)

28. Only a* and Mdot Determined from X-ray Spectrum • M,D,i from ground-based observations • fcol from disk atmosphere model • Zero torque at ISCO for L/Ledd < 0.3 • Fit for a* and Mdot (Mdot  L/Ledd) only T & flux  a* & Mdot

29. GRS 1915+105 ASCA: 1.2-10 keV RXTE: 3-25 keV a* = 0.994 L/Ledd = 0.21 a* = 0.988 L/Ledd = 0.18 Flux Flux 20 Thermal-Dominant Observations out of 640 2 5 Energy (keV) 5 10 20 Energy (keV) KERBB: Fit for a* and mass accretion rate Mdot (L/Ledd) McClintock, Shafee, Narayan et al. 2006

30. Observational Work in Progress HEASARC

31. Key Spin Targets • M33 X-7: Gemini-N, Chandra, XMM • GRS 1915+105: VLBA, Gemini-S • LMC X-1: Magellan, SMARTS • A0620-00: Spitzer/ground-based • XTE J1550-564: Magellan Additional targets:Nova Mus 1991, XTE J1859+226, XTE J1650-500, GS 2000+25, GRS 1009-45… about a dozen in total

32. M33 X-7 Preliminary Orosz et al. 2007 Porb 3.45 days D = 845 +/- 25 kpc i = 74 +/- 2 deg M = 14 +/- 3 Msun O6 giant M2 = 57 +/- 10 Msun R2 = 18.5 +/- 1 Rsun Teff = 35,000 +/- 2500K Spin analysis underway Liu et al. Pietsch et al. 2006

33. Radio Jet v/c = 0.92 GRS 1915+105 Mirabel & Rodriguez 1994 a* = 0.98-1.0 McClintock, Shafee, Narayan et al. 2006

34. GRS 1915+105 GRS 1915+105 6 8 10 12 14 Distance (kpc) Gemini-S GNIRS proposal pending McClintock, Shafee, Narayan et al. 2006

35. GRS 1915+105 Distance (kpc) VLBA observations underway

36. Nominal Spinsof 4 BHs LMC X-3: a* = 0.2 GRO J1655-40: a* = 0.7 4U 1543-47: a* = 0.8 GRS 1915+105: a* = 0.99 McClintock, Shafee, Narayan, et al.

37. Discussion

38. Black Hole Spins Chiefly Natal • Accretion torques inadequate to spin up BH in lifetime of system King & Kolb 1999 • GRS 1915+105 a prime example: Accretion of 4 Mo onto a 10 Mo hole  a* ~ 0.77 << a* = 0.98 – 1 Lee, Brown & Wijers 2002 Podsiadlowski, Rappaport & Han 2003 McClintock, Shafee, Narayan, et al. 2006 For discussion, see McClintock et al. 2006

39. Uses of Spin Data • Test Jet Models Blandford & Znajek (1977) Hawley & Balbus (2002) • Validate core-collapse GRB models Collapsar: Enough J to form disk? Woosley (1993) MacFadyen & Woosley (1999) Woosley & Heger (2006) • Inform modelers of GW waveforms Shafee et al. motivated first waveform work to include spin Campanilli, Lousto & Zlochower (2006) • Test evolutionary model of binary black-hole formation Were GRS 1915+105, GRO J1655-40?, etc. GRB sources? Lee, Brown & Wijers (2002) Brown, Lee & Walter (2007) van den Heuvel et al. (2007)

40. 3 Other Avenues to SpinRemillard & McClintock 2006, ARAA 44, 49 • Fe line profile Fabian et al. 1989 Reynolds & Nowak 2003 • High-frequency X-ray QPOs (100-450 Hz) Abramowicz & Kluzniak 2001 Torok et al. 2005 • X-ray polarimetry Lightman & Shapiro 1975 Connors, Piran & Stark 1980

41. Conclusions • 4 spins estimated: GRS 1915+105: a* > 0.98 • Straightforward methodology Fully relativistic disk model, KERRBB2: fit for a* and Mdot Thermal Dominant spectra only Accurate ground-based data on M, D & i essential Advanced treatment of spectral hardening fcol • Future work Amass a dozen spin estimate No torque assumption for L/Ledd < 0.3:hydro  GRMHD Test model for GRS 1915+105 Examine possible effects of warm absorber Attempt Fe K and HFQPO spin measurements