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

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

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

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 

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 

Radius of ISCO vs. Spin Spin a * R ISCO /M(G/c 2 ) 90 km 15 km (for 10 M  ) R ISCO /M a *

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

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

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

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

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

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 Penna et al NT Model R/(MG/c 2 )

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 Penna et al NT Model R/(MG/c 2 )

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 Spectrum dominated by strong thermal component Thin disk: H/R < 0.1 equivalent to L/L edd < 0.3 McClintock et al Accurate estimates of M, D, i

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) 

LMC X-3: Steiner et al L D / L Edd

LMC X-3: Steiner et al L D / L Edd

LMC X-3: Steiner et al L D / L Edd R in (GM/c 2 )

LMC X-3: Steiner et al R in (GM/c 2 ) L / L Edd

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

Spin Results to Date Source a*a* Reference GRS  0.01 McClintock et al LMC X  0.06 Gou et al U  0.05 Shafee et al M33 X  0.05 Liu et al GRO J  0.05 Shafee et al A  0.18 Gou et al. 2009

Spin Results to Date: 2 Featured Sources Source a*a* Reference GRS  0.01 McClintock et al LMC X  0.06 Gou et al U  0.05 Shafee et al M33 X  0.05 Liu et al GRO J  0.05 Shafee et al A  0.18 Gou et al. 2010

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

Soft X-ray Transient A : a * = 0.12  0.18 a * Time (days) Intensity (Crab) keV August Crab! (3  ) Gou et al. 2010

Soft X-ray Transient A : a * = 0.12  0.18 a * Time (days) Intensity (Crab) keV Flux density (mJy) _ _ 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

Three Spin Measurements in the Works for 2010 XTE J 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.)

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 A with a * ~ 0.1 indicates high spin not required to drive microquasar jets -- jets are likely disk driven