Measuring the Spin of the Accreting Black Hole In Cygnus X-1

Measuring the Masses and Spins of Stellar Black Holes Measuring the Spin of the Accreting Black Hole In Cygnus X-1 Lijun Gou Harvard-Smithsonian Center for Astrophysics Collaborators: Jeffrey McClintock, Ramesh Narayan, Mark Reid, Jerome, Orosz, Ronald Remillard, James Steiner, Jingen Xiang, Keith Arnauld, Shane Davis NAOC, Beijing, China Oct 25th, 2011

Outline Background introduction on black holes and spin measurement method Spin measurement for Cyg X-1 with Continuum fitting method Brief description on Iron line method Conclusions

Two Classes of Black Holes Stellar-Mass: 10 M Supermassive: 10 6 10 9 M Intermediate-mass black hole?? Courtesy: Rob Hynes

No-Hair Theorem Mass: M Spin: a * = ac/gm = J(c/GM 2 ) (-1 a * 1) (a * = a/m by setting c=g=1) Charge Electric neutralized Charge: and unimportant Q

Methods of Measuring Spin Now Delivering Results Continuum Fitting Method Fitting the thermal 1-10 kev spectrum of the accretion disk Fe K Method Fitting the relativistically-broadened profile of the 6.4 kev Fe K line Promising Methods for the Future

R >= R ms : Stable R < R ms : unstable r ms R ms = R ISCO (ISCO: innner-most stable circular orbit) Bardeen et al. 1972, ApJ, 172, 347

Spin a * (= a/m) Extreme Kerr

Innermost Stable Circular Orbit (ISCO) a * = 0 R ISCO = 6r g =6M = 90 km a * = 1 R ISCO = 1MG/c 2 = 15 km Extreme Kerr r g = GM/c 2 =M by setting c=g=1

Innermost Stable Circular Orbit (ISCO) Dependence on Spin Parameter a * = 0 R ISCO = 6M = 90 km a * = 1 R ISCO = 1M = 15 km

Stellar-Mass Black Hole Nursery A dozen hot massive stars in NGC 2244 Milky Way contains about 100,000,000 black holes

Black Hole X-ray Binary System Einstein for spin Inner disk: < 1000 km kt 1 kev 1,000,000 km Newton for mass Courtesy: Rob Hynes

The Twenty-one Black Hole Binaries 0.39 AU More at http://swift.gsfc.nasa.gov/docs/swift/results/transients/blackholes.html

The Four Persistent Systems Wind-fed accretion

Persistent System M33 X-7 Sun to scale Black Hole M = 15.7 1.7 M a * = 0.84 0.05 Orosz et al. (2007) Liu et al. (2008, 2010) M 2 = 70 M

The Seventeen Transient Systems Roche-lobe accretion

X-ray Intensity (Crab) 50 L L Eddington ~ 10 39 erg/s 1-10 kev 25 0 0 50 100 Time (days)

Measuring the Inner Disk Radius

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

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

df/d(lnr) Novikov & Thorne Thin-Disk Model: F(R) Four Identical Black Holes Differing Only in Spin 0.10 a * = 0.98 a * = 0.9 0.05 a * = 0.7 a * = 0 0 R / M Novikov & Thorne 1973

Requirements for the Continuum Fitting Method Spectrum dominated by Zhang, Cui & Chen 1997 Spectrum dominated by Thin disk: equivalent to

Requirements for the Continuum Fitting Method Spectrum dominated by Zhang, Cui & Chen 1997 Disk models of Li et al. 2005; Davis et al. 2005, 2006, 2009; Davis & Hubeny 2006; Blaes et al. 2006 Thin disk: equivalent to

Requirements for the Continuum Fitting Method Zhang, Cui & Chen 1997 Spectrum dominated by Disk models Li et al. 2005; avis et al. 2005, 2006, 2009; Davis & Hubeny 2006; Blaes et al. 2006 Thin disk: equivalent to

Requirements for the Continuum Fitting Method Zhang, Cui & Chen 1997 Spectrum dominated by Disk models of Li et al. 2005; avis et al. 2005, 2006, 2009; Davis & Hubeny 2006; Blaes et al. 2006 Thin disk: equivalent to input parameters:

Updated Disk Model: KERRBB2 A hybrid version of the KERRBB and BHSPEC. KERRBB is a fully relativistic model of a thin accretion disk around a kerr BH, including frame dragging, Doppler boosting, gravitational redshift, and light bending, selfirradiation, and limb darkening. It requires to fix the hardening factor f (Li et al. 2005). BHSPEC is also a relativistic disk model but without returning radiation. It is based on non-lte atmosphere model. Used to generate the hardening factor f input table for KERRBB (Davis & Hubeny, 2006).

Step Summary for Spin Measurement (1) Obtain the accurate dynamical system parameters of the system (2) Select spectra with strong thermal component (using the conventional nonrelativistic disk model, DISKBB) (3) Analyze spectra and obtain results using relativistic thin disk model to selected spectra: KERRBB2=BHSPEC+KERRBB

From Black holes and Time Warps by Kip Thorne

M 2 : black hole mass; Caballero-Nieves et al. (2009)

VLBA parallax (Reid et al., ApJ, in press) Modeling optical data (Orosz et al., ApJ, in press)

North offset (mas) East offset (mas) North offset (mas) 0.5 VLBA Parallax: 8.5 GHz Orbital Motion in the Plane of the Sky 0 Parallax = 0.539 ± 0.033 mas 0.5-0.5 0.5 0 0-0.5-0.5 2009 2010 Epoch (years) -0.5 0 0.5 East offset (mas)

Schematic Sketch of the X-ray Source

Two Examples of Soft-State Spectra (not Cyg X-1!) Flux XTE J1550-645 Steiner et al. (2011) Thermal 1 10 1 10

Cyg X-1: Spin via Continuum Fitting ASCA+RXTE a * =0.9911 ± 0.0009 ASCA+RXTE Chandra+RXTE a * =0.9911 ± 0.0009 a * =0.9999 ± 0.0171 a * =0.9999 ± 0.0081

Error Analysis via MC Simulation (1) Generate the 9000 sets of Gaussian-distributed parameters. (2) Solve the black hole mass from mass function, given inclination angle and optical star mass. (3) Repeat the fit.

Error Analysis via MC Simulation (cont.) ASCA+RXTE Chandra+RXTE > 10,000 CPU hours @ around 450 CPUs at Cluster Odyssey at Harvard

Extractable Spin Energy Christodolou & Ruffini (1971) Enough for powering a GRB via Penrose Process!

Origin of Extreme Spin Assuming by pure accretion King & Kolb (1999) (1) For a*> 0.95, accreted mass is > 7.3 Msun (2) Also assume the Eddington accretion rate, the accretion time scale is 31 million years. (3) Age of system lies between 4.6 and 7.8 million years (Wong et al. 2011) Spin is chiefly natal!!! Alternative: hypercritical mass accretion (Moreno Mendez 2011)

Schematic Sketch of the X-ray Source Continuum Fitting Iron Line

Energy (Energy Flux) 1 10 1000 The Reflected Spectrum 0.1 1 10 100 Energy (kev) Courtesy: R. Rubens

Intensity Intensity Dependence of Fe K Line Profile on Spin a * = 0 a * = 1 1 1 0 2 4 6 8 Energy (kev) 0 2 4 6 8 Energy (kev) Fabian et al. 1989

Spin from Iron Line Method for Cyg X-1 XMM-Newton EPIC-pn RXTE PCA XMM-Newton EPIC-pn a * =0.05 ± 0.01 (Miller et al. 2009) a * =0.88 ± 0.11 (Duro et al. 2011) No comment and no citation on the miller s result

Data / 1 1.2 1.4 Counts / sec / kev 0.1 1 Data 2 5 10 Energy (kev) a * =0.989 (-0.002, +0.009) (Brenneman & Reynolds, 2006) Alternatively, Noda et al. (2010) found non-spinning black hole.

Spin Result Summary For Twenty-one Black Hole Binaries 0.92 ± 0.06 0.84 ± 0.05 < 0.3 > 0.95 > 0.98 0.70 ± 0.05 0.12 ± 0.18 0.34 ± 0.24 0.80 ± 0.05

Two spin methods now in use Stellar BHs only Both stellar & supermassive BHs Both methods depend on disk inner edge Between these two methods, continuum fitting is much more robust For our favored model, the black hole primary in Cyg X-1 has a spin of at 3σ and spin data important to both astrophysics & physics

THANKS

Several questions should be addressed before obtaining the black hole spin: (1) Where is R ISCO located around a real black hole? (2) What states is optimal for the spin determination? (3) Which spectral component is the key ingredient for extracting the spin?

LMC X-3: 1983-2009 L / L Eddington

LMC X-3: 1983-2009 L / L Eddington R inner / M Steiner et al. 2010 R inner stable to 4%

Two Examples of Soft-State Spectra (not Cyg X-1!) Flux XTE J1550-645 Steiner et al. (2011) Thermal 1 10 1 10

Black Hole Spin a * Reference GRS 1915+105 > 0.98 McClintock et al. 2006 Cygnus X-1 > 0.97 Gou et al. 2011 LMC X-1 0.92 ± 0.06 Gou et al. 2009 M33 X-7 0.84 ± 0.05 Liu et al. 2008, 2010 4U 1543-47 0.80 ± 0.05 Shafee et al. 2006 GRO J1655-40 0.70 ± 0.05 Shafee et al. 2006 XTE J1550-564 0.34 ± 0.24 Steiner et al. 2011 LMC X-3 < 0.3 Davis et al. 2006 A0620-00 0.12 ± 0.18 Gou et al. 2009