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

Transcription

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

2 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

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

5 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

6 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

7 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

8 Spin a * (= a/m) Extreme Kerr

9 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

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

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

13 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

14 The Twenty-one Black Hole Binaries 0.39 AU More at

15 The Four Persistent Systems Wind-fed accretion

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

17 The Seventeen Transient Systems Roche-lobe accretion

18 X-ray Intensity (Crab) 50 L L Eddington ~ erg/s 1-10 kev Time (days)

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20 Measuring the Inner Disk Radius

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

22 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 *

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

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

25 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 Thin disk: equivalent to

26 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 Thin disk: equivalent to

27 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 Thin disk: equivalent to input parameters:

28 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).

29 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

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31 From Black holes and Time Warps by Kip Thorne

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

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

34 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 = ± mas Epoch (years) East offset (mas)

35 Schematic Sketch of the X-ray Source

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

37 Cyg X-1: Spin via Continuum Fitting ASCA+RXTE a * = ± ASCA+RXTE Chandra+RXTE a * = ± a * = ± a * = ±

38 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.

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

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

41 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)

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

44 Energy (Energy Flux) The Reflected Spectrum Energy (kev) Courtesy: R. Rubens

45 Intensity Intensity Dependence of Fe K Line Profile on Spin a * = 0 a * = Energy (kev) Energy (kev) Fabian et al. 1989

46 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

47 Data / Counts / sec / kev Data Energy (kev) a * =0.989 (-0.002, ) (Brenneman & Reynolds, 2006) Alternatively, Noda et al. (2010) found non-spinning black hole.

48 Spin Result Summary For Twenty-one Black Hole Binaries 0.92 ± ± 0.05 < 0.3 > 0.95 > ± ± ± ± 0.05

49 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

50 THANKS

51 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?

52 LMC X-3: L / L Eddington

53 LMC X-3: L / L Eddington

54 LMC X-3: L / L Eddington R inner / M Steiner et al R inner stable to 4%

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

56 Black Hole Spin a * Reference GRS > 0.98 McClintock et al Cygnus X-1 > 0.97 Gou et al LMC X ± 0.06 Gou et al M33 X ± 0.05 Liu et al. 2008, U ± 0.05 Shafee et al GRO J ± 0.05 Shafee et al XTE J ± 0.24 Steiner et al LMC X-3 < 0.3 Davis et al A ± 0.18 Gou et al. 2009

57 Black Hole Spin a * Reference GRS > 0.98 McClintock et al Cygnus X-1 > 0.97 Gou et al LMC X ± 0.06 Gou et al M33 X ± 0.05 Liu et al. 2008, U ± 0.05 Shafee et al GRO J ± 0.05 Shafee et al XTE J ± 0.24 Steiner et al LMC X-3 < 0.3 Davis et al A ± 0.18 Gou et al. 2009