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Measuring the Masses and Spins of Stellar Black Holes

Measuring the Spin of the Accreting Black Hole In Cygnus X-1. Measuring the Masses and Spins of Stellar Black Holes. Lijun Gou Harvard -Smithsonian Center for Astrophysics.

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Measuring the Masses and Spins of Stellar Black Holes

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  1. Measuring the Spin of the Accreting Black Hole In Cygnus X-1 Measuring the Masses and Spins of Stellar Black Holes Lijun Gou Harvard-Smithsonian Center for Astrophysics Collaborators: Jeffrey McClintock, RameshNarayan, Mark Reid, Jerome, Orosz, Ronald Remillard, James Steiner, Jingen Xiang, Keith Arnauld, Shane Davis Tsinghua University, Beijing, China Oct 27th, 2011 Courtesy: A. Broderick & E. Mer

  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

  3. Introduction

  4. Two Classes of Black Holes Stellar-Mass: 10 M Supermassive: 106 – 109 M The Accretion Disk Courtesy: Rob Hynes Intermediate-mass black hole ??

  5. No-Hair Theorem • Mass: M • Spin: a* = ac/GM = J(c/GM2) (-1 a* 1) (a* = a/M by setting c=G=1) • Electric Charge: Q Charge neutralized and unimportant Kerr metric gives complete descriptions of astronomical BHs

  6. Stellar BHs only Both stellar and supermassiveBHs 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 • High-frequency X-ray oscillations (100-450 Hz) • X-ray polarimetry • Gravitational waves (LIGO, LISA…) • Other Methods of Measuring Spin Now Delivering Results

  7. Theoretical Foundation for Spin Measurement R >= Rms: Stable R < Rms: unstable Rms = RISCO (ISCO: innner-most stable circular orbit) rms Bardeen et al. 1972, ApJ, 172, 347

  8. Retrograde 90 km RISCO / M Prograde (for 10 M) Theoretical Foundation for Spin Measurement (cont.) Extreme Kerr 15 km Spin a* (= a/M)

  9. Innermost Stable Circular Orbit (ISCO) Identify RISCO with the inner edge of the accretion disk a* = 0 RISCO = 6rg=6M= 90 km a* = 1 RISCO = 1MG/c2= 15 km Extreme Kerr (or ≈ 1 AU for M = 107 M) for M = 10 M rg= GM/c2=M by setting c=G=1

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

  11. Stellar-Mass Black Holes

  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 Newton for mass 1,000,000 km Courtesy: R. Hynes Courtesy: Rob Hynes

  14. The Twenty-one Black Hole Binaries 0.39 AU P = 30 days i = 80 deg P = 4 hours Courtesy: J. Orosz i = 20 deg More at http://swift.gsfc.nasa.gov/docs/swift/results/transients/BlackHoles.html

  15. The Four Persistent Systems Wind-fed accretion

  16. 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) M2 = 70 M

  17. The Seventeen Transient Systems Roche-lobe accretion

  18. L ≈LEddington ~ 1039 erg/s 50 1-10 keV X-ray Intensity (Crab) 25 X-ray Outburst of Transient A0620-00 in 1975 10-7 max intensity! 0 0 50 100 Time (days)

  19. Continuum Fitting(stellar black holes only)

  20. Measuring the Inner Disk Radius RISCO

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

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

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

  24. Requirements for the Continuum Fitting MethodZhang, Cui & Chen 1997 • Spectrum dominated by accretion disk component • Spectrum dominated byaccretion disk component • Thin disk: H/R < 0.05 equivalent to L/LEddington < 0.3 H R Assume alignment of BH spin and orbital angular momentum

  25. Requirements for the Continuum Fitting MethodZhang, Cui & Chen 1997 • Spectrum dominated by accretion disk component • Disk models of spectral hardening (KERRBB & BHSPEC) Li et al. 2005; Davis et al. 2005, 2006, 2009; Davis & Hubeny 2006; Blaes et al. 2006 • Thin disk: H/R < 0.05 equivalent to L/LEddington < 0.3 H R Assume alignment of BH spin and orbital angular momentum

  26. Requirements for the Continuum Fitting MethodZhang, Cui & Chen 1997 • Spectrum dominated by accretion disk component • Disk models (KERRBB & BHSPEC) Li et al. 2005; avis et al. 2005, 2006, 2009; Davis & Hubeny 2006; Blaes et al. 2006 • Thin disk: H/R < 0.05 equivalent to L/LEddington < 0.3 H R

  27. Requirements for the Continuum Fitting MethodZhang, Cui & Chen 1997 • Spectrum dominated by accretion disk component • Disk models of spectral hardening (KERRBB & BHSPEC) Li et al. 2005; avis et al. 2005, 2006, 2009; Davis & Hubeny 2006; Blaes et al. 2006 • Thin disk: H/R < 0.05 equivalent to L/LEddington < 0.3 • Accurate input parameters: M, i and D H R Assume alignment of BH spin and orbital angular momentum

  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, self-irradiation, and limb darkening. It requires to fix the hardening factor f (Li et al. 2005). • BHSPECis 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 • Obtain the accurate dynamical system parameters of the system (2) Select spectra with strong thermal component (using the conventional non-relativistic disk model, DISKBB) (3) Analyze spectra and obtain results using relativistic thin disk model to selected spectra: KERRBB2=BHSPEC+KERRBB

  30. Spin Measurement for Cyg X-1

  31. First Black hole Candidate From Black holes and Time Warpsby Kip Thorne

  32. Distance, Mass Results for Cygnus X-1 before 2010 M2: black hole mass; Caballero-Nieves et al. (2009)

  33. Distance and Mass Results for Cygnus X-1 D = 1.86 ± 0.12 kpc VLBA parallax (Reid et al., ApJ, in press) M = 14.8 ± 1.0 M and i=27.1 ± 0.8 deg Modeling optical data (Orosz et al., ApJ, in press)

  34. Cygnus X-1: Parallax VLBA Parallax: 8.5 GHz Orbital Motion in the Plane of the Sky 0.5 East offset (mas) Parallax = 0.539 ± 0.033 mas 0 0.5 D = 1.86 kpc = 6060 light-years (±6%) -0.5 North offset (mas) 0 0.5 North offset (mas) 0 -0.5 -0.5 -0.5 0 0.5 2009 2010 Epoch (years) East offset (mas)

  35. Schematic Sketch of the X-ray Source

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

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

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

  39. Error Analysis via MC Simulation (cont.) ASCA+RXTE Chandra+RXTE > 10,000 CPU hours @ 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)

  42. The Iron-Line Method(both supermassive and stellar black holes)

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

  44. The “Reflected” Spectrum 1000 Incident power-law spectrum Incident power-law spectrum 10 Energy × (Energy Flux) 1 Fe K Fe K Reflected spectrum Reflected spectrum 0.1 1 10100 Energy (keV) Courtesy: R. Rubens

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

  46. Spin from Iron Line Method for Cyg X-1 RXTE PCA XMM-Newton EPIC-pn 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. Fe Kα 1 Data Counts / sec / keV Model 0.1 1.4 The “tender” red wing 1.2 Data / Model One More Example from Seyfert Galaxy MCG-6-30-15 1 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.

  48. Spin Result Summary For Twenty-one Black Hole Binaries 0.84 ± 0.05 0.92 ± 0.06 > 0.95 < 0.3 Spins & Masses constrain models of binary evolution & BH formation. > 0.98 0.70 ± 0.05 0.12 ± 0.18 0.34 ± 0.24 0.80 ± 0.05

  49. Two spin methods now in use • Continuum fitting –Stellar BHs only • Modeling Fe K line –Both stellar & supermassiveBHs • Both methods depend on disk inner edge Rinner = RISCO • 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 a*>0.95 at 3σ Conclusions • Accurate and plentiful spin data important to both astrophysics & physics

  50. Thanks

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