The extreme spin of the black hole in Cygnus X-1

1. The extreme spin of the black hole in Cygnus X-1 McClintock et al.

2. Introduction • Cygnus X-1 - radio, optical, ultraviolet and X-ray • “Novikov-Thorne” model - relativistic, geometrically thin accretion disk - Kerr BH, no-turque boundary condition at disk’s inner edge (Novikov& Thorne 1973, Riffert & Herold 1995, Li et al. 2005 )

3. Low/hard states • typical • High/soft states • up to a year • prominent disk spectrum, • continuum-fitting method →spin • top: X-ray intensity relative to the Crab nebula • bottom: counts in hard X-ray band(5-12 keV)/those dected in soft band(1.5-5 keV) Suitable measurement for spin, SH<0.7, empirical choice

4. X-ray states : (Remillard & McClintock 2006) hard, thermal dominant (TD), soft, steep power law (SPL), and intermedate states (Homan & Belloni 2005) Cygnus X-1: low/hard, hard-intermediate and soft-intermediate ↔ hard, intermediate, SPL • Soft state ↔ steep power law (SPL), strong Compton component

5. Thermal dominant (TD) state (never observed) → spin via continuum-fitting method (Steiner et al. 2009a) • Spin a* ← Rin← RISCO (innermost stable circular orbit) • RISCO ← predicted by general relativity RISCO : 6Rg~1Rg ↔ a* : 0~1(Zhang et al. 1997) continuum-fitting, Fe Kαmethod Rin ~ RISCO, soft state of BHBs empirical : e.g. LMC X-3, stable, ~26yr(Done et al. 2007; Steiner et al. 2010) theorical : < RISCO disk emission falls off (Noble et al. 2010)

6. Before, TD-state data now, SPL data Rin→ a* consistent(<5%) with TD data if fSC ≤ 25% Comptonization SIMPL (Steiner et al. 2009b) • continuum-fitting method M, D, i + 3 soft-state X-ray spectra → spin a* fiducial value: M=14.8 ±1.0 M⊙ i=27⁰.1 ± 0⁰.8 (Orosz et al. 2011) D= kpc(Reid et al. 2011)

7. Data selection, observations, data reduction • A typical soft-state (and SPL) spectrum is comprised of three principal elements: a thermal component, a power-law component, and a reflected component(includes the Fe Kα emission line) needs: extend to 30 keV , SPL and reflected components; coverage down to ≈ 1 keV, thermal component (partially absorbed at low energies by intervening gas) • Few data contained in HEASARC data archive meet the requirement; seldom in disk-dominated state

8. Only find a single suitable spectrum SP1 → a* 1996 May 30th, using ASCA and RXTE Observation using RXTE all-sky monitor(ASM) Select: spectral hardness SH < 0.7, which occurs <10% of the time (reason for rarity) Enter soft-state in mid-2010 So obtain: broadband spectra on July 22th and July 24th

9. Observation on July 22th (SP2) , July 24th (SP3), using Chandra X-ray observatory and RXTE SP1: for ASCA, GIS2(0.7-8.0 keV) for RXTE, only use PCA(useful bandwith extends to 45 keV, 2.55-45.0 keV), disregard HEXTE SP2: HETG and ACIS(TE), “pile-up” SP3: HETG and ACIS(CC)

10. Data analysis • A typical spectrum of Cygnus X-1: a thermal component, a PL component and a reflected component that includes Fe Kα emission line accretion disk, corona

11. Data analysis and model fitting, using XSPEC version 12.6.0 (Arnaud 1996), errors at 1σ level of confidence • fiducial value: M=14.8 ±1.0 M⊙ i=27⁰.1 ± 0⁰.8 (Orosz et al. 2011) D= kpc(Reid et al. 2011) • Seven Preliminary Models 3 nonrelativistic models: Models NR1-NR3 - accretion-disk model component DISKBB(Mitsuda et al. 1984; Makishima et al. 1986) Model NR3, inner-disk radius and temperature

12. 4 relativistic models: Models R1-R4(progress sequentially) - fully relativistic accretion-disk model component KERRBB2, return 2 fit parameters, spin and the mass accretion rate • This paper presents the result for relativistic models(advanced, physically realistic) • The structure of adopted model(all components)

13. CRABCOR, correct detector effect • CONST, reconcile the calibration difference between detectors (normalization: RXTE, float: ASCA, Chandra) • TBABS, models low-energy absorption

14. results The results are in agreement with R1-R4, in the latter cases, a* >0.99 for all three spectra

16. For SP1, SP2 and SP3 respectively, Γ~2.5 → in SPL state Measure strength of Compton component TD state fSC≤5% (Steiner et al. 2009b) In SPL state, fSC≤25% → Rin→ a*(Steiner et al. 2009b)

17. Effect of iron line and edges • Omit component KERRDISK, 5-10 keV, Fe Kα line and edge results are unchanged, small shifts in parameters of reflection component → a* are detrmined by T and L of thermal component

18. Some challenges1. measurement of spin via a QPO Model Low-frequency(0.01-25Hz)QPOs, Axelsson et al. (2005) obtain Their result based on relativistic precession model of Stella et al. (1999) They predict a* =0.43, M = 14.8 Msun Discrepancy is because: a. in their model, BH rotates slow (a* << 1) b. their model’s assumption of geodesic motion may not apply in this instance

19. 2. Alignment of spin and orbital angular momentum • Recent studies predict that the majority of systems have small misalignment angles(<10⁰) (Fragos et al. 2010) D=1.86 kpc M=14.8 Msun i=27.1⁰ Misalignment angle as large as 16 ⁰, spin value is still >0.95

20. Conclusion • a* > 0.95 at 3σ level of confidence • Measurement of spin is determined by thermal component and is unaffected by the relatively faint Fe Kα line • The extreme spin we find for this BH is based on analysis of three spectra that each capable of soft theral component, the hard Compton component, and the reflected component. • Consider several case, find spin is insensitive to details of our analysis

21. Thank you !