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

McClintock et al.

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 )

• 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

• 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

• 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 Kα method 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)

1// 2 awithGMcJRaa g

• 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)12.011.086.1

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

• 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-2010So obtain: broadband spectra on July 22th and July 24th

• 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)

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

• 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

12.011.086.1

• 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)

)](2[

SIMPLCIREFLECTKERRCONVKERRDISKKERRBBSIMPLRTBABSCONSTCRABCOR

• CRABCOR, correct detector effect• CONST, reconcile the calibration difference between

detectors (normalization: RXTE, float: ASCA, Chandra)• TBABS, models low-energy absorption

)](2[

SIMPLCIREFLECTKERRCONVKERRDISKKERRBBSIMPLRTBABSCONSTCRABCOR

results

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

)28.1,17.1(2 v

%6.0%6.30%,2.1%5.30%,6.0%5.22

andfSC

For SP1, SP2 and SP3 respectively, Γ~2.5 → in SPL stateMeasure strength of Compton componentTD state fSC≤5% (Steiner et al. 2009b)

In SPL state, fSC≤25% → Rin → a* (Steiner et al. 2009b)

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

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

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 kpcM=14.8 Msuni=27.1⁰

Misalignment angle as large as 16 ⁰, spin value is still >0.95

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

Thank you !