1. Measuring the SPIN of Black Holes
Andy Fabian
Institute of Astronomy
University of Cambridge

2. Astrophysical Black Holes have only
MASS and SPIN
(like elementary particles, except BH can have any mass )

3. BLACK HOLES
Karl Schwarzschild
Roy Kerr

4. MASS can be measured over wide range of radii
but SPIN requires measuring properties at small radii
What effects are characteristic of small radii around a Black Hole?

5. Strong Gravity Effects
Gravitational redshift
Gravitational light bending
Dragging of inertial frames in Kerr metric (ISCO depends on BH spin)

6. GPS GR=45microsec/day (or ~10km/day)

7. GRAVITATIONAL LIGHT BENDING

8. Information from spectra and variability
X-ray ‘reflection’ gives important clues in the spectrum
Variability timescales and spectral changes show different spectral components

9. Reflection from photoionized matter
(Ross & Fabian 93, 05)
Also see Young+, Nayakshin+, Ballantyne+, Rozanska+, Dumont+

10. Fabian+89, Laor 90… Dovciak+04; Beckwith+Done05
Schwarzschild
Kerr
Fabian+89, Laor 90… Dovciak+04; Beckwith+Done05

11. MCG
Suzaku
Red wing due to large gravitational redshift
implying BH rapidly spinning
Strength and behaviour of line implies GRAVITATIONAL LIGHT BENDING

12. Lockman Hole 800 ks XMM-Newton observation
Hasinger

13. Lockman Hole 800 ks XMM-Newton observation
Hasinger
Streblyanskaya et al 2004

14. Radius of innermost stable circular orbit-ISCO
Assumption: measurements of rISCO determine (or constrain) a

15. Probing Black Hole Spin

17. Light bending model in Kerr spacetime
Miniutti et al 03; Miniutti & Fabian 04; earlier work by Martocchia, Matt+
see also Tsuebsuwong, Malzac+06

19. Armitage & Reynolds

20. SPIN also affects radiative efficiency of accretion, η

21. TNT
Nuclear fusion
Black Hole Accretion
Max spin BH accretion

22. Accretion makes massive black holes
Soltan 82
Mean redshift
Radiative efficiency
Light Mass density in BH
η > 0.1
Observations
Much of the radiation originates within 6Rg

23. Accretion makes massive black holes
Soltan 82
Mean redshift
Radiative efficiency
Light Mass density in BH
η > 0.1
Observations
Most Massive BH are rapidly spinning