1. Astrophysical
Black Holes
Ramesh Narayan

2. What Is a Black Hole? “Normal” Object Black Hole
Surface
Black Hole
Singularity
Event Horizon
Black Hole: A remarkable prediction of Einstein’s General Theory of Relativity – represents the victory of gravity
Matter is crushed to a SINGULARITY
Surrounding this is an EVENT HORIZON

3. Space Near a BH is Strange
Light rays are strongly bent
Close enough to a BH, you will be able to see the back of your head!
Other strange effects near a spinning BH: Space-time dragging BH

4. What is the Mass of a BH?
A BH can have any mass above 10-5 g (Planck mass --- quantum gravity limit)
Unclear if very low-mass BHs form naturally
BHs more massive than ~3M are very likely:
Form quite naturally by gravitational collapse of massive stars at the end of their lives
No other stable equilibrium available at these masses
Enormous numbers of such BHs in the universe

5. Astrophysical Black Holes
Two distinct varieties of Black Holes are known in astrophysics:
Stellar-mass BHs: M ~ 5–20 M
Supermassive BHs: M ~ 106–1010 M
There are intriguing claims of a class of Intermediate Mass BHs (103–105 M), but the evidence is not yet compelling

6. Image credit: Robert Hynes
X-ray Binaries
MBH ~ 5—20 M
Image credit: Robert Hynes

7. Galactic Nuclei MBH ~ 106—1010 M
Image credit: Lincoln Greenhill, Jim Moran

8. A Black Hole is Extremely Simple
Mass: M
Spin: a* (J=a*GM2/c)
Charge: Q
A Black Hole has no Hair! (No Hair Theorem)

9. The black holes of nature are the most perfect macroscopic objects there are in the universe: the only elements in their construction are our concepts of space and time. And since the general theory of relativity provides only a single unique family of solutions for their description, they are the simplest objects as well.
Chandrasekhar: Prologue to his book “The Mathematical Theory of Black Holes”

10. Chandrasekhar: Nora & Edward Ryerson Lecture “Patterns of Creativity”
In my entire scientific life, extending over forty-five years, the most shattering experience has been the realization that an exact solution of Einstein's equations of general relativity, discovered by the New Zealand mathematician, Roy Kerr, provides the absolutely exact representation of untold numbers of massive black holes that populate the universe.
Chandrasekhar: Nora & Edward Ryerson Lecture “Patterns of Creativity”

11. Measuring Mass is “Easy”
Astronomers have been measuring masses of heavenly bodies for centuries
Mass of the Sun measured using the motion of the Earth
Masses of planets like Jupiter, Saturn, etc., from motions of their moons
Masses of stars, galaxies,…

12. Measuring Mass in Astronomy
The best mass estimates in astronomy are dynamical: a test particle in a circular orbit satisfies (by Newton’s laws):
If v and P are measured, we can obtain M
Earth-Sun: v=30 km/s, P=1yr  M v M

13. Masses of Stars in Binaries
Observations give
vr : radial velocity of secondary
P : orbital period of binary
These two quantities give the mass function:
Often, Ms  MX, so finite Ms is not an issue for measuring MX
The inclination i is more serious : Various methods to estimate it Eclipsing systems are best
GRS Filippenko et al. (1999)

14. M33 X-7: eclipsing BH XRB (Pietsch et al. 2006; Orosz et al. 2007)
This BH is more than 100 times farther than most known BHs in our Galaxy and yet it has quite a reliable mass!

15. Binary Likely MX(M) f(M)=MX,min(M)
LMC X-1
9.4—12.4
0.130.05
Cyg X-1
13.8—15.8
0.244 0.005 4U
8.4—10.4
0.25  0.01
M33 X-7
14.2—17.1
0.46  0.08
GRO J
3.2—13.2
1.19  0.02
LMC X-3
5.9—9.2
2.3  0.3 A
6.3—6.9
2.72  0.06
GRO J
6.0—6.6
2.73  0.09
XTE J
>2.2
2.730.56
GRS
6.5—8.2
3.01  0.15
SAX J
6.8—7.4
3.13  0.13
GRS
6.3—8.0
3.17  0.12 H
5.6—8.3
4.86  0.13 GS
7.1—7.8
5.01 0.12 GS
>5.4
5.750.30
GX 339-4
>5.3
5.80.5 GS
10.1—13.4
6.08  0.06
XTE J
6.5—7.2
6.1  0.3
XTE J
8.5—9.7
6.86  0.71
XTE J
7.6—12.0
7.4  1.1
GRS
10—18
9.5  3.0

16. Stellar Dynamics at the Galactic Center
Schodel et al. (2002) Ghez et al. (2005)
M=4.5106 M

17. Supermassive Black Holes in Other Galactic Nuclei
BHs identified in nuclei of many other galaxies
BH masses obtained in several cases, though not as cleanly as in the case of our own Galaxy
MBH ~ 106—1010M
Virtually every galaxy has a supermassive black hole at its center!

18. The MBH- Relation
There is a remarkable correlation between the mass of the central supermassive black hole and the velocity dispersion of the stars in the galaxy bulge: MBH- relation
There is also a relation between MBH and galaxy luminosity L
Important clue on the formation/evolution of SMBHs and galaxies
Gultekin et al. (2009)

19. Black Hole Spin
Mass: M 
Spin: a* 
Charge: Q

20. Black Hole Spin
The material from which a BH forms always has some angular momentum
Also, accretion adds angular momentum
So we expect astrophysical BHs to be spinning: J = a*GM2/c, 0  a*  1
a*=0 (no spin), a*=1 (maximum spin)
How do we measure a* ?

21. Mass is Easy, Spin is Hard
Mass can be measured in the Newtonian limit using test particles (e.g., stellar companion) at large radii
Spin has no Newtonian effect
To measure spin we must be in the regime of strong gravity, where General Relativity operates
Need test particles at small radii
Fortunately, we have the gas in the accretion disk…

22. Estimating Black Hole Spin
X-Ray Continuum Spectrum 
Relativistically Broadened Iron Line 
Quasi-Periodic Oscillations ?

23. Circular Orbits
In Newtonian gravity, stable circular orbits are available at all R
Not true in General Relativity
For a non-spinning BH (Schwarzschild metric), stable orbits only for R  6M
R=6M is the innermost stable circular orbit, or ISCO, of a non-spinning BH
The radius of the ISCO (RISCO) depends on the BH spin

24. Innermost Stable Circular Orbit (ISCO)
RISCO/M depends on the value of a*
If we can measure RISCO, we will obtain a*
Note factor of 6 variation in RISCO
Especially sensitive as a*1

25. Innermost Stable Circular Orbit (ISCO)
RISCO/M depends on the value of a*
If we can measure RISCO, we will obtain a*
Note factor of 6 variation in RISCO
Especially sensitive as a*1

26. Measure radius of hole by estimating area of the bright inner disk
The Basic Idea
Measure radius of hole by estimating area of the bright inner disk

27. How to Measure the Radius?
How can we measure the radius of something that is so small even our best telescopes cannot resolve it?
Use Blackbody Theory!

28. BlackBody Radiation
The theory of radiation was worked out by many famous physicists: Rayleigh, Jeans, Wien, Stefan, Boltzmann, Planck, Einstein,…
Blackbody spectrum from a hot opaque object for different temperatures (ref: Wikipedia)

29. Measuring the Radius of a Star
Measure the flux F received from the star
Measure the temperature T* (from spectrum) R*

30. Measuring the Radius of the Disk Inner Edge
We want the radius of the “hole” in the disk emission
Same principle as for a star
From X-ray data we obtain FX and TX  bright
Knowing distance D and inclination i we get RISCO (some geometrical factors)
From RISCO/M we get a*
Zhang et al. (1997); Li et al. (2005); Shafee et al. (2006); McClintock et al. (2006); Davis et al. (2006); Liu et al. (2007); Gou et al. (2009,2010); …
RISCO
RISCO

31. Relativistic Effects Movie credit: Chris Reynolds
Consistent disk flux profile (Novikov & Thorne 1973)
Doppler shifts (blue and red) of the orbiting gas
Gravitational redshift
Deflection of light rays
Self-irradiation of the disk
All these have to be included consistently (Li et al. 2005)

32. LMC X-3:
L / LEdd
LMC X-3

33. LMC X-3:
Thick Disk
L / LEdd
Hard State
LMC X-3

34. 403 spectra (assuming M=10M, i=67o)
LMC X-3:
L / LEdd
LMC X-3
Rin
Steiner et al. (2010)
403 spectra (assuming M=10M, i=67o)

35. XTE J
Estimates of disk inner edge Rin and BH spin parameter a* from 35 TD (superb) and 25 SPL/Intermediate (so-so) data (Steiner et al. 2010)

36. BH Masses and Spins Source Name BH Mass (M) BH Spin (a*) A0620-00
6.3—6.9
0.12 ± 0.19
LMC X-3
5.9—9.2
~0.25
XTE J
8.5—9.7
0.34±0.24
GRO J
6.0—6.6
0.70 ± 0.05 4U
8.4—10.4
0.80 ± 0.05
M33 X-7
14.2—17.1
0.84 ± 0.05
LMC X-1
9.4—12.4
0.92 ± 0.06
Cyg X-1
13.8—15.8
> 0.97
GRS
10—18
> 0.98
Shafee et al. (2006); McClintock et al. (2006); Davis et al. (2006); Liu et al. (2007,2009); Gou et al. (2009,2010, 2011); Steiner et al. (2010)

37. Importance of BH Spin
Of the two parameters, mass and spin, spin is more fundamental
Mass is merely a scale – just tells us how big the BH is
Spin fundamentally affects the basic properties of space-time around the BH
More than a simple re-scaling

38. Spinning BHs Horizon shrinks: e.g., RHGM/c2 as a*1
Particle orbits are modified
Singularity becomes ring-like
Frame-dragging --- Ergosphere
Energy can be extracted from the BH (Penrose 1969)
Does this explain jets?

39. Relativistic Jets
Cygnus A

40. Superluminal Relativistic Jets
Chandra XRC
Chandra XRC
Radio Quasar 3C279 with MBH ~ few x 107 M⊙(?)
X-ray Binary GRS with MBH ~ 15 M⊙
16 March 1994
NRAO/AUI
27 March 1994
3 April 1994
9 April 1994
16 April 1994
3.5c
1.9c

41. Energy from a Spinning Black Hole
A spinning BH has free energy that can in principle be extracted (Penrose 1969),
The BH is like a flywheel
But how do we “grip” the BH and access this energy?!
Most likely with magnetic fields (“Magnetic Penrose Effect”)

42. Semenov et al. (2004)

43. BH Spin Values vs Relativistic Jets
Source Name
BH Mass (M)
BH Spin (a*)
A (J)
6.3—6.9
0.12 ± 0.19
LMC X-3
5.9—9.2
~0.25
XTE J (J)
8.5—9.7
0.34±0.24
GRO J (J)
6.0—6.6
0.70 ± 0.05
4U (J)
8.4—10.4
0.80 ± 0.05
M33 X-7
14.2—17.1
0.84 ± 0.05
LMC X-1
9.4—12.4
0.92 ± 0.06
Cyg X-1 (J)
13.8—15.8
> 0.97
GRS (J)
10—18
> 0.98
Shafee et al. (2006); McClintock et al. (2006); Davis et al. (2006); Liu et al. (2007,2009); Gou et al. (2009,2010, 2011); Steiner et al. (2010)

44. Can We Test the No-Hair Theorem?
After we measure M, a* with good accuracy for a number of BHs, what next?
Plenty of astrophysical phenomenology could potentially be explained…
Perhaps we can come up with a way of testing the No-Hair Theorem
No good idea at the moment…

45. Relevance of Black Hole Spin
Spin is likely important in a variety of contexts in ASTROPHYSICS:
May be responsible for relativistic jets
May be connected to gamma-ray bursts
Angular momenta of progenitor stars
Clues to galaxy merger history
Affects gravitational wave signals …

46. Summary
Many astrophysical BHs have been discovered during the last ~20 years
There are two distinct populations:
X-ray binaries: 5—20 M (107 per galaxy)
Galactic nuclei: M (1 per galaxy)
BH spin estimates are now possible
Profound effects may be connected to spin
Next frontier: The No-Hair Theorem