Ramesh Narayan

What Is a Black Hole?What Is a Black Hole?

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

“Normal” Object

Surface

Black Hole

Singularity

Event Horizon

What is the Mass of a BH?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

Astrophysical Black Holes

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

X-ray BinariesX-ray Binaries

Image credit: Robert Hynes

MBH ~ 5—20 M

Galactic NucleiGalactic Nuclei

Image credit: Lincoln Greenhill, Jim Moran

MBH ~ 106—1010 M

A Black Hole is Extremely Simple

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)

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”

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”

Measuring Mass is “Easy”

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,…

Measuring Mass in Astronomy

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

2

2

3

v

v

2

GM

r r

PM

G

M

v

Masses of Stars in Binaries

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

3 3

2

v sin( )

2 1 /r

X

s X

P if M M

G M M

GRS 1009-45 Filippenko et al. (1999)

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!

Binary Likely MX(M) f(M)=MX,min(M)

LMC X-1 9.4—12.4 0.130.05

Cyg X-1 13.8—15.8 0.244 0.005

4U1543-47 8.4—10.4 0.25 0.01

M33 X-7 14.2—17.1 0.46 0.08

GRO J0422+32 3.2—13.2 1.19 0.02

LMC X-3 5.9—9.2 2.3 0.3

A0620-00 6.3—6.9 2.72 0.06

GRO J1655-40 6.0—6.6 2.73 0.09

XTE J1650-500 >2.2 2.730.56

GRS 1124-683 6.5—8.2 3.01 0.15

SAX J1819.3-2525 6.8—7.4 3.13 0.13

GRS 1009-45 6.3—8.0 3.17 0.12

H1705-250 5.6—8.3 4.86 0.13

GS 2000+250 7.1—7.8 5.01 0.12

GS 1354-64 >5.4 5.750.30

GX 339-4 >5.3 5.80.5

GS 2023+338 10.1—13.4 6.08 0.06

XTE J1118+480 6.5—7.2 6.1 0.3

XTE J1550-564 8.5—9.7 6.86 0.71

XTE J1859+226 7.6—12.0 7.4 1.1

GRS 1915+105 10—18 9.5 3.0

Stellar Dynamics at the Galactic Center

Stellar Dynamics at the Galactic Center

Schodel et al. (2002) Ghez et al.

(2005)

M=4.5106 M

Supermassive Black Holes in Other Galactic Nuclei

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!

The MMBHBH-- RelationThe MMBHBH-- RelationThere 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)

Black Hole SpinBlack Hole Spin

Mass: M

Spin: a*

Charge: Q

Black Hole SpinBlack 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* ?

Mass is Easy, Spin is Hard

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…

Estimating Black Hole Spin

Estimating Black Hole Spin

X-Ray Continuum Spectrum

Relativistically Broadened Iron

Line

Quasi-Periodic Oscillations ?

Circular OrbitsCircular 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

Innermost Stable Circular Orbit (ISCO)

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

Innermost Stable Circular Orbit (ISCO)

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

The Basic IdeaThe Basic Idea

Measure radius of hole by estimating area of the bright inner disk

How to Measure the Radius?

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!

BlackBody RadiationBlackBody Radiation

The theory of radiation was worked out by many famous physicists: Rayleigh, Jeans, Wien, Stefan, Boltzmann, Planck, Einstein,…

max

4

Wien's Displacement Law

T 0.29cm K

Stefan-Boltzmann Law

F T

Blackbody spectrum from a hot opaque object for

different temperatures

(ref: Wikipedia)

Measuring the Radius of a Star

Measuring the Radius of a Star

Measure the flux F received from the star

Measure the temperature T* (from

spectrum)

R*

2 2 4* * *

2*2 4

*

1/2

* 1/2 2*

4 4L D F R T

R F

D T

F DR

T

Measuring the Radius of the Disk Inner Edge

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); …

RISCORISCO

Relativistic Effects

Relativistic Effects

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)

Movie credit: Chris Reynolds

LMC X-3: 1983 - 2009LMC X-3: 1983 - 2009L

/ LE

dd

LMC X-3

LMC X-3: 1983 - 2009LMC X-3: 1983 - 2009L

/ LE

dd

LMC X-3

Thick Disk

Hard State

LMC X-3: 1983 - 2009LMC X-3: 1983 - 2009L

/ LE

dd

Rin

Steiner et al. (2010)403 spectra (assuming M=10M,

i=67o)

LMC X-3

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)

XTE J1550-564

BH Masses and SpinsBH Masses and Spins

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)

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 J1550-564 8.5—9.7 0.34±0.24

GRO J1655-40 6.0—6.6 0.70 ± 0.05

4U1543-47 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 1915+105 10—18 > 0.98

Importance of BH SpinImportance 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

Spinning BHs

Spinning BHs

Horizon shrinks: e.g., RHGM/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?

Relativistic Jets

Relativistic Jets

Cygnus A

X-ray Binary GRS 1915+105 with MBH ~ 15

M⊙

1.9c

16 March 1994

27 March 1994

3 April 1994

9 April 1994

16 April 1994

NR

AO

/AU

I

Superluminal Relativistic JetsChandra XRC

Chandra XRC

Radio Quasar 3C279 with MBH ~ few x 107 M⊙(?)

3.5c

Energy from a Spinning Black Hole

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”)

Semenov et al. (2004)

BH Spin Values vs Relativistic Jets

BH Spin Values vs Relativistic Jets

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)

Source Name BH Mass (M) BH Spin (a*)

A0620-00 (J) 6.3—6.9 0.12 ± 0.19

LMC X-3 5.9—9.2 ~0.25

XTE J1550-564 (J)

8.5—9.7 0.34±0.24

GRO J1655-40 (J) 6.0—6.6 0.70 ± 0.05

4U1543-47 (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 1915+105 (J)

10—18 > 0.98

Can We Test the No-Hair Theorem?

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…

SummarySummary 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: 106-10 M (1 per galaxy)

BH spin estimates are now possible

Profound effects may be connected to

spin

Next frontier: The No-Hair Theorem