Transcript Black Hole Accretion

Ramesh Narayan
What Is a Black Hole?
“Normal”
Object
Black Hole
Surface
Event
Horizon
Singularity

Black Hole: A remarkable prediction of Einstein’s General
Theory of Relativity – represents the victory of gravity
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Matter is crushed to a SINGULARITY
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Surrounding this is an EVENT HORIZON
What is the Mass of a BH?
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A BH can have any mass above 10-5 g (Planck
mass --- quantum gravity limit)
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Unclear if very low-mass BHs form naturally
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BHs more massive than ~3M are very likely:
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Form quite naturally by gravitational collapse of
massive stars at the end of their lives
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No other stable equilibrium available at these masses
Enormous numbers of such BHs in the universe
Astrophysical Black Holes
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Two distinct varieties of Black Holes are
known in astrophysics:
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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 Binaries
MBH ~ 5—20 M
Image credit: Robert Hynes
Galactic Nuclei
MBH ~ 106—1010 M
Image credit: Lincoln Greenhill, Jim Moran
A Black Hole is
Extremely Simple
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Mass: M
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Spin: a* (J=a*GM2/c)
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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”
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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
The best mass estimates in astronomy are
dynamical: a test particle in a circular orbit
satisfies (by Newton’s laws):
GM
v2

2
r
r
v3 P
M 
2 G
If v and P are measured, we can obtain M
Earth-Sun: v=30 km/s, P=1yr  M
v
M
Masses of Stars
in Binaries
Observations give
vr : radial velocity of secondary
P : orbital period of binary
These two quantities give the mass
function:
v3r P
sin 3 i
f (M ) 
 MX
2
2 G
1  M s / M X 
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 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
0.130.05
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
2.730.56
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
5.750.30
GX 339-4
>5.3
5.80.5
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
Schodel et al. (2002)
Ghez et al. (2005)
M=4.5106 M
Supermassive Black Holes in
Other Galactic Nuclei
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BHs identified in nuclei of many other galaxies
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BH masses obtained in several cases, though
not as cleanly as in the case of our own Galaxy
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MBH ~ 106—1010M
Virtually every galaxy has a supermassive black
hole at its center!
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)
Black Hole Spin
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Mass: M 
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Spin: a* 
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Charge: Q
Black Hole Spin
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The material from which a BH forms
always has some angular momentum
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Also, accretion adds angular momentum
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So we expect astrophysical BHs to be
spinning: J = a*GM2/c, 0  a*  1
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a*=0 (no spin), a*=1 (maximum spin)
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How do we measure a* ?
Mass is Easy, Spin is Hard
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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
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X-Ray Continuum Spectrum 
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Relativistically Broadened Iron Line 
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Quasi-Periodic Oscillations ?
Circular Orbits
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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)
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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)
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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 Idea
Measure radius of hole by estimating area of the bright inner disk
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
Radiation
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The theory of radiation
was worked out by many
famous physicists:
Rayleigh, Jeans, Wien,
Stefan, Boltzmann,
Planck, Einstein,…
Wien's Displacement Law
Tmax  0.29 cm K
Stefan-Boltzmann Law
F  T 4
Blackbody spectrum
from a hot opaque
object for different
temperatures
(ref: Wikipedia)
Measuring the Radius of a Star
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Measure the flux F received from the star
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Measure the temperature T* (from spectrum)
L*  4 D 2 F  4 R*2 T*4
 R*2
F
  2 
D
 T*4
F 1/2 D
R*  1/2 2
 T*
R*
Measuring the Radius of the
Disk Inner Edge
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We want the radius of the “hole” in the disk emission
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Same principle as for a star
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From X-ray data we obtain
FX and TX  bright
RISCO
RISCO
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); …
Relativistic
Effects
Movie credit:
Chris Reynolds
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Consistent disk flux profile (Novikov & Thorne 1973)
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Doppler shifts (blue and red) of the orbiting gas
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Gravitational redshift
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Deflection of light rays
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Self-irradiation of the disk
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All these have to be included consistently (Li et al. 2005)
L / LEdd
LMC X-3: 1983 - 2009
LMC X-3
Thick Disk
L / LEdd
LMC X-3: 1983 - 2009
Hard State
LMC X-3
Rin
L / LEdd
LMC X-3: 1983 - 2009
LMC X-3
Steiner et al. (2010)
403 spectra (assuming M=10M, i=67o)
XTE J1550-564
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)
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 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
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)
Importance of BH Spin
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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
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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?
Relativistic
Jets
Cygnus A
Superluminal Relativistic Jets
Chandra XRC
Chandra XRC
Radio Quasar 3C279
with MBH ~ few x 107 M⊙(?)
X-ray Binary GRS 1915+105
with MBH ~ 15 M⊙
16 March 1994
3 April 1994
9 April 1994
16 April 1994
3.5c
1.9c
NRAO/AUI
27 March 1994
Energy from a Spinning
Black Hole
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A spinning BH has free energy that can
in principle be extracted (Penrose 1969),
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The BH is like a flywheel
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But how do we “grip” the BH and access
this energy?!
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Most likely with magnetic fields
(“Magnetic Penrose Effect”)
Semenov et al. (2004)
BH Spin Values vs
Relativistic Jets
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
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)
Can We Test the
No-Hair Theorem?
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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…
Summary
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Many astrophysical BHs have been
discovered during the last ~20 years
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There are two distinct populations:
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X-ray binaries: 5—20 M (107 per galaxy)
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Galactic nuclei: 106-10 M (1 per galaxy)
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BH spin estimates are now possible
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Profound effects may be connected to spin
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Next frontier: The No-Hair Theorem