Transcript Black Hole Accretion - Institute of Mathematical Sciences

THE BLACK HOLE
EVENT HORIZON
Ramesh Narayan
The Black Hole
“Normal”
Object
Black Hole
Surface
Event
Horizon
Singularity
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A remarkable prediction of the General Theory of Relativity
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Matter is crushed to a SINGULARITY
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Surrounding this is an EVENT HORIZON
BH is defined by the presence of an Event Horizon
Conceptually, a BH is Very
Strange & Mysterious
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Just because our theory/equations (GR)
give BH solutions, should we believe that
BHs actually do exist?
Surely, Nature must have some trick up
her sleeve to avoid forming BHs
Many great scientists (even Chandrasekhar
himself for a while?) have wondered
However…
The Universe Appears to be
Full of Black Holes
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Theory: Neutron stars, strange stars, or
other kinds of compact objects cannot
be more massive than ~ 3M
Observations: The most massive
neutron star discovered so far is ~ 2M
Any compact relativistic object with
mass > 3M MUST BE A BLACK HOLE
Huge numbers of these in the Universe
X-ray Binaries
MBH ~ 5—20 M
Millions of these
BHs in each galaxy
Image credit: Robert Hynes
Galactic Nuclei
MBH ~ 106—1010 M
One supermassive
BH in each galaxy
Image credit: Lincoln Greenhill, Jim Moran
But: Are Astrophysical Black
Holes Really Black Holes?
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We know that astrophysical “BHs” are:
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Compact: R  few RS (RS2GM/c2)
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Massive: M  3M (not neutron stars)
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But can we be sure that they are really BHs?
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Would be good to find independent evidence that
BH candidates actually possess Event Horizons
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Recall: BH is DEFINED by Event Horizon (not mass)
In Search of the
Event Horizon
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Accretion flows are
very useful, since
inflowing gas reaches
the center and “senses”
the nature of the central object:
Can distinguish Event Horizon from Stellar
Surface
Signatures of the Event
Horizon (Lack of a Surface)
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Differences in quiescent luminosities of XRBs (Narayan, Garcia &
McClintock 1997; Garcia et al. 2001; McClintock et al. 2003;…)
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Differences in Type I X-ray bursts between NSXRBs and
BHXRBs (Narayan & Heyl 2002; Tournear et al. 2003; Yuan,
Narayan & Rees 2004; Remillard et al. 2006)
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Differences in X-ray colors of XRBs (Done & Gierlinsky 2003)
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Differences in thermal surface emission of NSXRBs and BHXRBs
(McClintock, Narayan & Rybicki 2004)
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Infrared flux of Sgr A* (Broderick & Narayan 2006, 2007;
Broderick, Loeb & Narayan 2009)
Physics of
Accretion
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Gas with angular momentum goes into orbit
at a large radius around the BH
Slowly spirals in by “viscosity” (magnetic
stresses) and falls into the BH at the center
Potential energy is converted into orbital
kinetic energy and thermal energy:
Thermal energy is radiated, partly from the
disk and partly from the stellar surface
Basic
Idea
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Lsurf
Lacc
The surface luminosity from the central star is
predicted to be always important: Lsurf  Lacc
Unless there is no surface of course (i.e., a BH)
We look for systems that have negligible surface
luminosity  these must be BHs
This is potentially a very robust argument since
it uses only energy conservation
How Much Luminosity
from the Surface?
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In a Newtonian analysis, if the accretion
disk extends down to the radius of the
central star R*, the binding energy of
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a circular orbit at R* is GM/2R*
material at rest on stellar surface is ~GM/R*
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Lacc  GM M / 2 R*
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Lsurf
GM M / 2 R*  Lacc
Relativistic Case
Schwarzschild "Star"
[ R*  RISCO  6 M ]

2
Lacc  0.0572 M c 2
Energy per unit mass (units of c )
At infinity: e  1
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Lsurf  0.1263 M c 2
Circular orbit at radius R *: ecirc ( R* )
[ R*  RBuchdahl  (9 / 4) M ]
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At rest on stellar surface: erest ( R* )
Lacc  0.0572 M c 2
Luminosity
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Lsurf  0.6095 M c 2
(radiatively efficient)
[ R*  Rgravastar  2 M ]
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Accretion: Lacc  1  ecirc ( R* ) M
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Surface: Lsurf   ecirc ( R* )  erest ( R* ) M
Lacc  0.0572 M c 2

Lsurf  0.9428 M c 2
On To Our “Evidence” for
the Event Horizon
An exercise in logic using
simple physics
 Discussion is in two parts:
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The “Evidence”
 Search for Loopholes
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The Black Hole at the
Center of Our Galaxy
Dark Mass at the Galactic Center:
M ~ 4x106 M
(inferred from stellar motions)
Stellar Dynamics at the
Galactic Center
Schodel et al. (2002)
MBH=4.00.2106 M
Radio Source at the GC:
Sagittarius A*
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There is a compact radio source, Sagittarius A*
(Sgr A*) located at the Galactic Center
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Very Long Baseline Interferometer (VLBI)
observations place an exquisitely tight limit on
the velocity of Sgr A*:
-0.4  0.9 km s-1 (Reid & Brunthaler 2004)
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Brownian motion analysis suggests a mass of at
least 105 M i.e. Sgr A* is the BH candidate
Nearly all the motion is in longitude, due
to the orbital motion of the Sun
Small motion in latitude is entirely
consistent with the Sun’s peculiar velocity
Luminosity and Spectrum
of Sgr A*
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Sgr A* is a rather dim
source with a luminosity of
~1036 erg/s
Most of the emission is in
the sub-mm
Is this radiation from the
accretion flow or from the
surface?
Sub
mm
Sgr A* is Ultra-Compact
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Radio VLBI images show that Sgr A* is
extremely compact (Shen et al. 2005;
Doeleman et al. 2008; Fish et al. 2010)
Size ~ few RS
From the observed radio flux, estimated
brightness temperature is TB  1010 K
This means that the radiating gas has a
temperature: T  TB > 1010 K
Brightness Temperature TB
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TB is the temperature at which a
blackbody would emit the same flux at
a given wavelength as that observed
If the source is truly a blackbody, TB
directly gives the temperature of the
object
If not, then
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temperature of the object is larger: T > TB
optically thin emission (semi-transparent)
A Surface Will Emit
Blackbody Radiation
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Any astrophysical object that has been
accreting for a long time (~1010 years) will
be in steady state and will radiate from its
surface very nearly as a blackbody
Because
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Steady state  thermal equilibrium (T)
Optically thick (opaque)  blackbody (T)
Radio/Submm Radiation Must
Be From the Accretion Disk
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Blackbody emission from optically thick gas at
temperature T  TB > 1010 K would peak in -rays
(and would outshine the universe!!):
L = 4R2T4 ~ 1062 erg/s
Sgr A* is definitely not doing this!!
Therefore, the radiation from Sgr A* must be emitted
by gas that is optically thin in IR/X-rays/-rays
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This radiation cannot be from the “surface” of Sgr A*
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It must be from the (optically thin) accretion flow
Luminosity and Spectrum
of Sgr A*
Sub
mm
Is There Any “Surface”
Emission from Sgr A*?
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The surface luminosity is expected to be
Lsurf  Lacc (very likely Lsurf  Lacc )
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Since we know Lacc ~ 1036 erg/s, we expect:
Lsurf  1036 erg/s (or even  1036 erg/s)
For typical radii of Sgr A*’s “surface” the
radiation is predicted to come out in the IR
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But there is no sign of this radiation!!
Based on
Broderick &
Narayan
(2006)
All four IR bands have flux limits well below the predicted flux even though
model predictions are very conservative (e.g., assume radiatively efficient).
Therefore, Sgr A* cannot have a surface, i.e., it must be a BH
Summary of the Argument
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Sgr A* = dark object at the Gal. Center
The observed sub-mm emission in Sgr A*
is definitely from the accretion flow, not
from the surface of the compact object
If Sgr A* has a surface we expect at least
~1036 erg/s from the surface
This should come out in the IR
Measured limits are far below prediction
Therefore, Sgr A* cannot have a surface
Does the Argument Survive
in Strong Gravity?
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In some very unusual models of compact stars
(e.g., gravastar, dark energy star), it is possible
to have a surface close to the Event Horizon:
R* = 2M + R, R  2M
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Extreme relativistic effects, e.g., large
gravitational redshifts, are expected
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Can this hide the surface emission? NO!!
Radiation May Take
Forever to Get Out
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The extra delay relative to the Newtonian
case is TINY
tGR
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RS  Rstar

ln 
c  Rstar  RS

 Rstar
  40 ln 
 R


s
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At most it is ~ 1 hr (for R ~ Planck scale!)
--- no big deal
Unless R/Rstar~ exp[-1016] !!
Gravitational Redshift Will Kill
the Emission
 RS 
1  z  1  
R

L 
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Lloc
1  z 
2
1/2
1/2
 RS 


 R 
 R 
 Lloc 

R
 S 
Looks serious, especially if redshift is large
But energy has to be conserved, and it is easy to
show that this argument is false
R
0.1RS
1+z
3.3
1 mm
1 fm
lPl
3.3x106 3.3x1012 2.6x1022
Radiation Does Not have a
Blackbody Spectrum
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If R < 3GM/c2 = (3/2)RS, then some
rays from the surface are bent back
and return to the surface
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For large redshift, there is
only a tiny hole for radiation
to escape
Even though surface “looks”
convex in Schwarzschild
coordinates, it is actually
highly concave in terms of
photon geodesics!
In fact, it is the perfect
textbook example of a
blackbody: a furnace with a
pinhole!
Therefore, the larger the
redshift, the closer the
emission will be to blackbody!
1/2
RS 
3 
sin c 
1 

2 
R 
Escaping rays have
3/2
3  R 
  c 


2  RS 
27 / 8
 esc 
2
1  z 
3/2
Furnace
=
1/2
BB radn
RS
R
Particle Emission
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Could the emission come out in dark particles?
Surface emission is thermal – so we expect a
(nearly) perfect blackbody spectrum
Only photons, and particles with mc2 < kT
(neutrinos), will reach infinity
(At surface, Tloc T  many other particles)
Allowing for three types of neutrinos, the
observed photon luminosity is reduced by 16/29
(Broderick & Narayan 2007) – no big deal
One Key Assumption
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We do make one key assumption
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We assume that the radio/sub-mm
radiation is produced by accretion
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Hence, one way out of an Event Horizon
is to say that Sgr A* is powered by
something other than accretion
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Then where is the accretion luminosity?
Let us Accept that Sgr A*
and Other Astrophysical BH
Candidates have no
Surfaces
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Does this prove that these objects have
Event Horizons and are truly BHs?
Not really – there are other options
However, they are even more bizarre!
Wormholes
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Damour & Solodukhin (2007)
Wormholes can “look” just like BHs
Accreting gas falls and then bounces back
If bounce-back time is long enough, then
cannot distinguish a Wormhole from a BH
But it requires:   exp[-1015] (!!)
Is such an extreme value reasonable?
Could accreted mass modify the solution?
Naked Singularities (Joshi)
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E.g., Kerr solution with a*>1 (superspinars): Bambi & Freese (2009), Bambi
et al. (2009, 2010,…)
Q: Are naked singularities consistent
with the lack of “surface radiation”?
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If we can see down to the singularity, we
might expect to observe continued
emission from gas right down to the center
In this case the object will be very bright…
Summary
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A variety of strong astrophysical
arguments indicate that astrophysical
BH candidates have no surface
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No surface emission seen in Sgr A*
Each argument by itself is pretty strong
The combined evidence is Super-Strong
Our BHs must have Event Horizons
Unless wormholes, naked singularities?!