the black hole event horizon ramesh narayan. the black hole a remarkable prediction of the general...
TRANSCRIPT
THE BLACK HOLE EVENT
HORIZON
THE BLACK HOLE EVENT
HORIZONRamesh Narayan
The Black HoleThe Black Hole
A remarkable prediction of the General Theory of Relativity Matter is crushed to a SINGULARITY Surrounding this is an EVENT HORIZON
BH is defined by the presence of an Event Horizon
“Normal” Object
Surface
Black Hole
Singularity
Event Horizon
Conceptually, a BH is Very Strange &
Mysterious
Conceptually, a BH is Very Strange &
Mysterious 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
The Universe Appears to be Full of Black Holes
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 BinariesX-ray Binaries
Image credit: Robert Hynes
MBH ~ 5—20 M
Millions of these BHs in each
galaxy
Galactic NucleiGalactic Nuclei
Image credit: Lincoln Greenhill, Jim Moran
MBH ~ 106—1010 M
One supermassive BH
in each galaxy
But: Are Astrophysical Black Holes Really Black
Holes?
But: Are Astrophysical Black Holes Really Black
Holes?
We know that astrophysical “BHs” are:
Compact: R few RS (RS2GM/c2)
Massive: M 3M (not neutron stars)
But can we be sure that they are really BHs?
Would be good to find independent evidence that
BH candidates actually possess Event Horizons
Recall: BH is DEFINED by Event Horizon (not mass)
In Search of the Event Horizon
In Search of the Event Horizon
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)
Signatures of the Event Horizon (Lack of a
Surface) Differences in quiescent luminosities of XRBs (Narayan,
Garcia & McClintock 1997; Garcia et al. 2001; McClintock et
al. 2003;…)
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)
Differences in X-ray colors of XRBs (Done & Gierlinsky 2003)
Differences in thermal surface emission of NSXRBs and
BHXRBs (McClintock, Narayan & Rybicki 2004)
Infrared flux of Sgr A* (Broderick & Narayan 2006, 2007;
Broderick, Loeb & Narayan 2009)
Physics of AccretionPhysics of Accretion
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 IdeaBasic Idea
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
surfLaccL
How Much Luminosity from the Surface?
How Much Luminosity from the Surface?
In a Newtonian analysis, if the accretion disk extends down to the radius of the central star R*, the binding energy of a circular orbit at R* is GM/2R*
material at rest on stellar surface is ~GM/R*
acc *
surf * acc
/ 2
/ 2
L GM M R
L GM M R L
2
* circ *
rest *
acc circ *
s
At infinity: 1
Circular orbit at radius R : ( )
At rest on s
Energy per unit mass (units of )
Luminosity
(r
tellar surface: ( )
Accretion:
adiatively e
1 ( )
Surface
fficie
:
n
t)
c
e
e R
e R
L e R M
L
urf circ * rest *( ) ( )e R e R M
2acc
2surf
2acc
2surf
2a
* ISCO
* Buchdahl
* gravast
cc
2surf
ar
Schwarzschild "Star"
[ 6 ]
[ (9 / 4)
0.0572
0.1263
0.0572
0.6095
]
[ 2 ]
0.0572
0.9428
L M c
L M c
L M c
L M c
L M c
L
R R M
R R M
R R M
M c
Relativistic Case
On To Our “Evidence” for the Event HorizonOn To Our “Evidence” for the Event Horizon
An exercise in logic using simple physics
Discussion is in two parts: The “Evidence” Search for Loopholes
The Black Hole at the Center of Our Galaxy
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
Stellar Dynamics at the Galactic Center
Schodel et al. (2002)
MBH=4.00.2106 M
Radio Source at the GC: Sagittarius A*
Radio Source at the GC: Sagittarius A*
There is a compact radio source, Sagittarius
A* (Sgr A*) located at the Galactic Center
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)
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*
Luminosity and Spectrum of Sgr A*
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-CompactSgr A* is Ultra-Compact 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
Brightness Temperature TB
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 temperature of the object is larger: T > TB
optically thin emission (semi-transparent)
A Surface Will Emit Blackbody Radiation A Surface Will Emit
Blackbody Radiation
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 Steady state thermal equilibrium (T) Optically thick (opaque) blackbody (T)
Radio/Submm Radiation Must Be From the
Accretion Disk
Radio/Submm Radiation Must Be From the
Accretion Disk Blackbody emission from optically thick gas at
temperature T TB > 1010 K would peak in -rays
(and would outshine the universe!!): L = 4R2T4 ~ 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
This radiation cannot be from the “surface” of Sgr A* It must be from the (optically thin) accretion flow
Luminosity and Spectrum of Sgr A*
Luminosity and Spectrum of Sgr A*
Sub
mm
Is There Any “Surface” Emission from Sgr A*?Is There Any “Surface” Emission from Sgr A*?
The surface luminosity is expected to be
Lsurf Lacc (very likely Lsurf Lacc )
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 But there is no sign of this radiation!!
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
Based on Broderick & Narayan
(2006)
Summary of the Argument
Summary of the Argument
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?
Does the Argument Survive in Strong
Gravity? 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
Extreme relativistic effects, e.g., large
gravitational redshifts, are expected
Can this hide the surface emission? NO!!
Radiation May Take Forever to Get OutRadiation May Take Forever to Get Out
The extra delay relative to the Newtonian case is TINY
At most it is ~ 1 hr (for R ~ Planck scale!) --- no big deal
Unless R/Rstar~ exp[-1016] !!
star starGR
star
ln 40 ln sS
S
R R Rt
c R R R
Gravitational Redshift Will Kill the Emission
Gravitational Redshift Will Kill the Emission
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 mm 1 fm lPl
1+z 3.3 3.3x106 3.3x101
2
2.6x102
2
1/2 1/2
locloc2
1 1
1
S S
S
R Rz
R R
L RL L
Rz
Radiation Does Not have a Blackbody
Spectrum
Radiation Does Not have a Blackbody
Spectrum
If R < 3GM/c2 = (3/2)RS, then some rays from the surface are bent back and return to the surface
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!
1/23/2S S
c
1/23/2
cS
esc 2
Escaping rays h
R R3sin 1
2 R R
3 R2 R
27 /
ave
8
1 z
= BB radnFurnace
Particle EmissionParticle Emission 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 AssumptionOne Key Assumption We do make one key assumption
We assume that the radio/sub-mm
radiation is produced by accretion
Hence, one way out of an Event
Horizon is to say that Sgr A* is powered
by something other than accretion
Then where is the accretion luminosity?
Let us Accept that Sgr A* and Other
Astrophysical BH Candidates have no
Surfaces
Let us Accept that Sgr A* and Other
Astrophysical BH Candidates have no
Surfaces 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!
WormholesWormholes 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)
Naked Singularities (Joshi)
E.g., Kerr solution with a*>1 (super-spinars): Bambi & Freese (2009), Bambi et al. (2009, 2010,…)
Q: Are naked singularities consistent with the lack of “surface radiation”? 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…
SummarySummary A variety of strong astrophysical
arguments indicate that astrophysical BH candidates have no surface 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?!