THE BLACK HOLE EVENT

HORIZONRamesh Narayan

The 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 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

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

Image credit: Robert Hynes

MBH ~ 5—20 M

Millions of these BHs in each

galaxy

Galactic 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? 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

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) 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 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 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

surfL accL

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: 1Circular 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)

ce

e Re 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 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

Dark Mass at the Galactic Center: M ~ 4x106 M

(inferred from stellar motions)

Stellar Dynamics at the Galactic Center

Schodel et al. (2002) MBH=4.00.2106 M

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*

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 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

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

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 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*

Sub

mm

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

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? 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 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

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

22.6x102

2

1/2 1/2

locloc2

1 1

1

S S

S

R Rz

R R

L RL LRz

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 12 R R

3 R2 R

27 /

ave

81 z

= BB radnFurnace

Particle 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 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 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 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)

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…

Summary 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?!